More than half of the people in this “family tree” are listed in the UIUC database at http://www.scs.uiuc.edu/~mainzv/Web_Genealogy, and my only information about them comes from there.  For most of those people, I have only listed their names, dates of birth and death, the year and place they got their degree, and the names of their mentors.  A short description of their accomplishments is given in the UIUC database, as well as references with more information.  
In a few cases, where I knew about mentors that were not listed in the UIUC database, or wanted to give interesting stories not included there, I have given more detailed biographical sketches here.  Most of that information comes from Dictionary of Scientific Biography, edited by Charles Coulton Gillespie (Scribner’s, New York, 1970), and much of the biographical information given below consists of paraphrases or direct quotes from that source.  In many cases, the UIUC database also used the Dictionary of Scientific Biography, but I have only listed it as a reference here when I used it myself as a source for the material presented here. 
Some of my information comes from an article, apparently published in The Hexagon (a journal of the history of chemistry) in the late 1980s, which included a figure titled “A Genealogy—A Chemist’s Family Tree.”  The article may have been about J. H. Matthews (1881-1970), since his name was surrounded by a frame in the figure.  I don’t know who the author of the article was, or what his sources of information were.  
In a few cases in the 20th century, I have looked at theses to find out who people’s thesis advisors were, and very occasionally I have used other primary sources (e.g. an interview with Chodorow, and a letter written by Trowbridge).
I have also made use of the MacTutor History of Mathematics Archive, http://www-history.mcs.st-and.ac.uk/history, an online source with biographies of mathematicians and some physicists, maintained by St. Andrews University, similar to the articles in Dictionary of Scientific Biography.  It also includes portraits, when available, and references.  The Mathematics Genealogy Project maintained at Minnesota State University, http://hcoonce.math.mankato.msus.edu, has a more “strict constructionist” view of who is a thesis advisor, so the lineages there generally peter out after a few generations, and it does not give sources for its information, which consists only of names and dates.  But it includes all present day mathematicians who have submitted data, not just famous ones.
 The people I list here are for the most part direct academic ancestors of Ned Birdsall, or in some cases famous descendents of direct ancestors, i.e. they are all “blood relatives.”  I have not listed “in-laws” here, although in a few cases I have mentioned famous “in-laws” under the person to whom they are connected.
Johann Afzelius (1753-1837) got an MS in 1776 at Uppsala, under Tobern Olaf Bergman.  See UIUC database.
B. S. Albinus is listed as von Haller’s thesis advisor at Leiden (1727), in the UIUC database, but he is not listed in the database himself.
John Allen (1771-1843) got an MD at Edinburgh in 1791.  His mentor was Arnot.  See UIUC database.
Arnot is listed in the UIUC database as the mentor of John Allen, but the database does not have any further information on him.
Ernst Gottfried Baldinger (1738-1804) got an MD from Jena in 1760, under Christoph Andreas Mangold.  See UIUC database.
Isaac Barrow (1630-1677) was a student of Duport, who was a professor of Greek at Cambridge. Barrow got an MA from Cambridge in 1652.  He traveled to Paris in 1655, where he found that Gilles Personne de Roberval was the only mathematician he could learn anything from.  He also studied with Vincenzio Viviani in Florence in 1656.  See MacTutor History of Mathematics Archive.
Joseph Barth (1745-1818) got an MD in Vienna, about 1770, under Anton Stork.  See UIUC database.
Thomas Beddoes (1760-1808) studied medicine at London in 1780-82, and at Edinburgh in 1784-86.  At Edinburgh he wrote a manual of chemistry dedicated to Joseph Black, who taught at Edinburgh, since Beddoes considered Black a model to his profession.  Beddoes got an MD degree at Oxford, and taught there 1788-93, but had to leave due to his radical politics.  He started the Pneumatic Institute at Bristol, to investigate medical uses of gases.  He later concluded that gases were not the cure-all for health problems that he had hoped they would be, and devoted his time to the promotion of public health measures among the urban lower classes.  See web page at http://www.unilab.caltech.edu/unilab/Projects/Pneumatics/chemists/beddoes.html.
Georg Joseph Beer (1763-1821) got an MD degree in Vienna in 1786, under Joseph Barth.  See UIUC database.
Pierre Richer de Belleval (1564-1632) got an MD at Avignon in 1587.  No mentor is listed in the UIUC database.  He was a botanist and physician, and one of the founders of botany in France, the first to treat it as a science distinct from medicine.
Tobern Olaf Bergman (1735-1784) got a PhD in math at Uppsala in 1758, under Bengt Ferrner.  See UIUC database.
Jacob Bernoulli (1654-1705) got an MA in philosophy at U. of Basel in 1671, and got a degree in theology in 1676.  He studied with Malebranche about 1678-1680, and later studied with Robert Hooke and Robert Boyle.
Johann Bernoulli (1667-1748) majored in medicine at U. of Basel, 1683-1685, and studied math with his older brother Jacob Bernoulli, who taught there.  See MacTutor History of Mathematics Archive.
Pierre Berthier (1782-1861) got an Ing. Ordinaire (engineering) degree in 1805 at the Ecole des Mines.  His mentors were C. L. Berthollet and Johann Gottfried Schreiber.  See UIUC database.
Claude Louis Berthollet (1748-1822) got an MD at U. of Paris in 1778, studying under J. B. M. Bucquet and P. J. Macquer.  See UIUC database.  The article in The Hexagon only lists Macquer as his mentor.
Jons Jacob Berzelius (1779-1848) got an MD at Uppsala in 1802, under Afzelius.  He did research soon after that with Wilhelm Hisinger, a wealthy mine owner, on electrochemistry and mineralogy.  Berzelius was almost self-taught in chemistry.  His first papers were rejected by the Academy because they used anti-phlogistic nomenclature, but Berzelius had never learned phlogiston theory.  A leading 19th century chemist, Berzelius discovered several elements, and developed the modern nomenclature for chemical formulas. Twenty-four Swedes and twenty-one foreign students worked in his lab, especially Gustav and Heinrich Rose, Mitscherlich, and Wohler.  See UIUC database, and Dictionary of Scientific Biography. 
Charles Kennedy Birdsall (1925- ) wrote his Ph.D. thesis, “Interaction Between Two Electron Streams for Microwave Amplification,” at Stanford University in 1951.  Officially his thesis advisor was Lester M. Field.  Birdsall told me he also had some interaction with Marvin Chodorow, who also signed his thesis.
Joseph Black (1728-1799) got an MD in 1754 at Edinburgh.  His formal advisors were Alexander Monro, Sr., and Charles Alston.  But William Cullen, whom he worked for in Glasgow in 1749-1752, was a greater influence.  See UIUC database.
Frederick Columbus Blake wrote his Ph.D. thesis “Reflection and Transmission of Electric Waves by Screens of Resonators and by Grids,” at Columbia University in 1905. Columbia no longer has a copy of the thesis, so I have no proof of who his thesis advisor was. However, a paper based on the thesis was published by Blake and Claude R. Fountain (a fellow graduate student), in Physical Review 23, 257-278 (October 1906), in which they state “We are especially indebted to Professor E. F. Nichols [Ernest Fox Nichols], who suggested the problem and some details of the methods for solving it.”  So it seems almost certain that Blake’s thesis advisor was Ernest Fox Nichols.
Johann Friedrich Blumenbach (1752-1840) studied at Jena and received his Ph.D. at Gottingen, where he studied under Christian W. Buttner.  His thesis was “De generis humani varietate nativa liber,” considered one of the basic works of anthropology.  His students at Gottingen included Karl Ernst von Hoff.  Blumenbach’s fame is based on his role in the founding of scientific anthropology.  He was one of the first to view man as an object of natural history.  But he attacked all political and social abuses of anthropology, in particular the notion that black men were on a lower level of humanity than white men. He concluded from the spread of certain parasites found only in the domestic pig that these parasites could not have existed since the beginning of the world.  See Dictionary of Scientific Biography.
Hermann Boerhaave (1668-1738) got an MD degree at Hardewijk in 1693, under Burchard de Volder.  See UIUC database.
Ludwig Boltzmann (1844-1906) got a Ph.D. at U. of Vienna in 1866, under Josef Stefan, with a thesis on the kinetic theory of gases. During the next three years he studied under Bunsen, Kirkhoff, and Helmholtz.  See MacTutor History of Mathematics Archive. The Dictionary of Scientific Biography also mentions J. J. Loschmidt as a mentor.
Janos Bolyai (1802-1860) discovered non-Euclidean geometry, independently of Lobachevsky.  Gauss had discovered it earlier but never published it.  Janos Bolyai was taught by his father Wolfgang Bolyai.
Farkas Wolfgang Bolyai (1775-1856) was a student of A. G. Kaestner at Gottingen, at the same time as Gauss, and remained a friend of Gauss.  Wolfgang Bolyai expressed the opinion that the parallel postulate might not be provable, but did not follow this idea to its logical conclusion and discover non-Euclidean geometry, a task which was left to his son Janos Bolyai.
William Bombast von Hohenheim is mentioned as the father and mentor of Paracelsus, in the article on Paracelsus in Dictionary of Scientific Biography, but is not listed himself.
Nathaniel Bowditch (1773-1838) was self-taught.  He was a businessman, an insurance actuary at the time of his death.  Offers from American universities never strongly tempted Bowditch, for they had little to offer a man of his caliber.  He translated Laplace’s Celestial Mechanics, and refused to accept subsidies to publish it, from people who could not read it.  He also revised a major book on navigation.  See UIUC database, and Dictionary of Scientific Biography.
Robert Boyle (1627-1691) was a member of the “Invisible College,” later to become the Royal Society, which was founded by John Wilkins, and he moved to Oxford in 1654 to work with Wilkins, although he did not have an official position there.  He discovered Boyle’s Law relating the pressure and volume of a gas.  See MacTutor History of Mathematics Archive.
Heinrich Wilhelm Brandes (1774-1834) studied natural sciences at Gottingen under A. G. Kaestner and G. C. Lichtenberg, in 1800.  As a student in the late 1790s, together with J. F. Benzenberg, he used parallax to measure the height and absolute velocity of meteors.  (For an account of a more recent application of this method by Joseph L. Gerver, see “The Amateur Scientist” column in the May 1987 issue of Scientific American.  J. L. Gerver is a direct doctoral descendent of Dirichlet, through Felix Klein, see http://hcoonce.math.mankato.msus.edu.)  Brandes discovered the periodicity of the Perseids, worked on refraction of light by the atmosphere, and wrote popular books on astronomy.  See Dictionary of Scientific Biography.
Antonio Musa Brasavola (1500-1555) got an MD/PhD degree in 1520 at Ferrara, under Nicolo da Lonigo.  Brasavola was physician to Henry VIII of England, Francis I of France, Charles V of the Holy Roman Empire, and four popes.  See UIUC database.
Percy Williams Bridgman (1882-1961) wrote his thesis, “Mercury Resistance as a Pressure Gauge,” at Harvard in 1908.  It was signed by seven people, possibly the entire Harvard physics faculty, and there are no acknowledgments of help from anyone.  But from other biographical information, it seems that Wallace Sabine, one of the people who signed the thesis, was Bridgman’s mentor at Harvard.  Sabine is listed as his mentor in the UIUC database.  In any case, the line almost certainly goes back one way or another to John Trowbridge, another signatory of Bridgman’s thesis, who was largely responsible for establishing Harvard as a center for physics research when he founded the Jefferson Physical Laboratory in 1884.  Bridgman won the Nobel Prize in 1946.
Guy de la Brosse (c.1586-1641) is listed as one of the mentors of William Davison, and as a student of Jean Robin, in the article in The Hexagon.  I have no other information about him.
Henricus Brucaeus (1531-1593) studied at the College Royal in Paris about 1550, under Petrus Ramus, but did not get a degree there.  He did get an honorary MD from Bologna in 1560.  See UIUC database.
Ernst von Bruecke (1819-1892) obtained his MD degree in 1842 at Berlin, studying under Johannes Mueller, who was also the mentor of Helmholtz.
Jean Baptiste Michel Bucquet (1746-1780) got an MD in 1778 at U. of Paris.  He was a student of H. M. Rouelle, according to the article in The Hexagon.  According to the UIUC database, Bucquet was a student of G. F. Rouelle, and Lavoisier was also an important influence. No mentor is mentioned for Bucquet in Dictionary of Scientific Biography.
Comte de Buffon (Georges-Louis Leclerc) (1707-1788) was a student at Colleges des Jesuits in Dijon, 1717-1723, and then studied law at Dijon.  He met Gabriel Cramer, who was professor at the University of Geneva, in 1727, and started studying math.  In Angers, in 1728, he may have studied medicine, botany, and math with Pere de Landreville, professor at the College de l’Oratoire.  Buffon corresponded with Cramer.  He was interested in applying math to modeling the cooling of planets, for example, and he separated science from metaphysical ideas.  See Dictionary of Scientific Biography.
Christian W. Buttner was teaching at Gottingen during the early 1770s.  According to the article on J. F. Blumenbach in the Dictionary of Scientific Biography, Buttner “lectured on natural history, beginning with man, and fascinated Blumenbach with vivid accounts of travel and foreign peoples.”  Buttner himself is not listed in the Dictionary of Scientific Biography.

Salomon Calahorra (ca.1530-1596) was born and died in Cracow.  Some contend that he was a student of Brasavola in Ferrara.  Calahorra was appointed court physician to King Sigismund Augustus in 1570, and also served as court physician to Stefan Botory who became king in 1578.  See Encyclopedia Judaica.
Elias Rudolph Camerarius, Jr. (1673-1734) got his MD degree in 1691 at Tubingen, under his father, Elias Rudolph Camerarius, Sr.  See UIUC database.
Elias Rudolph Camerarius, Sr. (1641-1695) got his MD in 1663 at Tubingen.  No mentor is listed in the UIUC database.
Giulio Cesare Casseri (1552-1616) got his MD in 1580 at Padua, under Girolamo Fabrici (Aquapendente).  See UIUC database.
Johann Friedrich Wilhelm de Charpentier (1738-1805) got a degree from Leipzig about 1766.  No mentor is listed in the UIUC database.
Marvin Chodorow (1913- ) wrote his thesis, “Examination of a General Method of Calculating Energy Bands in Crystals with Particular Application to Copper,” at MIT, in 1938, under John C. Slater.  Chodorow told me that he also had a great deal of personal interaction with Slater’s postdoc Conyers Herring.  Slater’s last student before Chodorow was William Shockley, and an earlier student of his (1932) was Nathan Rosen, of Einstein-Podolsky-Rosen.  After World War II, Slater had many graduate students, including Burdick, Siegel (who went to GE), and Charles Naiman (about 1960).  Chodorow’s thesis, introducing what would later be called the Chodorow potential, did not attract much attention until after the war, when Slater’s students were able to verify the results numerically and experimentally.  After that it became well known, but by that time Chodorow had left solid state and gone into microwave research, first at Sperry and then at Stanford.
Josiah P. Cooke (1827-1894) did not have any academic degrees, but was inspired by Silliman, and, while spending time in France, by Dumas and Regnault, according to UIUC database.  He later taught chemistry at Harvard.
Gabriel Cramer (1704-1752) got his Ph.D. at U. of Geneva in 1722, with a thesis on the theory of sound waves. At the age of 19, he was appointed to a half-time faculty position at the U. of Geneva, which allowed him to spend half of his time travelling and visiting other mathematicians.  The first mathematicians he visited and studied extensively with were Johann Bernoulli and Euler (who was also a student of Bernoulli, and three years younger than Cramer).  Cramer is best known for Cramer’s Rule, a method of calculating the determinant of a 3 x 3 matrix.  See MacTutor History of Mathematics Archive, and Dictionary of Scientific Biography.
Cramer was giving lectures in chemistry at Erfurt about 1680, according to the article on Friedrich Hoffman the younger in Dictionary of Scientific Biography.  I have no other information on him.
William Cullen (1710-1790) got an MD in 1740 in Glasgow, under Andrew Plummer. See UIUC database.
A. Cyprian was a Dutch surgeon practicing in London in the early 1700s, according to the article on Caspar Neumann in Dictionary of ScientificBiography.  He is not listed there himself, and I have no other information on him.
Louis Jean-Marie Daubenton (1716-1800) attended anatomy and botany lectures at Jardin du Roi in Paris, although he originally went to study theology at the Sorbonne.  He got his MD from Rheims, in 1741.  The Comte de Buffon (Georges Louis Leclerc) who came from the same town (Montbard) as Daubenton, got him an appointment at Jardin du Roi.  They collaborated on Buffon’s great work, Histoire Naturelle.  See Dictionary of Scientific Biography.
William Davison (1593-c.1669) was a student of Jean Herouard and Guy de la Brosse, and the mentor of Nicaise LeFebvre, according to the article in The Hexagon.  I have no other information about him.
Humphry Davy (1778-1829) was an apothecary’s apprentice in Penzance, Cornwall.  In 1798, he was hired by Dr. Thomas Beddoes for the position of superintendent at Beddoes’ Pneumatic Institute in Bristol, an institution dedicated to researching the medical uses of gases.  Davy and the poets Coleridge and Southey experimented with nitrous oxide on themselves, and were criticized by Edmund Burke for fomenting atheism and sympathy for the French Revolution.  In 1801, Davy joined the Royal Institution, where he gave well-received public lectures (ladies swooned, and sent him poems), and used Volta’s newly invented battery, and Hare’s newly invented oxygen-hydrogen torch, to electrolyze molten sodium and potassium salts, discovering the elements sodium and potassium.  See the Royal Institution web page at http://www.ri.ac.uk/History/.
Charles Gaspard De La Rive (1770-1834) got an MD at Edinburgh in 1797, under John Allen.  An early plasma physicist, De La Rive studied the sound produced by a jet of hydrogen gas burning in a tube.  See UIUC database.
Rene Descartes (1596-1650) got a law degree from U. of Poitiers in 1616, and studied math and mechanics with the Dutch scientist Isaac Beeckman.  He was also part of Mersenne’s circle of mathematicians in Paris.  See MacTutor History of Mathematics Archive.
Johann Peter Gustav Lejeune Dirichlet (1805-1859) was taught high school math by Ohm, and studied with Poisson and Fourier at the U. of Paris 1822-1825.  He left without a degree, but got an honorary doctorate at U. of Cologne (he couldn’t get a real doctorate because he didn’t know Latin), which allowed him to submit his Habilitation thesis, on a certain class of polynomials with prime divisors, to U. of Breslau in 1827.  I think his thesis advisor was Gauss, and in any case Gauss was a strong influence.  Dirichlet got a position at U. of Berlin with the help of von Humboldt, and married Rebecca Mendelsohn, the sister of Felix Mendelsohn.  He was a close friend of Jacobi.  See MacTutor History of Mathematics Archive.
E. H. Dirksen is not listed himself in Dictionary of Scientific Biography, but is mentioned in the article on Jacobi.
Heinrich W. Dove (1803-1879) got a Ph.D. in climatology at the University of Koenigsberg in 1826.  He studied meteorology with H. W. Brandes at Breslau, in 1827.  He was the first to find a system governing weather changes, relating wind direction to precipitation, temperature and pressure, but thought that wind direction was primary, and did not accept his student Buys-Ballot’s discovery that wind is driven by pressure differences.  See Dictionary of Scientific Biography.
Anders Gabriel Duhre (1680-1739) did not have a degree, but studied at Uppsala about 1711, under Petrius Elvius the elder.  See UIUC database.
Jean Baptiste Andre Dumas (1800-1884) had no degree, but studied at U. of Geneva about 1823, and his mentors were Augustin LeRoyer and Charles Gaspard De La Rive, according to the UIUC database.  The article in The Hexagon lists his mentor as L. J. Thenard.
Johann Georg Duvernoy (1691-1759) got his MD degree at Tubingen in 1716.  His advisor there is not known, but prior to that, in 1708, he studied in Paris with Joseph Pitton de Tournefort.  See UIUC database.
Albert Einstein (1879-1955) was in several of Hermann Minkowski’s classes at U. of Zurich.  He got his Ph.D. there in 1905 with a thesis on Brownian motion, which he dedicated to Marcel Grossmann, who had been his friend since undergraduate days at ETH.  See MacTutor History of Mathematics Archive biographies for Einstein and Minkowski
Petrus Elvius the elder (1660-1718) got an MA at Uppsala in 1688, under Petrus Hoffvenius.  See UIUC database.
Johann Christian Erxleben (1744-1777) got an MD in Gottingen in 1767, under Abraham Gotthelf Kaestner.  See UIUC database.
Leonhard Euler (1707-1783) got an MA in philosophy at U. of Basel in 1723, and studied math there with Johann Bernoulli.  He got a Ph.D. in math in 1726.  See MacTutor History of Mathematics Archive.
William Littell Everitt (1900-?) wrote his Ph.D. thesis “The Calculation and Design of Alternating Current Networks Employing Triodes Operating During a Fraction of a Cycle,” at Ohio State University in 1933, under Frederick C. Blake.
Franz Serafin Exner (1849-1926) got his Ph.D. in 1871 at U. of Vienna, under August Kundt.  See UIUC database.
Girolamo Fabrici (Aquapendente) (1533-1619) got his MD degree in 1559 at Padua, under Gabriele Fallopio.  See UIUC database.
Gabriele Fallopio (1523-1562) got his MD in 1548 at Ferrara, under Antonio Musa Brasavola.  Not surprisingly, Fallopio discovered the Fallopian tubes.  He was a colleague of Vesalius.  See UIUC database.
Michael Faraday (1791-1867) was appointed Chemical Assistant at the Royal Institution by Humphry Davy in 1813, after Faraday wrote to Davy after hearing his lectures.  He accompanied Davy on a scientific tour of Europe, 1813-1815, and then studied chemistry under Prof. William Thomas Brande.  Faraday discovered magnetic induction.  See the Royal Institution web page at http://www.ri.ac.uk/History/.
Bengt Ferrner (1724-1802) did not have a degree, but studied in Uppsala in 1751, under Samuel Klingenstierna and Marten Stromer.  See UIUC database.
Lester Marshall Field wrote his Ph.D. thesis, “The Theory and Measurement of Electron Beam Dispersion Phenomena at High Vacuum,” at Stanford University in 1944, under Karl Spangenberg.  Field’s students at Stanford included C. K. Birdsall and Roy Gould.  He left Stanford about 1951 and spent the rest of his career at Hughes.
Antoine Francois de Fourcroy (1755-1809) studied anatomy at the Paris Faculty of Medicine at the suggestion of Felix Vicq d’Azyr, who also arranged financial support by the Societe Royale de Medecine, of which he was the secretary.  Fourcroy graduated as a doctor in 1780, but never practiced medicine.  He was interested in chemistry and natural history, and ended up working in chemistry.  Eventually he supported Lavoisier’s theory, and collaborated with him in revising chemical nomenclature.  Fourcroy supported the French Revolution, but may have appealed to Robespierre to spare Lavoisier’s life (unsuccessfully).  He and Vauquelin discovered iridium, and made other important discoveries in chemistry.  See UIUC database, and Dictionary of Scientific Biography.
Jean Baptiste Joseph Fourier (1768-1830) studied math at the Ecole Normale in1795, under Lagrange, Laplace, and Monge.  An ardent revolutionary, Fourier was arrested by a rival faction and narrowly missed being guillotined during the Reign of Terror.  He invented Fourier series in order to solve a problem involving heat conduction in a ring of metal.  See MacTutor History of Mathematics Archive.
Johann Peter Frank (1745-1821) got his degree in Heidelberg in 1766, under Georg Matthias Gattenhof.  See UIUC database.
Benjamin Franklin (1706-1790) had no formal training in science, but read extensively.  He was especially influenced by a book by Hermann Boerhaave.  According to the Dictionary of Scientific Biography, Franklin attended lectures on science by Adam Spencer, both while he was growing up in Boston, and later, in 1744, in Philadelphia.  Franklin, in addition to demonstrating that electricity played an important role in nature in the form of lightning, also formulated the concept of conservation of charge, showing for the first time that electricity, like mechanics and gravitation, obeys well defined laws of nature.
Sigmund Freud (1856-1939) received his MD degree in 1881 at the University of Vienna, studying under Ernst von Bruecke.  See Dictionary of Scientific Biography.
Galileo Galilei (1564-1642) learned math from the mathematician Ostilio Ricci, who was a friend of his father’s.  As a medical student at Pisa in 1581-1585, he heard lectures in Aristotelian astronomy and physics by Francesco Buonamici and Girolamo Borro, but wasn’t too impressed by them.  See Dictionary of Scientific Biography.
Georg Matthias Gattenhof (1722-1788) got his degree in Wurzberg in 1748, under Victor Albrecht von Haller.  See UIUC database.
Carl Friedrich Gauss (1777-1855) studied math with A. G. Kaestner at Gottingen, 1795-98, but often ridiculed him. He got a degree at Brunswick in 1799, and submitted a doctoral dissertation at U. of Helmstedt, where his advisor was Johann Friedrich Pfaff.  Gauss lived at his house, and “always retained a friendly memory of Pfaff both as a teacher and a man.” Riemann was a Privatdozent (a postdoctoral fellow) of Gauss.  See Dictionary of Scientific Biography, and MacTutor History of Mathematics Archive.
Joseph Louis Gay-Lussac (1778-1850) was a student of Berthollet.  He is best known for his discovery that the ratio of volumes of gases that participate in a chemical reaction (at a given temperature and pressure) is a ratio of small integers, which led Avogadro to his molecular hypothesis.  Gay-Lussac also measured the earth’s magnetic field and the composition of the atmosphere as function of altitude, in a hot air balloon ascent in 1804 (which set a world record, 23000 feet, that held for decades).  See UIUC database.
Josiah Willard Gibbs (1839-1903) got a Ph.D. from Yale in 1863.  He went to Europe from 1866 to 1869, spending the last year in Heidelberg with Helmholtz and Kirchhoff.  See MacTutor History of Mathematics Archive.
Oliver Wolcott Gibbs (1822-1908), not to be confused with the much more famous Josiah Willard Gibbs, received an M.A. in 1841, and an M.D. degree in 1845, both from Columbia.  But he was trained in chemistry by being an apprentice to Robert Hare in Philadelphia.
Christophle Glaser (1615 -1678) got an MD from Basel about 1640.  He was a student of Nicaise LeFebvre, according to the article in The Hexagon, which gives his dates as 1628-1672, but no mentor is listed for Glaser in the UIUC database.  Glaser was the first to describe the preparation of arsenic trichloride, and was imprisoned in the Bastille for supplying arsenic to Saint-Croix, who poisoned the Marchioness of Brinvilliers.  See UIUC database.
Johann Friedrich Gmelin (1748-1804) got an MD at Tubingen in 1769, under P. F. Gmelin.  See UIUC database.
Leopold Gmelin (1788-1853) worked in his family’s apothecary shop at Tubingen in the summer of 1804, after graduating high school, and attended lectures by his cousin Ferdinand Gmelin (there are a long line of Gmelin scholars in science, medicine, pharmacy, and teaching, going back to the early 1500s), and by another relative, K. F. Kielmeyer.  He then studied with F. X. Stromeyer at Gottingen for an undergraduate degree in 1809, and did doctoral research on black pigmentation of cattle eyes, at the lab of J. F. Jacquin in Vienna, and got an MD at Gottingen in1812.  He studied math with Bernard Thibaut, and then did more work with Stromeyer, and worked in Vauquelin’s lab in Paris, 1814-1815.  See UIUC database, and Dictionary of Scientific Biography.
Philipp Friedrich Gmelin (1721-1768) got his degree in 1742 at Tubingen, under Burchard David Mauchart.  See UIUC database.
Jacques Gohory (Leo Suavius) (1520-1576) was a student of Paracelsus, and the mentor of Jean Robin, according to the article in The Hexagon.  I have no other information about him.
Johann Friedrich August Gottling (1753-1809) got an apothecary degree in 1775 at Langensalza, under Johann Christian Wiegleb.  See UIUC database.
Johannes Frederick Gronovius II (1690-1760) got a degree at Leiden in 1715.  No mentor is listed in the UIUC database.
Laurent Theodor Gronovius II (1730-1777) got an MD in Leiden in 1750, under Johannes Frederick Gronovius II.  See UIUC database.
Theodore von Grotthus was a mentor of Heinrich Rose, according to the article on Rose in Dictionary of ScientificBiography, but is not listed there himself.
Victor Albrecht von Haller (1708-1777) got his degree at Leiden in 1727, under B. S. Albinus, and Boerhaave was a major influence on him there.  He also studied under Johann Georg Duvernoy at Tubingen.  See UIUC database.
Georg Erhardt Hamberger (1697-1755) got an MD at Jena in 1721, under Johann Adolph Wedel.  See UIUC database.
Robert Hare (1781-1858) did not have any formal training in chemistry. He was most famous for inventing the oxygen-hydrogen torch, when he was 20, in 1801.  This made it possible to achieve higher temperatures in the laboratory than had been possible previously, and paved the way for the discovery of sodium a few years later by Humphrey Davies, by the electrolysis of molten sodium chloride. Hare was a member of the Philosophical Society of Philadelphia around 1800, and it is reasonable to assume that his interest in chemistry was sparked by other members of the society.  By far the most famous of these was Joseph Priestley, whose discovery of oxygen made Hare’s invention possible.
William Harvey (1578-1657) got his MD degree at Padua under Girolamo Fabrici (Aquapendente). He discovered the circulation of blood.  See UIUC database.
Friedrich Hasenohrl (1874-1915) got his Ph.D. from Vienna in 1897, under Franz Exner and Ludwig Boltzmann. Hasenohrl showed, before Einstein, that the effective inertia of a moving cavity with trapped electromagnetic radiation would increase according to E = mc2.  He was killed in action in World War I.  See Dictionary of Scientific Biography and UIUC database.
Christian August Hausen (1693-1743) got an MS degree at Wittenberg in 1712.  No mentor is listed in the UIUC database.
Georg Wilhelm Friedrich Hegel (1770-1831), the German philosopher, was a mentor of the mathematician C. G. J. Jacobi, according to the article on Jacobi in Dictionary of Scientific Biography.  I have not investigated Hegel’s own academic ancestry.
Werner Heisenberg (1900-1976) got his PhD under Arnold Sommerfeld at U. of Munich.
Hermann Ludwig Ferdinand von Helmholtz (1821-1894) got an MD degree from Friedrich-Wilhelms-Institut in Berlin in 1842.  He did his dissertation in physiology under Johannes Mueller, whom he said had “definitively altered my intellectual standards,” and also studied chemistry under Mitscherlich.  Mueller’s older student Emil du Bois-Reymond was a big influence, then and later.  Helmholtz’s early research was on the generation of heat in animal muscles, and this led to his interest in thermodynamics.  See Dictionary of Scientific Biography.
Henckel was a student of Stahl. Henckel’s own students included Marggraf and Lomonosov.  See Dictionary of Scientific Biography.  
Jean Le Hennuyer was a Dominican theologian, teaching at the University of Paris in the 1530s, when he was the mentor of Petrus Ramus, according to the UIUC database listing for Ramus.  He is not listed in the database himself.
Jean Herouard (?-1627) is listed as one of the mentors of William Davison, and as a student of Jean Robin, in the article in The Hexagon.  I have no other information about him.
Conyers Herring got his PhD at Princeton, under Eugene Wigner, in 1937.  Other graduate students of Wigner in the 1930s included John Bardeen (1935) and Frederic Seitz (1933).  See Conyers Herring, “Recollections from the Early Years of Solid-State Physics,” Physics Today, April 1992, p. 26-33.
Heinrich Rudolph Hertz (1857-1894) was a student of Helmholtz.  See Dictionary of Scientific Biography.
David Hilbert (1862-1943) got his Ph.D. in 1885 at Koenigsberg, under C. L. F. Lindemann,.  Hurwitz was also an important influence.  See Dictionary of Scientific Biography, and MacTutor History of Mathematics Archive.
Wilhelm Hisinger (1766-1852) enrolled in Bergskollegium in Sweden in 1786, but did not graduate, and no mentor is mentioned in Dictionary of Scientific Biography.
Friedrich Hoffman the younger (1660-1742) studied medicine under G. W. Wedel at Jena, and got his MD in 1681, after first attending chemistry lectures of Cramer at Erfurt (not to be confused with the 18th century Swiss mathematician Gabriel Cramer).  As Galenic concepts of medicine became obsolete in the 1600s, and new discoveries were made (circulation of blood, the microscope, Newtonian physics), attempts were made, by Hoffman and others, to interpret new knowledge according to Descartes’ physiological ideas, and establish a mechanical theoretical basis for medicine.  Hoffman replaced “humors” by “corpuscles,” which were nerve spirits directed by the soul, a material whose motion was directly caused by God; hence Hoffman was not a strict dualist like Descartes.  He asserted that all unexplained biological phenomena could be explained in terms of then unknown physics.  He did not believe Stahl’s phlogiston theory, but held that calx was formed by acids acting on metals.  He also disagreed with Stahl’s medical theories, but supported other chemical ideas of Stahl.  He studied carbonic acid, carbon monoxide poisoning, the difference between magnesium and calcium, etc.  See Dictionary of Scientific Biography.
Petrus Hoffvenius (1630-1682) got an MD at Leiden in 1660, under Johannes Antondides van der Linden.  See UIUC database.
Robert Hooke (1635-1703) was Robert Boyle’s assistant when Boyle was doing his experiments leading to Boyle’s Law.  Hooke discovered the linear relation between stress and strain in an elastic material, and was also well known for his work on microscopy.  He wrote to Newton about his speculations, which he couldn’t prove, that elliptical orbits implied an inverse square law of gravitation, and ended up in a dispute with Newton over priority to this discovery.  See MacTutor History of Mathematics Archive.
Thomas Charles Hope (1766-1844) got an MD in 1787 at Edinburgh, under Joseph Black. See UIUC database.
Adoph Hurwitz (1859-1919) got a Ph.D. at Leipzig in 1881, under Felix Klein.
Christiaan Huygens (1629-1695).  Descartes, a friend of Huygens’ father, was an occasional visitor to his home, and “took a great interest in young Christiaan’s mathematical progress.”  Huygens learned math from Frans van Schooten at Leiden in 1645-47, and from John Pell at College of Orange at Breda in 1647-49.  He corresponded with Mersenne, who gave him the idea for the pendulum clock.  Huygens was the first to realize that Saturn had rings, and invented Huygens’ Principle of wave propagation.  See MacTutor History of Mathematics Archive.
C. G. J. Jacobi (1804-1851) got his Ph.D. in 1825.  His mentors were E. H. Dirksen, and the philosopher Hegel.  Born Jewish, Jacobi converted to Christianity in order to obtain a university position.  See Dictionary of Scientific Biography.
Joseph Franz Jacquin (1766-1839) got an MD in Vienna in 1788, under N. J. Jacquin.  See UIUC database.
Nikolaus Joseph Jacquin (1727-1817) studied medicine at Vienna.  He was supported by Gerard van Swieten, his father’s friend, since his father’s business had failed and he had died.  Jacquin also studied botany at Leiden in 1752, where he was influenced by L. T. Gronovius II.  See Dictionary of Scientific Biography.
Abraham Gotthelf Kaestner (1719-1800) got an LLM degree at Leipzig in 1737, under Christian August Hausen.  See UIUC database.
Karl Friedrich Wilhelm Gottlob Kastner (1783-1857) got a Ph.D. in 1805 at Jena, under J. F. A. Gottling.  See UIUC database.
Carl Friedrich Kielmeyer (1765-1844) received medical certification in 1786.  He then studied at Gottingen under Johann Friedrich Blumenbach, Johann Friedrich Gmelin, and most important, Georg Christof Lichtenberg.  Kielmeyer was the pre-eminent teacher of physiology in Germany before the generation of Johannes Muller, and was the first to emphasize physiology over anatomy.  He gave early expression to what subsequently became known as the doctrine of ontogenic recapitulation.  He wanted to introduce unity into all human knowledge, using the concept of a common developmental force responsible for the growth of organisms, evolution of the earth, etc., but without the arrogance and self-deception of the Naturphilosophen.  Instead, he insisted on empirical evidence, following Kant.  See Dictionary of Scientific Biography, which lists several of his students, and says that he influenced his contemporary, Cuvier.
Gustav Robert Kirchhoff (1824-1887) received his Ph.D. from the University of Koenigsberg in 1847.  He discovered Kirchhoff’s law for the distribution of currents in a network of resistors while he was a student, I do not know if that was the topic of his thesis. His mentor at Koenigsberg was Franz Neumann, and he also studied under his father-in-law Friedrich J. Richelot.  (Another student of Neumann at Koenigsberg was H. Weld, the inventor of the photometer and polarimeter.)  At Breslau, where Kirchhoff taught for a few years, he was very influenced by Bunsen, who became a lifelong friend. Kirchhoff is best known for discovering the relation between optical emission and absorption rates, and the fact that all black bodies have the same emission spectrum. He just missed discovering the displacement current.  See Dictionary of Scientific Biography.
Martin Heinrich Klaproth (1743-1817) was apprenticed to a pharmacist until 1764. While managing an apothecary shop (after the owner, his friend Valentin Rose the elder, had died) in Berlin in the 1770s, he studied chemistry with A. S. Marggraf, whose niece he married in 1780.  Klaproth’s first published paper, in 1776, was on the chemical properties of copal.  He went on to discover uranium and several other elements, developed chemical methods, and helped win acceptance for Lavoisier’s anti-phlogiston theory.  See Dictionary of Scientific Biography.
Felix Christian Klein (1849-1925) got his Ph.D. in 1868 at U. of Bonn, supervised by Julius Plucker, and examined by Rudolph Lipschitz.  He married Anne Hegel, the granddaughter of the philosopher G. W. F. Hegel.  Among other things, he invented the Klein bottle, a surface with one side and no edges, made by joining together two Mobius strips.  See MacTutor History of Mathematics Archive, and Dictionary of Scientific Biography.
Samuel Klingenstierna (1698-1765) got an LLB degree at Uppsala in 1717, under Anders Gabriel Duhre.  See UIUC database.
Leopold Kronecker (1823-1891) studied math under Kummer in high school, and got his Ph.D. at U. of Berlin in 1845, under Dirichlet, with a thesis on “Complex Units.”  (Kummer, by the way, was married to Felix Mendelsohn’s cousin.)  He also studied under Jacob Steiner.  See MacTutor History of Mathematics Archive, and Dictionary of Scientific Biography.
August Kundt (1839-1894) got his Ph.D. under H. G. Magnus at the U. of Berlin in 1864, and took over Helmholtz’s position at Berlin in 1888.  Kundt was a leading experimental physicist, doing work in optics, acoustics, and gas theory.  He used standing waves (“Kundt tube”) made visible by suspended lycopodium seeds (“dust figures”) to measure the speed of sound in gases.  He measured the thermal conductivity of gases under pressure, and with E. G. Warburg, the specific heats of monatomic gases.  With W. C. Roentgen, he observed the Faraday effect in gases.  He also measured the spectrum of lightning, and did work on the piezoelectric effect.  See Dictionary of Scientific Biography.
Joseph-Louis Lagrange (1736-1813) was self-taught in math, except for a class he took at the College of Turin that was taught by Beccaria.  But Lagrange’s earliest papers were sent to Euler for comments, and he corresponded extensively with Euler starting in 1754.  See MacTutor History of Mathematics Archive.
Pierre Laugier received an MD degree at Montpellier in 1603, under Pierre Richer de Belleval.  See UIUC database.
Antoine Laurent Lavoisier (1734-1794) was a student of Gillaume Francois Rouelle.  See UIUC database.  Generally considered the father of modern chemistry, he disproved the phlogiston theory, and gave hydrogen and oxygen their present names.  A member of the nobility, he was guillotined during the French Revolution.
Nicaise LeFebvre (c.1610-1669) was a student of William Davison, and the mentor of Christophle Glaser, according to the article in The Hexagon.  I have no other information about him.
Gottfried Wilhelm von Leibnitz (1646-1716) got an MA in philosophy at Leipzig, with a thesis combining philosophy, math, and law, based on studies under Erhardt Weigel at U. of Jena in 1663.  He got an LLD at Altdorf in 1667, and studied physics with Christiaan Huygens in Paris in 1672.  See MacTutor History of Mathematics Archive.
Nicholas Lemery (1645-1715) was a student of Christophle Glaser, according to the UIUC database, and the article in The Hexagon.
Augustin LeRoyer (1793-1863) had no degree, but studied at U. of Geneva.  His mentor was Pierre Francois Tingry.  See UIUC database.
Georg Christof Lichtenberg (1742-1799) studied natural science at Gottingen under Kaestner, as well as literature and history.  His primary interest was in experimental physics, but he made important contributions to geodesy, volcanology, meteorology, astronomy, chemistry, mathematics, and literature.  He erected the first grounded lightning rod in Germany.  After long holding out, he eventually accepted Lavoisier’s new chemistry.  A popular lecture in physics at Gottingen, he held the first chair of experimental physics at any German university.  He treated hypotheses as models, and distrusted dogmatism.  He suggested the Euclid’s parallel postulate might not be true, that the wave and corpuscular theories of light be able to be unified, and that the ether might not exist.  He discovered the basic process of xerographic copying, producing “Lichtenberg figures.”  He wrote about concepts of subconscious motivation, sublimation, and repression, and was frequently quoted by Freud.  He was a friend of Volta, F. W. Herschel, Kant, Goethe, Humboldt, and King George III of England.  See Dictionary of Scientific Biography.
Justus von Liebig (1803-1873) started studying mineral analysis under K. F. W. G. Kastner at Bonn, and followed him to Erlangen.  But, “finding it prudent to leave Erlangen after instigating a student riot,” according to the UIUC database, Liebig went to Paris and studied organic chemistry under J. L. Gay-Lussac, getting his Ph.D. from Erlangen in absentia, in 1822.  He was a major figure in 19th century chemistry. See UIUC database.
Carl Louis Ferdinand Lindemann (1852-1939) got his Ph.D. in 1873 at Erlangen, under Felix Klein.  Lindemann is best known for his proof that pi is transcendental, in 1882.  See UIUC database, and MacTutor History of Mathematics Archive.
Johannes Antondides van der Linden (1609-1664) got an MD at Franeker in 1630, under Menelaus Winsemius.  See UIUC database.
H. Link received an MD degree with a dissertation on botany.  No mentor is mentioned in the article on Link in Dictionary of Scientific Biography.
Rudolph Otto Sigismund Lipschitz (1832-1903) got a Ph.D. in 1853.  He studied under Franz Neumann at Koenigsberg, and then under Dirichlet at Berlin.  See MacTutor History of Mathematics Archive.
Christian Hieronymus Lommer (?-1787) taught at the Academy of Mines in Freiberg. He did not have a degree, and no mentor is listed in the UIUC database.
Nicolo da Lonigo (Leonicemo) (1428-1524) received an MD/PhD degree in 1453 in Padua, under Pelope.  See UIUC database.
Pierre Joseph Macquer (1718-1784) got an MD at U. of Paris in 1742, under Gillaume Francois Rouelle.  See UIUC database, and the article in The Hexagon.
Pierre Magnol (1638-1715) received an MD degree at Montpellier in 1659, under Pierre Laugier.  Magnol was a botanist, and the magnolia was named after him. See UIUC database.
Heinrich Gustav Magnus (1802-1870) did research on his first published paper, on pyrophoric iron, cobalt, and nickel, under Mitscherlich at Berlin in 1825, and then did his doctoral dissertation on tellurium in 1827.  Wohler, Heinrich Rose and Gustav Rose advised him to study as a kind of postdoctoral fellow with Berzelius, who became his lifelong friend and advisor.  He returned to Berlin in 1828, and several of his students became famous chemists, including Warburg.  He started out in inorganic chemistry, then worked on organic chemistry, physiology and physics (theory of heat, boiling of liquids, electrolysis, thermoelectric currents).  Discovered the Magnus effect.  See UIUC database and Dictionary of Scientific Biography.
Johann Georg Magnus is not listed in the Dictionary of Scientific Biography or the UIUC database, but must have received his medical degree in the 1500s, since Daniel Sennert first practiced medicine under his supervision.
Nicolas Malebranche (1638-1715) was strongly influenced by Descartes’ books.  He studied for the priesthood at the Congregation of Oratory, in 1660-1664, an institution known as the Berullians, because it was founded by De Berulle, a friend of Descartes, and emphasized Cartesian philosophy.  No doubt some of Malebranche’s teachers had studied philosophy directly or indirectly with Descartes, who died 10 years before Malebranche began to study there, but I do not know their names.  Later, in 1672, Malebranche studied math with Leibnitz, who had a big influence on him, although Leibnitz was a few years younger.  See MacTutor History of Mathematics Archive.
Christoph Andreas Mangold (1719-1767) got an MD in 1751 from Erfurt, under Georg Erhardt Hamberger.  See UIUC database.
Andreas Sigismund Marggraf (1709-1782). From 1725 to 1730 he was a pupil of Caspar Neumann, who was a colleague of Marggraf’s father at the court pharmacy in Berlin, and taught at the Collegium Medico-Chirurgicum. Marggraf then became an assistant to the apothecary Rosler in Frankfurt-am-Main, studied chemistry with Spielmann the elder at U. of Strasbourg, attended lectures in chemistry and medicine at Halle, and studied metallurgy with Henckel in Freiberg,  Marggraf’s work was an illustration of the 18th century search for precision in lab techniques, for purity in chemical reagents, as well as for the refusal to construct grand theory.  Although an adherent of the Stahl-Juncker phlogiston theory, his interest in chemistry for its own sake, his refinement of analytic tools and his use of the balance anticipated some facets of Lavoisier’s chemical revolution.  See Dictionary of Scientific Biography.
Burchard David Mauchart (1696-1751) got his degree at Tubingen in 1722, under Elias Rudolph Camerarius, Jr.  Mauchart was also influenced by John Thomas Woolhouse.  See UIUC database
Marin Mersenne (1588-1648) translated Galileo into French, and was largely responsible for making Galileo’s work known outside Italy.  He also corresponded with Galileo, and defended him against his critics, but I don’t know that he ever met Galileo in person.  Mersenne’s circle of mathematicians included Fermat, Etienne Pascal (who was Mersenne’s age) and Etienne’s son Blaise Pascal.  See MacTutor History of Mathematics Archive.
Hermann Minkowski (1864-1909) was a student of Adolph Hurwitz at Koenigsberg, where he got his Ph.D. in 1885. Although primarily a pure mathematician, he is best known for his concept of the space-time continuum.  Einstein was his student in several classes he taught in Zurich.  See MacTutor History of Mathematics Archive.
Eilhard Mitscherlich (1794-1863) got a Ph.D. in oriental languages, with a thesis on ancient Persian texts, in 1817.  He then studied chemistry at Gottingen with F. X. Stromeyer.  He worked in the lab of the botanist Heinrich Link at Berlin, and studied crystallography with link and in Gustav Rose in 1818.  He asked Rose to instruct him in exact crystallographic methods so he could make precise measurements.  He discovered in 1819 that certain elements, which he called “isomorphous,” form compounds with the same atomic ratios and crystal form, for example potassium phosphate and arsenate.  See Dictionary of Scientific Biography and UIUC database.
Johannes Peter Mueller (1801-1858) got an MD at U. of Bonn in 1822, under Philipp Franz von Walther.  Philipp Jakob Rehfues, the curator of the U. of Bonn, helped him get financial aid after his father died.  He then studied in Berlin under Carl Rudolphi, whom he considered the major influence on his work.  Mueller held a preeminent position in medical and biological research in mid-19th century Germany.  He replaced natural philosophical speculation with careful observation and physiological experimentation.  His last student was Ernst Haeckel.  See Dictionary of Scientific Biography and UIUC database.
Hermann Walther Nernst (1864-1941) got his Ph.D. at Wurzburg in 1887. He studied under Ludwig Boltzmann, and F. W. G. Kohlrausch (who was a student of Wilhelm Weber).  See Dictionary of Scientific Biography, and UIUC database (which only lists Kohlrausch as a mentor).
Caspar Neumann (1683-1737) was an assistant to the traveling pharmacist of Frederick I of Prussia.  He then studied chemistry with Boerhaave in Holland, at the urging of F. Hoffman, and he was a lab assistant to the Dutch surgeon A. Cyprian in London, and did chemistry experiments with C. J. and E. F. Geoffrey in Paris.   Neumann was a disciple of G. E. Stahl, on whose recommendation he was appointed royal apothecary in Berlin. He was not a highly original chemist, but spread knowledge of German theories and techniques to London and Paris, and inspired Marggraf to develop “wet” analysis. Like Stahl’s other disciples, he clearly distinguished pure and applied chemistry, and insisted that the chemical approach to nature was superior to the mechanical approach. Unlike Stahl’s other disciples (Pott, Henckel, Juncker) he concentrated on pharmaceutical chemistry, inpsiring a generation of pharmacists, including Steele and Klaproth.  See Dictionary of Scientific Biography.
Franz Neumann (1798-1895) received his Ph.D. from the University of Berlin in 1825, where he studied mineralogy and crystallography under Christian S. Weiss, after first studying theology. He published a monograph Beitrage zur Kristallonomie in 1823, I do not know whether this was his thesis. He is best known among physicists today for Neumann functions and Neumann boundary conditions, but also developed methods for calculating induced currents. He tried to do this entirely in terms of “action at a distance” since he considered it bad form to make use of fields.  See Dictionary of Scientific Biography.
Isaac Newton (1643-1727) got a BA in Cambridge in 1665, and may have been influenced there by Isaac Barrow.  See MacTutor History of Mathematics Archive.
Edward Leamington Nichols (1854-1937) was inspired to go into physics by William A. Anthony, as an undergraduate at Cornell.  He wrote his Ph.D. thesis “Ueber das von gluehenden Platin ausgestrahlte Licht,” at the University of Gottingen in 1879.  Papers in English based on this thesis, “On the Character and Intensity of the Rays emitted by Glowing Platinum,” were published in the American Journal of Science 118 (or 18), 446-468 (Dec. 1879), and 119 (or 19), 42 (1880). Although his degree was from Gottingen, Nichols did his research with Gustav Wiedemann at Leipzig, and with Hermann von Helmholtz and Gustav R. Kirchhoff at Berlin. I do not know which one, if any, was officially his thesis advisor.  However, the topic of his thesis seems most in line with the research interests of Kirchhoff.  After receiving his Ph.D., Edward Nichols was a postdoc of Henry Rowell at Johns Hopkins, and worked as an assistant to Thomas Edison in his work on electric lighting.  Most of his career was devoted to research on color, physiological optics, and illumination.  When he retired, 35 heads of physics departments in the United States were former students of his.  See Dictionary of American Biography Vol. 22, p. 487; NAS Biographical Memoirs 21, 343 (1941), especially the nice quote on top of p. 348; Phys. Rev. Jan. 1, 1938; Amer. Philosophical Yearbook, 1938.
Ernest Fox Nichols (1869-1924) wrote his Ph.D. thesis “Radiometric Researches in the Remote Infrared Spectrum,” at Cornell University in 1897. Although I have not attempted to locate a copy of the thesis, it seems clear from biographical material (e.g. the memoir on Ernest Fox Nichols published by the National Academy of Sciences in Biographical Memoirs, 1929) that his thesis advisor was Edward Leamington Nichols (no relation).  Most of his thesis research was actually done in the laboratory of Emil Warburg at the University of Berlin, where he developed a new type of infrared radiometer with Ernst Pringheim, and also worked with Heinrich Rubens. Earlier research he did at Cornell is the topic of his paper in Physical Review 1, 1 (1893).  Nichols taught at Colgate, Columbia, Dartmouth (where he was president 1909-1916), and Yale, was president of MIT (1920), and director of research for the National Electric Light Association.  He was one of the first to measure light pressure, infrared transmission and reflection coefficients, and the temperature of stars.  See Dictionary of Scientific Biography; Dictionary of American Biography XIII 491-494; NAS Biographical Memoirs 12, 97-131 (1929).
Heinrich Wilhelm Matthaus Olbers (1758-1840) was a student of A. G. Kaestner.  He discovered the asteroids Pallas and Vesta, but is best known for expressing Olbers’ paradox.  This is the question of why the sky is not uniformly glowing as brightly as the sun, since, if the universe is infinite and filled with stars, a line of sight in any direction will eventually intersect a star.  The paradox was only resolved by Hubble’s discovery of the expansion of the universe.
K. E. Pabst von Ohain is listed in the UIUC database as a mentor of A. G. Werner at the Academy of Mines in Freiberg in 1771, but they have no other information on him.
Paracelsus (1493-1541) was a pen name; his real name was Theophrastus Phillipus Aureolus Bombastus von Hohenheim.  He studied under his father William Bombast von Hohenheim, and under Johannes Trithemius.  Paracelsus may have received an MD degree in Ferrara or elsewhere in Italy.  See Dictionary of Scientific Biography.  The influence of Paracelsus’ medical theories on modern western cuisine is discussed by Rachel Laudan, “The Birth of the Modern Diet,” Scientific American, Aug. 2000, p. 62.
Wolfgang Pauli (1900-1958) got his PhD under Arnold Sommerfeld at U. of Munich in 1920.  He was a postdoc of Max Born at Gottingen, and then of Niels Bohr.
Petrus Pauw (1564-1617) got an MD at Rostock in 1587, under Henricus Brucaeus.  Pauw was a colleague of Fabricius.  See UIUC database.
Benjamin Peirce (1809-1880) got his MA in math from Harvard in 1833.  Nathaniel Bowditch discovered Peirce’s mathematical talent, and worked with him as an undergraduate, at least.  Benjamin Peirce was a distant cousin of Benjamin Osgood Peirce, who was John Trowbridge’s first research student as an undergraduate at Harvard.  B. O. Peirce later joined the Harvard Physics Department, after first getting a PhD from Leipzig, under Wiedemann, and serving as a postdoc of Helmholtz in Berlin.  See UIUC database, and Dictionary of Scientific Biography.
John Pell (1611-1685) got an MA at Cambridge in 1630.  No mentor is listed in the biography in MacTutor History of Mathematics Archive.
Pelope was teaching medicine in Padua in 1453, when he was the mentor of Nicolo da Lonigo, but no further information about him is available.  See UIUC database.
Johann Friedrich Pfaff (1765-1825) studied math with A. G. Kaestner at Gottingen, and astronomy with J. E. Bode in Berlin, where he wrote his first paper.  See MacTutor History of Mathematics Archive.
Max Planck (1858-1947) was a student of Felix Klein as an undergraduate at Technische Hochschule in Munich, and got a Ph.D. under Helmholtz and Kirchhoff at U. of Berlin in 1879.
Andrew Plummer (1698-1756) got an MD at Leiden in 1722, under Hermann Boerhaave.  See UIUC database.
Simeon Denis Poisson (1781-1840) studied under Lagrange at Ecole Polytechnique in 1798.
Joseph Priestley (1733-1804) had a degree in divinity, but a good case can be made that his main mentor in science was Benjamin Franklin.  Franklin, who visited London in 1764, encouraged Priestley to write a book, The History and Present State of Electricity , published in 1767, which has the first detailed account of Frankin’s kite and lightning experiment.  Franklin also, on two occasions, found Priestley a job which would provide him with time and funds to do experiments in chemistry.  Priestley was an ardent supporter of the colonists during the American Revolution, and emigrated to the United States in 1794 after an angry Tory mob destroyed his house and laboratory.  See Dictionary of Scientific Biography, and Lord Ritchie-Calder, “The Lunar Society of Birmingham,” Scientific American, June 1982, p. 136-145, which also mentions connections to James Watt, Erasmus Darwin (Charles’ grandfather), Josiah Wedgwood, and Thomas Jefferson.
Petrus Ramus (1515-1572) got an MA in philosophy at U. of Paris in 1536, under Jean Le Hennuyer.  See UIUC database.
Henri Victor Regnault (1810-1878) got a PhD at U. of Paris in 1837.  His mentors were Pierre Berthier, and Justus von Liebig.  See UIUC database.
Ostilio Ricci was a student of Tartaglia.  See Dictionary of Scientific Biography..
Friedrich J. Richelot, although not listed in the Dictionary of Scientific Biography himself, was a student of Jacobi, according to the articles on H. E. Schroeter and Jacobi.
Gilles Personne de Roberval (1602-1675) studied math with Mersenne’s circle in Paris, in particular with Mersenne, Etienne Pascal, and Fermat, although Fermat, who was only a year older than Roberval, should probably be considered a fellow student rather than a mentor.  See MacTutor History of Mathematics Archive.
Jean Robin (1520-1629) was a student of Jacques Gohory (Leo Suavius), and the mentor of Jean Herouard and Guy de la Brosse, according to the article in The Hexagon.  I do not have any other information on him.
Guerner Rolfincke (Werner Rolfinck) (1599-1673) studied medicine at Wittenberg under Daniel Sennert, then at Leiden, Oxford and Paris, and received an MD degree from the University of Padua in 1625, under Adriaan van den Spieghel.  He became a professor of anatomy, surgery, and botany at the University of Jena, where he built the first anatomical theatre there, and gave lectures involving dissection, an innovation that aroused controversy.  Two recently executed criminals were the subjects of dissection, which for a time became known as “Rolfincking” and-- by implication-- served as an additional deterrent to the “criminal classes.” He was the first German to teach Harvey's theory of blood circulation, and the first to demonstrate that cataracts were located in the lens of the eye.  He later became the first professor of chemistry at Jena, and opposed alchemy, stating that the purpose of chemistry was medicine, not transmutation. His contributions to science were minor, but those to the organization of science for a new age were major.  During his life he trained 104 doctoral candidates.  See Dictionary of Scientific Biography and UIUC database.
Gustav Rose (1798-1873) was influenced in his youth by Martin Klaproth, who was a family friend.  He studied mineralogy with Christian S. Weiss at Berlin, did his dissertation, De sphenis atque titanitae systematae crystallino (using a reflecting goniometer to show that crystal sphene and titanate are identical) at Kiel in 1820, and spent time in Berzelius’ lab.  Rose’s students included the explorer Ferdinand von Richthofen, G. von Rath, Paul von Groth, and C. F. M. Websky.  See Dictionary of Scientific Biography and UIUC database.
Heinrich Rose (1795-1864) was trained as a pharmacist.  He was influenced by Berthollet, whom he met during the occupation of Paris in 1815.  He worked with Martin Klaproth, Theodore von Grotthus, and Berzelius.  Heinrich Rose, Mitscherlich, and Wohler were Berzelius’ main disciples in Berlin.  See Dictionary of Scientific Biography and UIUC database.
Rosler was an apothecary in Frankfurt-am-Main in the 1730s, according to the article on Marggraf in the Dictionary of Scientific Biography.  He is not listed himself there, and I have no other information about him.
Guillaume-Francois Rouelle (1703-1770) was a student of J. G. Spitzley.  See UIUC database, and the article in The Hexagon.
Hillaire-Marin Rouelle (1718-1779) was a student of Guillaume-Francoise Rouelle, and the mentor of J. B. M. Bucquet, according to the article in The Hexagon.  The UIUC database does not list H. M. Rouelle, and lists G. F. Rouelle as Bucquet’s mentor. 
Heinrich Rubens (1865-1922) followed his thesis advisor August Kundt from the U. of Strasbourg to the U. of Berlin, where he got his Ph.D. in 1889.  He also worked with Franz Stenger at Strasbourg.  He showed that far infrared radiation was polarized, confirming Maxwell’s belief that light was electromagnetic radiation, and he corresponded with Hertz.  At one meeting, Rubens discussed his data on blackbody radiation, which showed discrepancies with Wien’s law, and compared his data to a suggestion by Rayleigh.  Inspired by this, Max Planck discovered his own radiation law on the same day.  See Dictionary of Scientific Biography; there are photos of him in Naturwissenschaften 10, 1015 (1922), and Physikalische Zeitschrift 23, 377 (1922).
Karl (or Carl) Asmund Rudolphi (1771-1832) did a dissertation on intestinal worms for his medical degree at Greifswald in 1794, under Christian Ehrenfried Weigel.  He also got a degree in philosophy there in 1793, and finished a course at the Berlin Veterinary School in 1801.  He did some work in botany with H. F. Link, and, according to the Dictionary of Scientific Biography, “Rudolphi was criticized for his erroneous [sic] assertion that mushrooms differ so greatly in their structure from other plants that they don’t belong in the plant kingdom.”  He was an important figure in the transition from romantic science (the idea of soul, phrenology, Cuvier’s catastrophes) to the modern approach to biology and medicine.  He helped establish the cell as the basic unit of life in his botanical work, and discovered many parasitic worms, but thought they were generated by the diseased body, and he believed in Berzelius’ “animal chemistry.”  He was reluctant to experiment on live animals.  See UIUC database, and Dictionary of Scientific Biography.
Benjamin Rush (1745-1813) got an MD in 1768 at Edinburgh, under Joseph Black and William Cullen.  Rush, who lived in Philadelphia, was a signer of the Declaration of Independence.  He was a pioneer in advocating humane treatment for the mentally ill, and in promulgating the view that mental illness was a disease, which could be treated.  See UIUC database.
Wallace Clement Sabine (1868-1919) never got a Ph.D., but wrote his master’s thesis, on the spectral absorption of ultraviolet light in metals, in 1888 at Harvard, under John Trowbridge.  Sabine went on to found the science of acoustics.  See Leo L. Beranek, “Wallace Clement Sabine and acoustics,” Physics Today, Feb. 1985, p. 44-51.
Sartorius was an apothecary in Dresden about 1750, according to the listing for J. C. Wiegleb in the UIUC database.  Sartorius is not listed himself.
Frans van Schooten the younger (1615-1660) studied math at U. of Leiden in 1631.  In 1637 he met Descartes, who introduced him to Mersenne’s circle in Paris, where he studied 1641-1642.  Van Schooten became one of the main promoters of Cartesian geometry.  See MacTutor History of Mathematics Archive.
Johann Gottfried Schreiber (1746-1827) got a degree about 1772 from the Academy of Mines in Freiberg.  His mentors were Christian Hieronymus Lommer and J. F. W. de Charpentier.  See UIUC database.
Erwin Schroedinger (1887-1961) got his Ph.D. in 1910, under Hasenohrl.  See Dictionary of Scientific Biography.
Heinrich Eduard Schroeter (1829-1892) studied under Gustav Dirichlet and Jakob Steiner at U. of Berlin, but did his Ph.D. thesis, on elliptic functions, under Friedrich J. Richelot at Koenigsberg, where he got his Ph.D. in 1854.  See Dictionary of Scientific Biography and MacTutor History of Mathematics Archive.
Daniel Sennert (1572-1637) got a master's degree (studying philosophy) at the University of Wittenberg in 1598, studied medicine at Leipzig, Jena, Frankfurt an der Oder, and Basel, and got an MD degree from Wittenberg in 1601.  In the same year, before getting his MD degree, he entered medical practice under the supervision of Johann Georg Magnus.  He was a well known teacher, physician, and scientific writer.  He tried to reconcile Aristotle, Galen, Paracelsus, and traditional atomic hypotheses, but rejected Paracelsus' view of the influence of celestial bodies on the elements.  He incorporated the craft of chemistry into scientific medicine, and was interested in understanding chemistry in terms of first principles and philosophical ideas about nature.  See Dictionary of Scientific Biography.
Benjamin Silliman, Sr. (1779-1864) got an AB degree in law from Yale in 1796, but his mentors in science were James Woodhouse and Thomas Charles Hope.  See UIUC database.
John Clark Slater wrote his thesis, “Compressibility of the Alkali Halides,” at Harvard University in 1923, and it was signed by Percy Bridgman and Edwin C. Kemble.  From the acknowledgments it seems that Bridgman was his thesis advisor, and in any case Bridgman was Kemble’s thesis advisor (according to Kemble’s obituary, Physics Today, Sept. 1987, p. 97-99).
Arnold Johannes Wilhelm Sommerfeld (1868-1951) got his Ph.D. under C. L. F. Lindemann.
Karl Spangenberg (1910-?) wrote his Ph.D. thesis “The Effect of Grid Current Flow upon the Dynamic Characteristics of Vacuum Tube Power Amplifiers,” at Ohio State University in 1937, under William L. Everitt.
Adam Spencer was giving lectures on science in Boston in the early 1720s, according to the article on Benjamin Franklin in Dictionary of Scientific Biography, but I do not have any further information on him.
Adriaan van den Spieghel (1578-1625) got an MD at Padua, ca. 1603.  His mentors were Girolamo Fabrici (Aquapendente) and Giulio Cesare Casseri (who was himself a student of Fabrici).  Another student of Fabrici was William Harvey.  See UIUC database.
Spielmann the elder taught chemistry at U. of Strasbourg in the 1730s, according to the article on Marggraf in the Dictionary of Scientific Biography.  He is not listed himself there, or in the UIUC database, and I have no other information about him.
J. G. Spitzley was a student of Nicholas Lemery, according to the UIUC database, and the article in The Hexagon.
Georg Ernst Stahl (1660-1734) received an MD degree from the University of Jena in 1684, where one of his professors, and a major influence, was G. W. Wedel. In 1694, at the recommendation of Friedrich Hoffman, Stahl was appointed professor of medicine at the University of Halle, which had just been founded by Frederick III of Brandenburg (who was also Frederick I of Prussia).  Much of Stahl’s work concerned the mind-body problem. He thought that mechanical theories like Newton’s could not possibly explain the purposeful action of living beings, and like Descartes he believed that mind (anima) was distinct from matter, but unlike Descartes, he took the Neoplatonist position that anima was just a subtle form of matter. He felt that chemistry and anatomy were not of much practical use in medicine, that health depended more on processes involving the body as a whole. Stahl is best known for developing the phlogiston theory of combustion and calcination, based in part on earlier ideas of Paracelsus. He did not coin the word “phlogiston,” which had been used earlier by Sennert to refer to sulfur, but phlogiston in Stahl’s theory was only a component of sulfur.  See Dictionary of Scientific Biography.
Anton Stork (1731-1803) got an MD degree at Vienna in 1757 under Gerard van Swieten.  Stork was the physician of Empress Marie-Therese of Austria.  See UIUC database.
Marten Stromer (1707-1770) did not have a degree, but studied at Uppsala about 1730.  No mentor is listed in the UIUC database.
F. X. Stromeyer (1776-1835) got a PhD at Gottingen in 1800.  His mentors were J. F. Gmelin, and Vauquelin.  Stromeyer’s own students at Gottingen included Bunsen.  See UIUC database.
Stupaeus is listed as the mentor of Franciscus Sylvius at Basel (MD, 1637) in the UIUC database, but is not listed in the database himself.
Gerard van Swieten (1700-1772) got an MD in Leiden in 1725, under Hermann Boerhaave.  See UIUC database.
Franciscus Sylvius dele Boe (1614-1672) got an MD in Basel, in 1637, under Stupaeus.  See UIUC database.
Tartaglia (Niccolo Fontana) (1499 or 1500-1557) was self-taught in math, since he was too poor to afford a teacher.  He figured out (using a flawed argument) that a projectile travels furthest if launched at an angle of 45 degrees.  He is best known for his independent discovery of the cubic formula, and the bitter dispute with Cardan that followed.  See MacTutor History of Mathematics Archive and Dictionary of Scientific Biography.
Louis Jacques Thenard (1777-1857) got an MA from U. of Paris in 1797, under N. L. Vauquelin, according to the UIUC database.  The article in The Hexagon lists his mentor as A. F. de Fourcroy. 
Pierre Francois Tingry (1743-1821) studied at the U. of Paris about 1770, under Guillaume Francois Rouelle.  See UIUC database.
Evangelista Toricelli (1608-1647) was a student of Castelli at U. of Sapienza in Rome, 1626-32, and was Galileo’s secretary in 1641-42.  Toricelli was the first person to create a vacuum, and discovered the principle of the barometer.  See MacTutor History of Mathematics Archive (which does not have a biography for Castelli).
Joseph Pitton de Tournefort (1656-1708) did not receive a degree, but studied with Pierre Magnol at Montpellier in 1681.  See UIUC database.
Johannes Trithemius is mentioned as the mentor of Paracelsus in the article on Paracelsus in Dictionary of Scientific Biography, although he is not listed himself.  Trithemius was a friend of Heinrich Cornelius Agrippa von Nettesheim (1486-1535), and encouraged Agrippa to finish writing De occulta philosophie.  Agrippa, who is considered to be the historical prototype of Goethe’s Faust, had studied earlier with Peter Ravenna.
John Trowbridge (1843-1923) received his Ph.D. from Harvard in 1873.  His thesis consisted of a series of previously published papers, including one on the electrical conductivity of gas flames.  In this paper he acknowledges the help of Oliver Wolcott Gibbs (one of four people on his doctoral committee) for making a suggestion for an experiment, the only such acknowledgment in any of the papers.  The other people on the committee were Joseph Lovering (listed in the UIUC database as his mentor for his B.S. degree in 1865), Josiah Cooke (whom he acknowledged for lending him equipment), and Benjamin Peirce.  According to Cooke’s obituary, Amer. Acad. Proc. 30, 541-542 (1894-95), he did not have much personal contact with Trowbridge.  Trowbridge founded the Jefferson Physical Laboratory at Harvard.  See UIUC database; Gerald Holton, “How the Jefferson Physical Laboratory came to be,” Physics Today, Dec. 1984, p. 32-37; letter from Trowbridge to Prof. Frank, dated Feb. 6, 1907 (or 1909?), pasted into the flyleaf of Trowbridge’s thesis at Harvard’s Nathan Pusey Library.
Nicolas Louis Vauquelin (1763-1829) became Fourcroy’s lab assistant in Paris about 1784, and collaborated on research with him off and on until Fourcroy died in 1809.  Vauquelin got his MD degree in 1811, with a thesis on the chemical analysis of the human brain, so he could qualify to be appointed professor in Fourcroy’s place.  He discovered chromium, and showed that beryllium was a distinct element, but didn’t isolate it (that was done by Wohler in 1828). See UIUC database, and Dictionary of Scientific Biography.
Felix Vicq d’Azyr (1748-1794) earned a medical degree in Paris in 1774, studying with Antoine Petit (1722-1794), and with Daubenton, professor at the Jardin du Roi, whose niece he married.  He did work on anatomy of the brain, and on control of epizootic diseases (epidemics in animals).  From 1788 he was personal physician to Marie Antoinette, who called him “mon philosophe.”  His position in the French Revolution was ambiguous.  He served the queen, and was a friend of Baily and Lavoisier, who were guillotined, but he was also a friend of Fourcroy, who at least condoned executions.  Vicq d’Azyr died of a violent fever, caused, it was said, by his inner tensions and obsessions.  See Dictionary of Scientific Biography.
Vincenzo Viviani (1622-1703) was a student of Galileo, 1639-1642, and of Toricelli.  See MacTutor History of Mathematics Archive.
Rudolph Augustin Vogel (1724-1774) got an MD at Erfurt in 1747.  The UIUC database does not list a mentor.
Burchard de Volder (1643-1709) got an MD in 1664, at Leiden, under Franciscus Sylvius dele Boe.  See UIUC database.
Philipp Franz von Walther (1782-1849) got degrees in theology and medicine at Landshut in 1803.  His mentors were Johann Peter Frank and Georg Joseph Beer.  See UIUC database.
Georg Wolfgang Wedel (1645-1721) studied philosophy and medicine at U. of Jena, 1661-1667.  He got a medical license and practiced in various places, taking an MD degree from Jena in 1669.  His mentor at Jena was Rolfincke.  Wedel studied in Holland, then became a professor at Jena.  He stood midway between the medieval and modern world views, defending astrology, alchemy, and iatrochemistry.  His teaching at Jena influenced a whole generation of physicians, including Hoffman and Stahl.  See UIUC database, and Dictionary of Scientific Biography.
Johann Adolph Wedel (1675-1747) got an MD from Jena in 1697, under G. W. Wedel.
Christian Ehrenfried Weigel (1748-1831) got an MD from Gottingen in 1771.  His mentors were J. C. P. Erxleben and Rudolph Augustin Vogel.  See UIUC database.
Erhardt Weigel taught at U. of Jena and was Leibnitz’s thesis advisor, according to the MacTutor History of Mathematics Archive, but they do not have a biography of Weigel, and I have no other information about him.
Christian Samuel Weiss (1780-1856) received a doctorate in chemistry and physics from the University of Leipzig in 1800.  From 1800 to 1802, he worked in the Berlin laboratory of Martin Klaproth and Valentin Rose the younger, which was a center for quantitative mineral analysis. He then worked with Abraham Gottlob Werner at Freiberg Bergakademie (Mining Academy). He was the first professor of mineralogy at the University of Berlin, founded in 1810. Later in his career, Weiss began developing the system for classification of crystals that was completed in modern form by Beauvais.  His students included Gustav Rose, Karl Rammelsberg, Friedrich Quenstedt, Adolph de Kupffer, and Franz Neumann.  See Dictionary of Scientific Biography.
Victor Frederick Weisskopf (1908-    ) got his Ph.D. in 1931 at Gottingen under Max Born, with a thesis on the reemission of absorbed light from atoms.  James Franck was also on his thesis committee, and Ehrenfest and Wigner were the important influences on him when he was a graduate student.  He was also a postdoc of Heisenberg and Bohr, graded homework for Schroedinger, and was an assistant to Pauli, who was a major influence.  He planned to work as a postdoc of Dirac, but found him “a withdrawn person who didn’t talk much and was not much interested in the work of other scientists.” Weisskopf’s own students at MIT included Murray Gell-Mann, J. D. Jackson, David Frisch, and Kurt Gottfried. See Weisskopf’s autobiography, The Joy of Insight: Passions of a Physicist (Basic Books, 1991).
Abraham Gottlob Werner (1749-1817) did not have a degree, but studied at the Freiberg Academy of Mines about 1771, under K. E. Pabst von Ohain, and C. H. Lommer.  See UIUC database.
Hermann Klaus Hugo Weyl (1885-1955) got his Ph.D. at Gottingen in 1908.  He was a student of Arnold Sommerfeld.
Gustav Heinrich Wiedemann (1826-1899) got a Ph.D. from the University of Berlin in natural sciences in 1847, with a thesis on the urea derivative biuret.  He studied math with Dirichlet and Joachimsthal, chemistry with Heinrich Rose, F. L. Sonnenschein and E. Mitscherlich (whose daughter he married), and physics with H. G. Magnus and H. W. Dove.  His main training in physics came from Magnus, and he met Helmholtz in Magnus’ lab.  See Dictionary of Scientific Biography.
Johann Christian Wiegleb (1732-1800) got an apothecary degree about 1765 at Langensalza.  Prior to that (1748-1754) he studied in Dresden with the apothecary Sartorius, but didn’t learn chemistry from him.  His mentor in chemistry was Ernst Gottfried Baldinger.  See UIUC database.
Eugene Wigner (1902-1995) got a Ph.D. in chemical engineering at U. of Berlin in 1925. See Physics Today article on his life, and MacTutor History of Mathematics Archive.
John Wilkins (1614-1672) has an interesting biography in the MacTutor History of Mathematics Archive, but no mentor is mentioned there. He married Oliver Cromwell’s sister Robina, founded the Royal Society (which was called “The Invisible College” at first), believed that the Moon was habitable and that travel there would one day be possible, and wrote a book on universal language that was used by Roget in developing his Thesaurus.
Menelaus Winsemius (1591-1637) got an MD at Leiden in 1613, under Petrus Pauw.  See UIUC database.
Friedrich Wohler (1800-1882) received an MD degree, in gynecology, from Heidelberg in 1823.  He studied chemistry with Leopold Gmelin at Heidelberg, doing experiments with cyanates, and with Berzelius in Sweden.  He formed a firm friendship with Berzelius and they continued to correspond.  He was also a lifelong friend of Liebig.  His most distinguished student was Herman Kolbe.  Wohler discovered the first chemical isomer (AgCNO, silver cyanate or fulminate), made the first synthesis of an organic compound (urea), the first extraction of reasonably pure aluminum, first isolated beryllium, discovered the first organic radical (benzoyl), and much other important work.  See UIUC database, and Dictionary of Scientific Biography.
James Woodhouse (1770-1809) got an MD at U. of Pennsylvania in 1792, under Benjamin Rush.  See UIUC database.
John Thomas Woolhouse (1650-1734) was oculist to King James II of England.  No academic degrees or mentors are listed in the UIUC database.