Appendix A
People register
212 people, sorted by birth year, each with life dates, pronunciation, region, contribution, and sources. A life date in the disputed style is argued about in the sources; a dash means the dates are simply not known.
| Name | Lived | Say it | Region | Why they are here | Sources | |
|---|---|---|---|---|---|---|
| Zeno of Elea Appears in: Chapter 2 |
490 BCE to 430 BCE | ZEE-noh of EL-ee-uh | Elea, southern Italy (Greek) | Framed the paradoxes of motion and plurality that state, 2300 years early, the problems limits and measure theory were built to solve | Source 7, Huggett | |
| Antiphon | 480 BCE to 411 BCE | AN-tih-fon | Athens (Greek) | Inscribed polygons of ever more sides in a circle - the germ of the method of exhaustion | Source 8, O'Connor | |
| Democritus Appears in: Chapter 2 |
460 BCE to 370 BCE | dih-MOK-rih-tus | Abdera, Thrace (Greek) | First asserted that a cone is one third of its cylinder, apparently by treating solids as stacks of indivisible slices | Source 2, Heath; Source 8, O'Connor | |
| Eudoxus Appears in: Chapter 2 |
408 BCE to 355 BCE | yoo-DOK-sus | Cnidus, Asia Minor (Greek) | Made the method of exhaustion rigorous and defined equal ratios in a way that survives as Euclid Book V | Source 1, Heath; Source 2, Heath; Source 8, O'Connor | |
| Archimedes Appears in: Chapter 2, Chapter 10, Chapter 11, Appendix E, Appendix G |
287 BCE to 212 BCE | ar-kih-MEE-deez | Syracuse, Sicily (Greek) | Squared the parabola, bounded pi with a 96-gon, and left a mechanical 'method' of discovery recovered only in 1906 | Source 1, Heath; Source 2, Heath; Source 3, Netz | |
| Liu Hui Appears in: Chapter 3, Appendix K |
220 to 280 | lyoh HWAY | Kingdom of Wei, China | Proved the results of the Nine Chapters in his 263 CE commentary, cut the circle to a 3072-gon for pi, and published his failure on the sphere | Source 20, Guo; Source 22, O'Connor; Source 23, Wagner | |
| Zu Chongzhi Appears in: Chapter 3, Appendix K |
429 to 501 | dzoo chong-JRR | Jiankang (Nanjing), Liu Song China | Bounded pi between 3.1415926 and 3.1415927 and gave 355/113, unmatched for roughly 900 years | Source 21, O'Connor; Source 23, Wagner | |
| Zu Gengzhi Appears in: Chapter 3, Chapter 5 |
450 to 520 | dzoo gung-JRR | Liang dynasty China | Stated the equal-cross-sections principle and used it to derive the volume of a sphere, about 1100 years before Cavalieri | Source 21, O'Connor; Source 23, Wagner | |
| Aryabhata I | 476 to 550 | AAR-yuh-bhuh-tuh | Kusumapura (Pataliputra), India | Wrote the Aryabhatiya at 23, containing the first known table of sines and a pi value he explicitly labelled approximate | Source 50, Ramasubramanian; Source 59, O'Connor; Source 60 | |
| Brahmagupta | 598 to 668 | BRUH-muh-GOOP-tuh | Rajasthan, India | Gave a second-order interpolation formula for sine tables and the first systematic arithmetic of zero | Source 50, Ramasubramanian | |
| Li Chunfeng Appears in: Chapter 3 |
602 to 670 | lee chwun-FUNG | Tang dynasty China | His commentary on the Nine Chapters is the only reason Zu Gengzhi's sphere proof survives | Source 23, Wagner | |
| al-Khwarizmi | 780 to 850 | al-KHWAA-riz-mee (kh as in Scottish loch) | Khwarazm and Baghdad | His name became "algorithm" and his book title al-jabr became "algebra" | Source 463, (this project) | |
| Thabit ibn Qurra Appears in: Chapter 3, Appendix K |
836 to 901 | THAA-bit ib-n KOOR-ruh | Harran and Baghdad | Computed areas and volumes of parabolas and paraboloids by upper and lower sums, dividing the interval into unequal parts | Source 57, O'Connor | |
| Ibn al-Haytham Appears in: Chapter 3 |
965 to 1040 | IB-n al-HY-tham | Basra and Cairo | Summed fourth powers and used it to find the volume of a paraboloid as 8/15 of its cylinder - a Riemann-sum computation around 1000 CE | Source 54, Dennis; Source 58, O'Connor | |
| Bhaskara II Appears in: Appendix G, Reference |
1114 to 1185 | BHAAS-kuh-ruh | Bijjada Bida, India | Distinguished average from instantaneous velocity (tatkalika gati) around 1150, using the Rcosine as the rate of change of the Rsine | Source 50, Ramasubramanian | |
| Sharaf al-Din al-Tusi | 1135 to 1213 | SHA-raf ad-DEEN at-TOO-see | Tus, Persia | Found the maximum of the cubic bx - x^3 at x = sqrt(b/3) and gave the condition for a positive root, around 1209 | Source 53, O'Connor | |
| Thomas Bradwardine Appears in: Chapter 4, Appendix K |
1295 to 1349 | BRAD-wer-deen | Oxford / Canterbury (England) | Bradwardine's rule: velocity grows arithmetically as the force-to-resistance ratio grows geometrically - an implicitly logarithmic law of motion in 1328 | Source 103, O'Connor; Source 104, Lovell-Read; Source 100, Kirschner | |
| Richard Kilvington Appears in: Chapter 4 |
1302 to 1361 | KIL-ving-tuhn | Oxford (England) | Wrote the Sophismata before 1325, using calculatory techniques on motion and instantaneous speed, and prompted Bradwardine's rule | Source 102, Jung | |
| William Heytesbury Appears in: Chapter 4 |
1313 to 1372 | HAYTS-bur-ee | Oxford (England) | Gave the first clear statement of the mean speed theorem, in a 1335 logic textbook about how to solve sophisms | Source 101, Jung; Source 104, Lovell-Read | |
| Nicole Oresme Appears in: Chapter 4, Appendix E |
1320 to 1382 | oh-REM | Normandy / Paris (France) | Proved the mean speed theorem geometrically by showing the area under a velocity graph is the distance traveled, and proved the harmonic series diverges | Source 100, Kirschner; Source 107, Oresme; Source 108, Caroti | |
| Madhava of Sangamagrama | 1340 to 1425 | MAAD-huh-vuh | Sangamagrama, near Cochin, Kerala | Found infinite series for pi, sine, cosine and arctangent around 1400, with error terms, roughly 250 years before Newton and Leibniz | Source 50, Ramasubramanian; Source 51, Almeida; Source 55, O'Connor | |
| Narayana Pandita | 1340 to 1400 | naa-RAA-yuh-nuh PUN-dih-tuh | India | Gave the general formula for repeated summations (vara-sankalita), the combinatorial engine the Kerala series needed | Source 50, Ramasubramanian | |
| Parameshvara | 1380 to 1460 | puh-ruh-MAY-shvuh-ruh | Kerala, India | Madhava's pupil; sustained a fifty-year program of eclipse observation used to correct the models | Source 50, Ramasubramanian | |
| Nilakantha Somayaji | 1444 to 1550 | NEE-luh-KUN-tuh soh-muh-YAA-jee | Trikkantiyur, Kerala | Wrote the Tantrasamgraha and the Aryabhatiya-bhasya, argued that pi is incommensurable with the diameter, and summed infinite geometric series | Source 50, Ramasubramanian; Source 56, O'Connor | |
| Jyeshthadeva Appears in: Reference |
1500 to 1575 | JYESHT-huh-DAY-vuh | Kerala, India | Wrote the Yuktibhasa in Malayalam prose, setting out demonstrations (upapatti) of the Kerala series including the error terms | Source 50, Ramasubramanian; Source 51, Almeida | |
| Sankara Variyar | 1500 to 1560 | SHUN-kuh-ruh VAA-ree-yar | Kerala, India | His commentaries Kriyakramakari and Yukti-dipika preserve the verses in which Madhava's series are stated | Source 50, Ramasubramanian | |
| Christopher Clavius | 1538 to 1612 | KLAH-vee-us | Germany / Rome | Taught Ricci at the Collegio Romano and headed the 1582 Gregorian calendar reform - the motive in the transmission argument | Source 51, Almeida | |
| Matteo Ricci | 1552 to 1610 | mat-TAY-oh REE-chee | Italy / Goa / China | Mathematically trained Jesuit who reached Goa in 1578 with instructions to investigate Indian science - a central figure in the Kerala transmission argument | Source 51, Almeida | |
| Johannes Kepler Appears in: Chapter 5, Chapter 11, Appendix D, Appendix G, Appendix K |
1571 to 1630 | yo-HAH-nes KEP-luh | Wuerttemberg / Prague / Linz | Computed volumes of 90-odd solids of revolution by summing infinitely thin slices (Nova stereometria, 1615), and made time proportional to swept area in his second law | Source 134, Cardil; Source 151, [attributed to Jourdain, P. E. B. - UNVERIFIED]; Source 152, Davis; Source 154, O'Connor; Source 159, Kepler | |
| Paul Guldin Appears in: Chapter 5 |
1577 to 1643 | POWL GOOL-deen | Switzerland / Vienna / Graz | The leading Jesuit critic of indivisibles, arguing that there is never a ratio between one infinity and another | Source 135, O'Connor; Source 156, Andersen; Source 132, Sherry | |
| Claude Gaspard Bachet Appears in: Chapter 5, Reference |
1581 to 1638 | klohd gas-PAR bash-AY | Bourg-en-Bresse (France) | His Latin Diophantus turned the Greek parisotes into adaequalitas by a morpheme-for-morpheme calque, handing Fermat the word 'adequality' | Source 130, Katz | |
| Gregoire de Saint-Vincent | 1584 to 1667 | greg-WAHR duh san van-SAHN | Bruges / Ghent (Spanish Netherlands) | Proved (Opus geometricum, 1647) that equal ratios of abscissae under a hyperbola cut off equal areas - the functional equation of the logarithm, found geometrically | Source 141, O'Connor; Source 151, [attributed to Jourdain, P. E. B. - UNVERIFIED]; Source 155, Coolidge | |
| Rene Descartes Appears in: Chapter 5, Chapter 6, Chapter 9, Appendix G |
1596 to 1650 | ruh-NAY day-KART | Touraine (France) / Netherlands / Stockholm | La Geometrie (1637) turned curves into equations, making tangents and areas problems you can compute rather than construct | Source 148, O'Connor; Source 144, O'Connor; Source 151, [attributed to Jourdain, P. E. B. - UNVERIFIED] | |
| Bonaventura Cavalieri Appears in: Chapter 3, Chapter 5, Appendix D, Appendix G, Appendix K, Reference |
1598 to 1647 | kah-vah-LYEH-ree | Milan / Bologna (Italy) | Built the method of indivisibles (Geometria, 1635) and stated as Prop. II.4 what is now called Cavalieri's principle | Source 135, O'Connor; Source 156, Andersen; Source 132, Sherry; Source 151, [attributed to Jourdain, P. E. B. - UNVERIFIED] | |
| Pierre de Fermat Appears in: Chapter 3, Chapter 5, Chapter 6, Chapter 9, Appendix E, Appendix G, Reference |
1601 to 1665 | pyair duh fair-MAH | Beaumont-de-Lomagne / Toulouse (France) | Invented the method of adequality for maxima, minima and tangents (c.1636) and quadratured y=x^n by cutting the axis in geometric progression | Source 130, Katz; Source 144, O'Connor; Source 151, [attributed to Jourdain, P. E. B. - UNVERIFIED] | |
| Gilles Personne de Roberval Appears in: Chapter 3, Chapter 5, Appendix E, Appendix G, Appendix K |
1602 to 1675 | zheel pair-SUN duh roh-bair-VAL | Paris (France) | Quadratured the cycloid before 1636 and found tangents by composing the velocities of the generating motions | Source 137, O'Connor; Source 131, O'Connor; Source 151, [attributed to Jourdain, P. E. B. - UNVERIFIED] | |
| Evangelista Torricelli Appears in: Chapter 5, Appendix G |
1608 to 1647 | tor-ree-CHEL-lee | Faenza / Florence (Italy) | Showed in 1641 (published 1644) that an infinitely long solid of revolution can have finite volume - the acute hyperbolic solid | Source 131, O'Connor; Source 157, Wijeratne | |
| Humphrey Babington Appears in: Chapter 6 |
1615 to 1691 | HUM-free BAB-ing-tuhn | England | Senior fellow of Trinity and rector of Boothby Pagnell, who housed Newton during the plague of 1665 and probably secured his place at Trinity in the first place. | Source 190, Whiteside; Source 180, Stukeley | |
| John Wallis Appears in: Chapter 5, Chapter 6, Chapter 7, Appendix G |
1616 to 1703 | WOL-iss | Kent / Oxford (England) | Arithmetica Infinitorum (1656) gave the infinite product for pi by interpolation, and De sectionibus conicis (1655) introduced the symbol infinity | Source 145, O'Connor; Source 139, Miller; Source 151, [attributed to Jourdain, P. E. B. - UNVERIFIED]; Source 155, Coolidge | |
| Alphonse Antonio de Sarasa Appears in: Chapter 5, Appendix E, Appendix G, Appendix K |
1618 to 1667 | al-FONS an-TOH-nee-oh duh sah-RAH-sah | Spanish Netherlands | Recognized in 1649 that Saint-Vincent's hyperbolic areas behave as logarithms, joining the hyperbola to the logarithm for the first time, in a tract written to defend his teacher against a challenge problem of Mersenne's | Source 66, Sarasa; Source 141, O'Connor; Source 155, Coolidge | |
| Henry Oldenburg Appears in: Appendix K |
c.1619 to 1677 | OLE-den-boork (German) / OLE-den-berg (English) | Bremen / London | First Secretary of the Royal Society; the postal channel through which Newton and Leibniz communicated in 1676, including the anagram letters. | Source 230, Child; Source 281, Newton; Source 285, Dhombres | |
| Nicolaus Mercator Appears in: Chapter 5 |
1620 to 1687 | mer-KAH-tor | Holstein / London / Paris | Logarithmotechnia (1668) printed the first infinite series for a logarithm, ln(1+x) = x - x^2/2 + x^3/3 - ... | Source 149, O'Connor; Source 155, Coolidge | |
| Rene-Francois de Sluse | 1622 to 1685 | ruh-NAY frahn-SWAH duh SLOOZ | Visé / Liege (Prince-Bishopric of Liege) | Published a general rule for tangents to algebraic curves in the Philosophical Transactions, effectively implicit differentiation without calculus | Source 146, O'Connor | |
| Blaise Pascal Appears in: Chapter 5, Chapter 7, Appendix D, Appendix G, Reference |
1623 to 1662 | BLEZ pahs-KAL | Clermont-Ferrand / Paris (France) | The Traite des sinus du quart de cercle (1659) contains the characteristic triangle, the figure Leibniz later credited with opening up his calculus | Source 143, [author unverified]; Source 153, O'Connor; Source 137, O'Connor | |
| John Collins Appears in: Chapter 6, Chapter 8 |
1625 to 1683 | JON KOL-inz | England | Kept the archive of English mathematical letters that Leibniz was shown in October 1676 and that became the Commercium Epistolicum in 1713. | Source 230, Child; Source 280, [Newton]; Source 282, Newton | |
| Pietro Mengoli Appears in: Chapter 5, Chapter 9 |
1626 to 1686 | PYEH-troh MEN-goh-lee | Bologna (Italy) | Proved the harmonic series diverges (1650), summed reciprocals of triangular numbers, and posed the Basel problem he could not solve | Source 142, O'Connor; Source 155, Coolidge | |
| Johann Hudde Appears in: Chapter 5 |
1628 to 1704 | YOH-hahn HUD-duh | Amsterdam (Netherlands) | Hudde's rule (1657/1659) multiplies polynomial coefficients by an arithmetic progression to find repeated roots and extrema - algebraic differentiation before the calculus | Source 147, O'Connor | |
| Christiaan Huygens Appears in: Chapter 5, Chapter 7, Appendix G |
1629 to 1695 | Dutch: KRIS-tee-yahn HOY-khuns (the g is a throaty kh). Anglicised: HY-genz. | The Hague (Netherlands) / Paris | Horologium oscillatorium (1673) proved the cycloid tautochronous and introduced evolutes and involutes; he taught Leibniz his mathematics from 1672 | Source 150, O'Connor; Source 141, O'Connor; Source 235, O’Connor & Robertson; Source 237, Arthur; Source 334, British Society for the History of Mathematics; Source 315, Truesdell | |
| Isaac Barrow Appears in: Chapter 5, Chapter 6, Appendix D, Appendix G, Appendix K |
1630 to 1677 | EYE-zuk BARR-oh | London / Cambridge (England) | Lectiones Geometricae (1670), Lecture X Prop. 11, gives the geometric form of the fundamental theorem of calculus | Source 140, O'Connor; Source 138, Nauenberg; Source 158, Barrow; Source 151, [attributed to Jourdain, P. E. B. - UNVERIFIED] | |
| Christopher Wren Appears in: Chapter 5, Appendix G, Appendix K |
1632 to 1723 | KRIS-tuh-fer REN | England | Rectified the cycloid in 1658, showing one arch has length exactly four times the diameter of its generating circle | Source 64, Whitman | |
| Robert Hooke Appears in: Chapter 6 |
1635 to 1703 | ROB-ert HUUK | England | Curator of Experiments at the Royal Society; proposed to Newton in 1679 the decomposition of orbital motion into tangential motion plus central attraction, and claimed priority for the inverse-square law. | Source 203, Chin; Source 197, Newton | |
| James Gregory Appears in: Chapter 5 |
1638 to 1675 | JAYMZ GREG-uh-ree | Aberdeenshire / St Andrews / Edinburgh (Scotland) | Geometriae pars universalis (1668), the first systematic calculus textbook, proved that differentiation and integration are inverse operations | Source 136, O'Connor | |
| Isaac Newton Appears in: Chapter 1, Chapter 3, Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 11, Appendix D, Appendix G, Appendix K, Reference |
1642 to 1727 | EYE-zuhk NEW-tuhn | England | Invented the calculus of fluxions and fluents in 1664-66, founded classical mechanics in the Principia (1687), and spent more of his life on alchemy and anti-Trinitarian theology than on either. | Source 180, Stukeley; Source 183, Newton; Source 184, Newton; Source 185, Newton; Source 186, Newton; Source 187, Newton; Source 188, Newton; Source 189, [Newton]; Source 190, Whiteside; Source 191, Whiteside; Source 192, Whiteside; Source 195, Newton; Source 196, Chaloner; Source 200, Westminster Abbey | |
| Seki Takakazu Appears in: Chapter 11, Appendix G |
1642 to 1708 | SEH-kee tah-kah-KAH-tsoo | Edo Japan (Kozuke and Edo) | First study of determinants (1683), ten years before Leibniz and in more general form; the Bernoulli numbers before Jacob Bernoulli | Source 463, (this project); Source 429, OConnor and Robertson; Source 430, OConnor and Robertson | |
| Otto Mencke | 1644 to 1707 | OT-oh MENK-uh | Leipzig | Founded the Acta Eruditorum at Leipzig in 1682 and edited it: the journal that printed the first calculus paper in 1684. | Source 231, Leibniz; Source 233, Leibniz | |
| Gottfried Wilhelm Leibniz Appears in: Chapter 1, Chapter 3, Chapter 5, Chapter 6, Chapter 7, Chapter 8, Chapter 9, Chapter 10, Chapter 11, Chapter 12, Appendix D, Appendix E, Appendix G, Appendix K, Reference |
1646 to 1716 | German: LYPE-nits (the b devoices to p, as in Leib). Common English: LYBE-nitz. Both are in use; the German is the one he answered to. | Saxony / Hanover (Holy Roman Empire) | Invented the differential and integral calculus independently of Newton, and gave it the notation (dy/dx and integral-sign f(x)dx) the world still uses. | Source 230, Child; Source 231, Leibniz; Source 232, Leibniz (trans. Walker); Source 233, Leibniz; Source 235, O’Connor & Robertson; Source 236, Look; Source 237, Arthur; Source 241, Leibniz (ed. Gerhardt) | |
| William Chaloner Appears in: Chapter 6, Appendix K |
1650 to 1699 | WILL-yuhm CHAL-uh-ner | England | The most audacious coiner in London, who twice petitioned Parliament claiming he could secure the Mint, and was caught, convicted and hanged through Isaac Newton's personal prosecution. | Source 196, Chaloner | |
| Michel Rolle Appears in: Chapter 3, Appendix D, Appendix G |
1652 to 1719 | mee-SHEL ROLL | France | Stated the theorem now named after him (1691) and then spent 1700-1705 attacking the infinitesimal calculus as "a collection of ingenious fallacies" | Source 459, OConnor and Robertson; Source 453, Miller and Aldrich | |
| Jacob Bernoulli Appears in: Appendix G |
1655 to 1705 | YAH-kop bair-NOO-lee | Basel, Switzerland | Put the word 'integral' into print (May 1690), set the catenary challenge, founded the calculus of variations with his brachistochrone method, and wrote Ars Conjectandi | Source 324, Miller; Source 328, O'Connor; Source 329, Ashworth; Source 330, O'Connor; Source 334, British Society for the History of Mathematics; Source 322, Monks | |
| Hans Sloane Appears in: Chapter 8 |
1660 to 1753 | HANZ SLOHN | Ireland / London | Secretary of the Royal Society; the recipient of Leibniz's two formal complaints (4 March 1711 NS and 29 December 1711) demanding that Keill retract. | Source 280, [Newton] | |
| Charles Montagu | 1661 to 1715 | MON-tuh-gyoo | England | President of the Royal Society in 1697; Newton sent him the anonymous brachistochrone solution for publication | Source 330, O'Connor; Source 321, Brewster | |
| Guillaume de l'Hopital | 1661 to 1704 | gee-YOHM duh loh-pee-TAL | Paris, France | Published the first calculus textbook, Analyse des infiniment petits (1696), containing the rule for 0/0 that Johann Bernoulli had sold him | Source 315, Truesdell; Source 316, L'Hospital; Source 330, O'Connor | |
| Takebe Kataaki | 1661 to 1716 | TAH-keh-beh kah-tah-AH-kee | Edo Japan | Wrote volumes 13-20 of the 20-volume Taisei sankei (1710), completed after Seki's death | Source 430, OConnor and Robertson | |
| Nicolas Fatio de Duillier Appears in: Chapter 6, Chapter 8, Appendix K |
1664 to 1753 | nee-koh-LAH fa-TYOH duh dwee-LYAY | Geneva / London | In his 1699 Lineae brevissimi descensus investigatio geometrica duplex he first put in print the claim that Newton was first inventor and Leibniz at best a second; the opening move of the dispute. | Source 284, Kollerstrom | |
| Takebe Katahiro Appears in: Chapter 11, Appendix D |
1664 to 1739 | TAH-keh-beh kah-tah-HEE-roh | Edo Japan | Series for (s/2)^2 in the sagitta - in modern terms the Taylor series of arcsin-squared - and a convergence-acceleration method equivalent to Romberg's, used to get pi to 40+ places in 1722 | Source 430, OConnor and Robertson; Source 429, OConnor and Robertson | |
| John Harris | 1666 to 1719 | JON HARR-iss | England | Compiler of the Lexicon Technicum (1704-1710), the first English technical encyclopedia, and translator of Newton's De quadratura curvarum into English in 1710. | Source 187, Newton | |
| Johann Bernoulli Appears in: Chapter 6, Chapter 7, Chapter 9, Appendix D, Appendix G, Appendix K, Reference |
1667 to 1748 | YOH-hahn bair-NOO-lee | Basel and Groningen | Taught the calculus to L'Hopital under a contract of exclusivity, posed the brachistochrone in 1696, named the integral calculus, and taught Euler | Source 315, Truesdell; Source 316, L'Hospital; Source 324, Miller; Source 330, O'Connor; Source 331, O'Connor; Source 333, Tou; Source 337, Bernoulli | |
| Guido Grandi Appears in: Chapter 9, Appendix D |
1671 to 1742 | GWEE-doh GRAHN-dee | Pisa, Italy | Named the curve versoria (Latin, the rope that turns a sail) and la versiera (Italian) in 1718, the name Agnesi used and Colson mistranslated | Source 327, O'Connor | |
| John Keill Appears in: Chapter 8 |
1671 to 1721 | KEEL | Scotland / Oxford | Wrote the September-October 1708 sentence in Philosophical Transactions accusing Leibniz of republishing Newton's method "with the name and manner of notation changed", the shot that started the war. | Source 280, [Newton]; Source 283, Keill | |
| Samuel Clarke | 1675 to 1729 | SAM-yoo-ul KLARK | England | Newton's proxy in the 1715-16 correspondence with Leibniz on space, time and God; published the exchange in 1717 after Leibniz's death. | Source 240, Leibniz & Clarke (ed. Bennett); Source 280, [Newton] | |
| William Jones Appears in: Chapter 6, Chapter 8, Appendix G |
1675 to 1749 | WIL-yum JOHNZ | Wales and London | First to use the symbol pi for the circumference-to-diameter ratio, in Synopsis palmariorum mathesios (1706), forty-two years before Euler made it standard | Source 325, Miller; Source 451, Cajori; Source 462, OConnor and Robertson | |
| Charles Hayes Appears in: Chapter 12 |
1678 to 1760 | charlz HAYZ | London, England | Wrote A Treatise of Fluxions (1704), the first book in English on the calculus | Source 439, Hayes | |
| Jean-Jacques Dortous de Mairan Appears in: Chapter 9 |
1678 to 1771 | zhahn zhahk dor-TOO duh meh-RAHN | Paris, France | Dedicatee of Euler's Introductio and du Chatelet's opponent in the vis viva dispute | Source 318, Euler; Source 332, Project Vox | |
| John Colson Appears in: Chapter 6, Chapter 9, Appendix D, Appendix G |
1680 to 1760 | JON KOHL-suhn | England | Lucasian Professor at Cambridge; annotated Newton's Method of Fluxions (1736) and translated Agnesi into English, coining 'the Witch of Agnesi' by misreading versiera as avversiera | Source 185, Newton; Source 192, Whiteside; Source 320, Agnesi; Source 311, Maclaurin; Source 327, O'Connor | |
| Caroline of Ansbach | 1683 to 1737 | KA-roh-lee-nuh fon AHNS-bakh (German); KARR-uh-line (English) | Ansbach / Hanover / London | Leibniz's former pupil; as Princess of Wales she carried every paper of the Leibniz-Clarke correspondence between the two men. | Source 240, Leibniz & Clarke (ed. Bennett) | |
| James Jurin Appears in: Chapter 9 |
1684 to 1750 | JOOR-in | England | Replied to Berkeley as 'Philalethes Cantabrigiensis' in Geometry No Friend to Infidelity (1734) | Source 310, Berkeley; Source 311, Maclaurin | |
| Brook Taylor Appears in: Chapter 5, Chapter 8, Chapter 9, Chapter 12, Appendix D |
1685 to 1731 | BRUUK TAY-lur | England | Methodus Incrementorum Directa et Inversa (1715), Prop. VII Cor. 2: the series named after him, which he had by July 1712 | Source 312, Gibson; Source 331, O'Connor | |
| George Berkeley Appears in: Chapter 5, Chapter 6, Chapter 9, Chapter 10, Chapter 12, Appendix E, Appendix G, Reference |
1685 to 1753 | BARK-lee (not BURK-lee) | Ireland and England | Wrote The Analyst (1734), showing that the calculus rested on reasoning nobody could defend, and thereby set the agenda for a century of foundational work | Source 310, Berkeley; Source 311, Maclaurin; Source 335, Grabiner | |
| William Stukeley Appears in: Chapter 6, Appendix G |
1687 to 1765 | WILL-yuhm STEW-klee | England | Knew Newton personally and wrote the 1752 Memoirs that preserve the only first-hand record of Newton telling the apple story himself. | Source 180, Stukeley; Source 190, Whiteside | |
| John Conduitt | 1688 to 1737 | JON KON-dit | England | Newton's half-niece's husband and his successor as Master of the Mint; collected the recollections that became the basis of every Newton biography. | Source 181, Conduitt; Source 182, Conduitt; Source 191, Whiteside | |
| James Stirling Appears in: Chapter 9, Appendix D |
1692 to 1770 | STUR-ling | Scotland | Published in Lineae Tertii Ordinis (1717, p. 32) the expansion now universally called Maclaurin's series, twenty-five years before Maclaurin's Fluxions | Source 312, Gibson; Source 311, Maclaurin; Source 453, Miller and Aldrich | |
| Andrew Motte | 1696 to 1734 | AN-droo MOT | England | Made the 1729 English translation of the Principia that almost every English reader has used ever since. | Source 186, Newton | |
| Colin Maclaurin Appears in: Chapter 9, Appendix D |
1698 to 1746 | muh-KLOR-in | Scotland | Answered Berkeley with A Treatise of Fluxions (1742), the century's most serious attempt at rigorous foundations, and refused to use infinitesimals at all | Source 311, Maclaurin; Source 312, Gibson; Source 335, Grabiner | |
| Daniel Bernoulli Appears in: Chapter 9 |
1700 to 1782 | DAH-nee-el bair-NOO-lee | Basel and St Petersburg | Wrote Hydrodynamica (1738), founding fluid dynamics, and was rewarded by his father with a rival book carrying an earlier date | Source 333, Tou; Source 336, Craik; Source 341, Darrigol; Source 326, O'Connor | |
| Emilie du Chatelet Appears in: Appendix G |
1706 to 1749 | ay-mee-LEE dew shat-LAY | Paris and Cirey, France | Made the only complete French translation of Newton's Principia, with her own analytical commentary, and argued the Leibnizian mv^2 measure of force that became kinetic energy | Source 332, Project Vox | |
| Benjamin Robins Appears in: Chapter 9 |
1707 to 1751 | ROB-inz | England | Wrote A Discourse Concerning ... Newton's Methods of Fluxions (1735), the most mathematically careful reply to Berkeley | Source 310, Berkeley; Source 311, Maclaurin | |
| Leonhard Euler Appears in: Chapter 9, Chapter 11, Chapter 12, Appendix E, Appendix G, Appendix K |
1707 to 1783 | LAY-on-hart OY-ler (never YOO-ler) | Basel, St Petersburg, Berlin | Solved the Basel problem at 28, made analysis a science of functions, standardised f(x), e, pi and i, and produced almost half his work after going blind | Source 318, Euler; Source 322, Monks; Source 323, Bogart; Source 325, Miller; Source 326, O'Connor; Source 313, Brown; Source 314, Gillings; Source 333, Tou | |
| Thomas Simpson Appears in: Appendix D |
1710 to 1761 | TOM-us SIMP-sun | UK | The rule named after him is Newtons (and Keplers, and Cavalieris, and Gregorys); the method named after Newton and Raphson is, in the form taught, HIS (1740) | Source 462, OConnor and Robertson; Source 453, Miller and Aldrich | |
| Frederick II of Prussia | 1712 to 1786 | FREED-rikh | Berlin, Prussia | Brought Euler to Berlin in 1741 and undervalued him for twenty-five years; Brown suggests he or his courtiers invented the Diderot canard | Source 313, Brown; Source 314, Gillings; Source 326, O'Connor | |
| Alexis-Claude Clairaut Appears in: Chapter 9, Appendix G |
1713 to 1765 | ah-lek-SEE klohd kleh-ROH | Paris, France | Du Chatelet's mathematics mentor: he checked the calculations in her Principia commentary and, ten years after her death, saw the complete translation through the press in 1759 | Source 68, Zinsser; Source 332, Project Vox | |
| Denis Diderot Appears in: Chapter 9, Appendix G |
1713 to 1784 | duh-NEE dee-duh-ROH | Paris and St Petersburg | Editor of the Encyclopedie and author of five creditable mathematical memoirs; the alleged victim of an anecdote that never happened | Source 313, Brown; Source 314, Gillings | |
| Maria Gaetana Agnesi Appears in: Chapter 9, Appendix D, Appendix G, Appendix K, Reference |
1718 to 1799 | mah-REE-ah gah-eh-TAH-nah ah-NYEH-zee | Milan, Italy | Wrote Instituzioni analitiche (1748), the first surviving mathematics book by a woman and the first textbook to treat differential and integral calculus together; first woman appointed to a chair of mathematics (Bologna, 1750) | Source 319, Agnesi; Source 320, Agnesi; Source 327, O'Connor; Source 340, Truesdell | |
| John Landen | 1719 to 1790 | JON LAN-dun | UK | Invented an entire rival notation for the derivative in 1758 that nobody ever used | Source 451, Cajori | |
| Dieudonne Thiebault Appears in: Appendix G |
1733 to 1807 | dyuh-doh-NAY tyay-BOH | Berlin and Paris | Sole original source of the Euler-Diderot anecdote, which he told without naming Euler and expressly declined to vouch for | Source 313, Brown; Source 314, Gillings; Source 339, Thiebault | |
| Joseph-Louis Lagrange Appears in: Chapter 9, Appendix E |
1736 to 1813 | zhoh-ZEF lwee lah-GRAHNZH | Turin, Berlin, Paris | Tried to found the calculus on power series with no infinitesimals and no limits (1797), and in doing so gave us the word 'derivative' and the notation f'(x) | Source 317, Lagrange; Source 324, Miller; Source 325, Miller | |
| Nicolas de Condorcet | 1743 to 1794 | nee-koh-LAH duh kohn-dor-SAY | Paris, France | First user of the 'curly d' partial-derivative symbol, 1770; also the Enlightenment's leading advocate of women's education | Source 325, Miller | |
| Pierre-Simon Laplace Appears in: Chapter 11 |
1749 to 1827 | pyair see-MON lah-PLASS | France | His name is on the operator Maxwell wanted to call "concentration" and on the transform | Source 451, Cajori; Source 453, Miller and Aldrich | |
| Simon LHuilier | 1750 to 1840 | see-MON lwee-LYAY | Geneva, Switzerland | First person to write "lim." for a limit (1786), in the prize essay the Berlin Academy set on the nature of infinity | Source 451, Cajori; Source 452, Miller | |
| Adrien-Marie Legendre | 1752 to 1833 | ah-dree-AN mah-REE luh-ZHAHNDR | Paris, France | First used the partial-derivative symbol in the modern form in 1786, in a memoir on maxima and minima in the calculus of variations | Source 325, Miller | |
| Louis Arbogast | 1759 to 1803 | lwee ar-boh-GAST | Alsace, France | Introduced D as the operator of differentiation and D^-1 for its inverse, in Du calcul des derivations (1800) | Source 451, Cajori; Source 452, Miller; Source 462, OConnor and Robertson | |
| Fourier Appears in: Chapter 10, Appendix G |
1768 to 1830 | foor-YAY | Auxerre and Paris, France | His 1822 Theorie analytique de la chaleur claimed that arbitrary functions have trigonometric expansions, which broke the existing idea of 'function' and forced the rigorisation of analysis. | Source 383, O'Connor; Source 391, Riemann; Source 379, O'Connor | |
| Sophie Germain Appears in: Appendix G, Appendix K |
1776 to 1831 | mah-REE so-FEE zher-MAN | Paris, France | Won the Institut de France elastic-surfaces prize (third round, 1815) and produced the most important result on Fermat's Last Theorem between 1738 and Kummer | Source 410, OConnor and Robertson | |
| Mary Somerville Appears in: Chapter 11, Appendix G |
1780 to 1872 | SUM-uh-vil | Scotland and England | Turned a commission to translate Laplace into Mechanism of the Heavens (1831), which Whewell and Peacock introduced into the Cambridge course of study | Source 412, Somerville; Source 413, Somerville; Source 414, OConnor and Robertson; Source 411, Whewell | |
| Bolzano Appears in: Chapter 10, Appendix K |
1781 to 1848 | bol-TSAH-noh | Prague, Bohemia (Habsburg Empire) | Proved the intermediate value theorem and defined continuity arithmetically in 1817, four years before Cauchy, and built a continuous nowhere-differentiable function around 1830. | Source 363, Bolzano; Source 370, Morscher; Source 371, O'Connor; Source 384, O'Connor; Source 386, Johansson; Source 387, Ruch; Source 369, Bell; Source 360, Grabiner | |
| David Brewster Appears in: Chapter 9, Appendix G |
1781 to 1868 | DAY-vid BROO-stur | Scotland | In The Life of Sir Isaac Newton (1831, p. 194) rendered Bernoulli's remark as the Latin 'tanquam ex ungue leonem', the form now universally quoted | Source 321, Brewster; Source 337, Bernoulli | |
| Cauchy Appears in: Chapter 9, Chapter 10, Chapter 11, Appendix D, Appendix G, Appendix K, Reference |
1789 to 1857 | koh-SHEE | Paris, France | Defined limit, continuity, derivative, convergence and (in 1823) the definite integral as a limit of sums, and proved the fundamental theorem in something close to the modern way. | Source 361, Cauchy; Source 362, Cauchy; Source 360, Grabiner; Source 367, Bascelli; Source 368, Borovik; Source 372, O'Connor; Source 369, Bell | |
| Charles Babbage Appears in: Chapter 8, Chapter 11, Appendix G |
1791 to 1871 | BAB-ij | England | Co-founded the Analytical Society at Cambridge (1812) to replace Newton's dots with Leibniz's d, and coined "pure D-ism in opposition to the Dot-age of the University". | Source 239, Babbage | |
| George Peacock Appears in: Chapter 8, Chapter 11 |
1791 to 1858 | PEE-kok | England | Analytical Society founder member; as a Cambridge examiner he put Leibnizian notation into the Tripos, which is what made the change stick. | Source 239, Babbage | |
| John Herschel Appears in: Chapter 8 |
1792 to 1871 | HUR-shul | England | Co-founder of the Analytical Society; with Babbage wrote the whole of its 1813 Memoirs. | Source 239, Babbage | |
| Charles Whish Appears in: Chapter 3 |
1794 to 1833 | WISH | Britain / Malabar, India | East India Company civil servant who in 1834-35 published the first European account of the Kerala infinite series | Source 51, Almeida; Source 52, Pearce | |
| William Whewell Appears in: Chapter 11, Appendix G |
1794 to 1866 | HYOO-uhl | Cambridge, England | The 1834 review in which the word "scientist" first appears in print; co-adopter of Somerville's book into the Cambridge course | Source 411, Whewell; Source 412, Somerville; Source 442, OConnor and Robertson | |
| Pierre Frederic Sarrus | 1798 to 1861 | pyair fray-day-REEK sa-ROOS | France | Introduced the evaluation bar [F(x)] with limits, in 1823 | Source 451, Cajori; Source 452, Miller | |
| Abel Appears in: Chapter 10, Chapter 11, Appendix G |
1802 to 1829 | AH-bel | Norway | Published in 1826 the counterexample sin(x) - (1/2)sin(2x) + (1/3)sin(3x) - ... that broke Cauchy's theorem on sums of continuous functions, and rigorised the binomial series. | Source 364, Abel; Source 385, O'Connor; Source 372, O'Connor | |
| Carl Gustav Jacob Jacobi | 1804 to 1851 | karl GOOS-tahf YAH-kop yah-KOH-bee | Prussia (Potsdam, Konigsberg, Berlin) | Revived the curly d for partial derivatives in 1841 and made it stick | Source 451, Cajori; Source 452, Miller | |
| Viktor Bunyakovsky Appears in: Appendix D |
1804 to 1889 | boo-nyih-KOFF-skee | Russian Empire (St Petersburg) | Published the integral form of the Cauchy-Schwarz inequality in 1859, twenty-six years before Schwarz | Source 457, OConnor and Robertson; Source 458, Kichenassamy | |
| Dirichlet Appears in: Chapter 10 |
1805 to 1859 | dee-ree-KLAY | Rhineland, Berlin and Goettingen | Gave in 1837 the modern definition of a function as an arbitrary rule of assignment, and the first rigorous convergence theorem for Fourier series. | Source 379, O'Connor; Source 391, Riemann; Source 383, O'Connor | |
| William Rowan Hamilton | 1805 to 1865 | WIL-yum ROH-un HAM-il-tun | Ireland | Introduced the vector differential operator, first in the modern orientation and then rotated to avoid clashing with other uses of the symbol | Source 452, Miller; Source 451, Cajori | |
| Augustus De Morgan Appears in: Chapter 5, Chapter 8, Chapter 9, Appendix G, Appendix K |
1806 to 1871 | AW-gus-tus duh MOR-gun | England | In A Budget of Paradoxes (1872) named Euler, added 'algebra was Hebrew to Diderot', and miscopied Thiebault's z as n, creating the version everyone repeats | Source 313, Brown; Source 314, Gillings | |
| Luigi Menabrea | 1809 to 1896 | loo-EE-jee meh-nah-BREH-ah | Piedmont, Italy | Wrote the 1842 Sketch of the Analytical Engine that Lovelace translated and annotated | Source 415, Menabrea (trans. and notes by Lovelace) | |
| Galois Appears in: Chapter 10, Appendix G, Appendix K |
1811 to 1832 | gal-WAH | Paris, France | Included here only to correct the record: the memoir that vanished was the February 1830 Grand Prize submission, which was with Fourier, who died that April. | Source 380, O'Connor; Source 372, O'Connor | |
| James Joseph Sylvester | 1814 to 1897 | SIL-vis-ter | UK and USA | Coined the word "matrix" in 1850, meaning the womb from which determinants are born | Source 453, Miller and Aldrich | |
| Ada Lovelace Appears in: Chapter 11 |
1815 to 1852 | AY-duh LUV-layss | London, England | Note G of the 1843 Sketch: a looping, recurrence-based algorithm for the Bernoulli numbers with a full trace table, plus the first published speculation on symbolic differentiation by machine | Source 415, Menabrea (trans. and notes by Lovelace); Source 416, OConnor and Robertson | |
| Weierstrass Appears in: Chapter 10, Chapter 11, Chapter 12, Appendix G |
1815 to 1897 | VY-er-shtrahss | Westphalia and Berlin, Prussia | Settled the epsilon-delta definitions in his Berlin lectures and presented on 18 July 1872 a function continuous everywhere and differentiable nowhere. | Source 373, O'Connor; Source 369, Bell; Source 386, Johansson; Source 388, Kesavan; Source 389, Calder; Source 360, Grabiner | |
| Cellerier Appears in: Appendix G |
1818 to 1889 | sel-ay-RYAY | Geneva, Switzerland | Independently constructed a continuous nowhere-differentiable function around 1860; published posthumously in 1890. | Source 386, Johansson | |
| Hermite Appears in: Chapter 10, Appendix G |
1822 to 1901 | air-MEET | Paris, France | Wrote to Stieltjes on 20 May 1893 that he turned away 'avec effroi et horreur' from the lamentable plague of continuous functions with no derivatives. | Source 365, Hermite; Source 388, Kesavan | |
| Kronecker Appears in: Chapter 10, Appendix G |
1823 to 1891 | KROH-nek-er | Berlin, Prussia | Opposed Cantor's transfinite mathematics on constructivist grounds and delayed publication of his 1877 dimension paper. | Source 376, O'Connor; Source 390, Katz | |
| Riemann Appears in: Chapter 3, Chapter 4, Chapter 10, Appendix D, Appendix E, Appendix G, Appendix K, Reference |
1826 to 1866 | REE-mahn | Hanover, Germany | Defined the integral by arbitrary partitions and arbitrary sample points in his 1854 Habilitationsschrift on trigonometric series, and reinvented geometry in his 1854 Habilitation lecture. | Source 391, Riemann; Source 375, O'Connor; Source 386, Johansson | |
| Dedekind Appears in: Chapter 10 |
1831 to 1916 | DAY-duh-kint | Braunschweig and Zurich | Constructed the real numbers by cuts, an idea he dates precisely to 24 November 1858 while preparing his first calculus lectures at Zurich. | Source 366, Dedekind; Source 382, O'Connor; Source 369, Bell | |
| James Clerk Maxwell | 1831 to 1879 | JAYMZ KLARK MAKS-wel | Scotland | Coined curl, convergence (now divergence), slope (now gradient) and concentration (the Laplacian), in one letter to Tait on 7 November 1870 | Source 454, Knott; Source 453, Miller and Aldrich | |
| Peter Guthrie Tait | 1831 to 1901 | PEE-ter GUTH-ree TAYT | Scotland | Developed and named the nabla operator; established the inverted-delta symbol in his Quaternions (1867) | Source 454, Knott; Source 452, Miller | |
| du Bois-Reymond Appears in: Chapter 10, Appendix G |
1831 to 1889 | dyoo bwah ray-MOHN | Germany | Published Weierstrass's nowhere-differentiable function in 1875, three years after Weierstrass presented it and never published it himself. | Source 386, Johansson; Source 368, Borovik | |
| Meray | 1835 to 1911 | may-RAY | Dijon, France | Published in 1869 the first coherent and rigorous theory of irrational numbers to appear in print, three years before Dedekind, Cantor and Heine. | Source 378, O'Connor | |
| Gaston Darboux Appears in: Chapter 10, Appendix D |
1842 to 1917 | gas-TON dar-BOO | France | His 1875 memoir gave the upper-and-lower-sum construction of the integral that every textbook calls the Riemann integral | Source 453, Miller and Aldrich | |
| Hermann Schwarz Appears in: Appendix D |
1843 to 1921 | HAIR-mahn SHVARTS | Germany (Berlin, Gottingen) | His 1885 paper is the source of the proof of the inequality now taught | Source 458, Kichenassamy | |
| Cantor Appears in: Chapter 5, Chapter 10, Appendix G |
1845 to 1918 | KAN-tor | Halle, Germany | Built the reals from fundamental sequences in 1872, proved the reals uncountable in 1874, and gave the diagonal argument in 1891. | Source 376, O'Connor; Source 369, Bell; Source 366, Dedekind | |
| William Robertson Smith Appears in: Chapter 6 |
1846 to 1894 | ROB-ert-sun SMITH | Scotland | Suggested the name "nabla" to Tait, after the Assyrian harp the symbol resembles | Source 454, Knott; Source 453, Miller and Aldrich | |
| Horace Lamb | 1849 to 1934 | HORR-iss LAM | UK | Coined "gradient" in 1897 - for the slope of a plane curve, not for the vector | Source 453, Miller and Aldrich | |
| Kovalevskaya Appears in: Chapter 11 |
1850 to 1891 | kuh-vuh-LYEF-skuh-yuh | Russia and Sweden | Weierstrass's private pupil because Berlin would not enrol a woman; the Cauchy-Kovalevskaya theorem; doctorate from Goettingen in absentia in 1874; full professor at Stockholm in June 1889. | Source 374, O'Connor; Source 373, O'Connor | |
| Henri Poincare | 1854 to 1912 | zhool on-REE pwan-ka-RAY | France | Named Fuchsian and Kleinian functions after other people, over Kleins objections, and defended the choice in print | Source 453, Miller and Aldrich | |
| Johan Ludvig Heiberg Appears in: Chapter 2 |
1854 to 1928 | YOH-ahn LOOD-vee HY-berg | Denmark | Followed up an 1899 catalog notice, traveled to Constantinople in 1906, and read Archimedes' lost Method out of a prayer book | Source 2, Heath; Source 3, Netz; Source 6, Miller | |
| Stieltjes | 1856 to 1894 | STEELT-yuhs | Netherlands and Toulouse, France | Recipient of Hermite's famous letter; his integral generalises Riemann's by integrating against an arbitrary increasing function. | Source 365, Hermite | |
| Peano | 1858 to 1932 | peh-AH-noh | Turin, Italy | Introduced the set-membership symbol in 1889 as an abbreviation for the Latin 'est', plus union, intersection and the existential quantifier. | Source 393, Miller | |
| Florian Cajori Appears in: Chapter 5, Chapter 7, Chapter 9, Appendix D, Appendix G |
1859 to 1930 | kuh-JOR-ee (as he was called in America) | Graubunden, Switzerland; then USA | Wrote the two-volume History of Mathematical Notations (1928-29), still the only place most calculus symbols have ever been traced to their first sentence | Source 450, Cajori; Source 451, Cajori; Source 456, Cajori | |
| William Henry Young | 1863 to 1942 | WIL-yum YUNG | England and Switzerland | Co-author with Grace Chisholm Young of 220 papers and of The Theory of Sets of Points | Source 419, OConnor and Robertson | |
| Grace Chisholm Young Appears in: Appendix G |
1868 to 1944 | grayss CHIZ-uhm YUNG | England, Germany, Switzerland | Gottingen doctorate 1895; co-author of The Theory of Sets of Points (1906); independent work on infinite derivatives, 1914-1916 | Source 419, OConnor and Robertson | |
| J. M. Child Appears in: Chapter 5, Chapter 7, Chapter 8, Appendix G |
1871 to 1960 | CHYLD | England | Translated Leibniz's Paris manuscripts into English (1920), making the dated notebooks readable outside Germany. | Source 230, Child | |
| John Gaston Leathem | 1871 to 1923 | JON GAS-tun LEE-thum | Ireland and Cambridge, UK | Introduced the arrow for "tends to" in 1905, in a tract on volume and surface integrals | Source 451, Cajori; Source 452, Miller | |
| Lebesgue Appears in: Chapter 10, Appendix K, Reference |
1875 to 1941 | luh-BEG | France | Announced his integral in a Comptes Rendus note of 29 April 1901 and set it out in his 1902 thesis Integrale, longueur, aire. | Source 377, O'Connor | |
| Thomas Bromwich | 1875 to 1929 | BROM-ij | UK | With Hardy, spread Leathems arrow notation in 1908; Hardys Preface credits him by name | Source 451, Cajori; Source 452, Miller | |
| G. H. Hardy Appears in: Chapter 11 |
1877 to 1947 | GOD-free HARR-uld HAR-dee | UK | His Course of Pure Mathematics (1908) made the arrow standard and argued, on teaching grounds, that x = infinity should never be written | Source 451, Cajori; Source 452, Miller | |
| Jasek | 1879 to 1945 | YAH-shek | Bohemia, Czechoslovakia | Found Bolzano's Functionenlehre manuscript in the National Library in Vienna in 1920 and announced it in a lecture on 3 December 1921. | Source 386, Johansson | |
| Emmy Noether Appears in: Chapter 11, Appendix G, Appendix K |
1882 to 1935 | NUR-ter (round the lips as if for "oo") | Erlangen and Gottingen, Germany; Bryn Mawr, USA | Noether's theorem (1918): every continuous symmetry of a physical system corresponds to a conservation law | Source 463, (this project); Source 418, OConnor and Robertson | |
| John Maynard Keynes Appears in: Chapter 6, Appendix G, Appendix K |
1883 to 1946 | JON MAY-nerd KAYNZ | England | Bought back about half the Newton papers dispersed at auction in 1936, read the alchemy, and called Newton 'the last of the magicians' in a 1946 lecture read posthumously. | Source 193, Keynes | |
| Rychlik | 1885 to 1968 | RIKH-leek | Prague, Czechoslovakia | Proved in February 1922 that Bolzano's function is continuous and nowhere differentiable, and edited its first publication in 1930. | Source 386, Johansson; Source 384, O'Connor | |
| Johann Radon Appears in: Chapter 12 |
1887 to 1956 | YOH-hahn RAH-don | Austria | Radon measures (1913) and the Radon transform | Source 435, OConnor and Robertson | |
| Otton Nikodym Appears in: Chapter 12 |
1887 to 1974 | OT-on nyih-KOH-dim | Poland and USA | Completed the Radon-Nikodym theorem, 1930 | Source 435, OConnor and Robertson | |
| Srinivasa Ramanujan | 1887 to 1920 | SHREE-nih-VAH-suh rah-MAH-nuu-jun | Tamil Nadu, India, and Cambridge, England | Divergent series, continued fractions, elliptic and modular functions; Euler's constant to 15 places at sixteen | Source 431, OConnor and Robertson | |
| Thoralf Skolem | 1887 to 1963 | TOO-rahlf SKOO-lem | Norway | 1934 ultraproduct construction of the hyperintegers, with the analogue of the Transfer Principle | Source 440, Keisler | |
| Jarnik | 1897 to 1970 | YAR-nyeek | Prague, Czechoslovakia | Independently and simultaneously with Rychlik proved in 1922 that Bolzano's function is nowhere differentiable. | Source 386, Johansson | |
| Mary Cartwright Appears in: Chapter 11 |
1900 to 1998 | KART-ryte | England | With Littlewood, found chaotic solutions of the van der Pol equation in the 1940s, decades before the word "chaos" existed for them | Source 420, OConnor and Robertson | |
| Marshall Stone Appears in: Chapter 12 |
1903 to 1989 | MAR-shul STOHN | USA | Stone-Weierstrass theorem (1937), generalising Weierstrass's polynomial approximation to any compact Hausdorff space | Source 435, OConnor and Robertson | |
| Henri Cartan | 1904 to 2008 | ahn-REE kar-TAHN | France | Bourbaki founder; the first person Schwartz told about distributions, in the middle of the night | Source 433, OConnor and Robertson; Source 434, OConnor and Robertson | |
| Dorothy Vaughan | 1910 to 2008 | DOR-uh-thee VAWN | Virginia, USA | Supervisor of the segregated West Area Computing section at NACA Langley; assigned both Jackson and Johnson to the work that made them famous | Source 422, Shetterly; Source 425, Shetterly | |
| Robert K. Merton Appears in: Chapter 4, Appendix D, Appendix K |
1910 to 2003 | MUR-tun | USA | The scholar Stiglers 1980 paper was written to honor, and to whom the law of eponymy is commonly said to be credited by Stigler himself - a claim I could not verify | Source 460, Stigler | |
| Marjorie Lee Browne | 1914 to 1979 | MAR-juh-ree lee BROWN | USA | Michigan doctorate completed 1949 (conferred February 1950); built mathematics teaching for black students at North Carolina Central University | Source 428, OConnor and Robertson | |
| Laurent Schwartz Appears in: Chapter 12 |
1915 to 2002 | loh-RAHN SHVARTS | Paris, Nancy, France | Theory of distributions (conceived 1944, published 1948-1951): made the Dirac delta a legitimate mathematical object and every distribution infinitely differentiable | Source 463, (this project); Source 433, OConnor and Robertson | |
| Abraham Robinson Appears in: Chapter 10, Reference |
1918 to 1974 | ROB-in-sun | Germany, Israel, UK, USA | Introduced nonstandard analysis in 1961 and in the 1966 book, giving infinitesimals obeying the same laws as ordinary numbers, as Leibniz had claimed. | Source 381, O'Connor; Source 367, Bascelli; Source 368, Borovik; Source 390, Katz | |
| Katherine Johnson Appears in: Chapter 11, Appendix G |
1918 to 2020 | KATH-rin JON-sun | West Virginia and Virginia, USA | Co-authored NASA TN D-233 (1960), the report solving for launch azimuth from a chosen landing point; hand-checked the Friendship 7 trajectory at John Glenn's request | Source 422, Shetterly; Source 423, Skopinski and Johnson; Source 424, OConnor and Robertson | |
| Julia Robinson | 1919 to 1985 | JOO-lee-uh ROB-in-sun | USA | Reduced Hilbert's Tenth Problem to a single missing hypothesis, supplied by Matiyasevich in 1970 | Source 421, OConnor and Robertson | |
| Mary Jackson Appears in: Chapter 11 |
1921 to 2005 | MAIR-ee JAK-sun | Hampton, Virginia, USA | NASA's first black female engineer, 1958; a dozen or so reports on the boundary layer | Source 425, Shetterly | |
| Evelyn Boyd Granville | 1924 to 2023 | EV-lin boyd GRAN-vil | USA | Yale doctorate 1949 in functional analysis; IBM programmer on NASA contracts; later a leader in teacher education | Source 427, OConnor and Robertson | |
| Bishop Appears in: Chapter 9, Chapter 10, Appendix K |
1928 to 1983 | ERR-it BISH-up | USA | Objected that nonstandard analysis, especially in calculus teaching, risked 'a debasement of meaning' because its objects carry no numerical content. | Source 390, Katz; Source 395, Bishop | |
| Gladys West Appears in: Chapter 11, Appendix D |
1930 to 2026 | GLAD-iss WEST | Virginia, USA | Led the team that computed the geoid, the Earth's true gravitational shape, on which satellite positioning depends | Source 426, OConnor and Robertson | |
| D. T. Whiteside Appears in: Chapter 5, Chapter 6, Appendix G, Appendix K |
1932 to 2008 | DERR-uhk WYTE-syde | England | Edited all eight volumes of The Mathematical Papers of Isaac Newton (1967-1981), the critical edition that made real Newton scholarship possible and dismantled several popular myths. | Source 190, Whiteside; Source 191, Whiteside; Source 192, Whiteside | |
| Laugwitz Appears in: Chapter 10 |
1932 to 2000 | LOWK-vits | Germany | Argued in Historia Mathematica and the Archive for History of Exact Sciences that Cauchy's procedures must be read as infinitesimal mathematics, not paraphrased into epsilon-delta. | Source 367, Bascelli; Source 368, Borovik | |
| Michael Nauenberg Appears in: Appendix K |
1934 to 2023 | MY-kuhl NOW-uhn-berg | USA | Physicist who reconstructed Newton's orbital methods and defended the mathematical adequacy of Principia Proposition I against Whiteside and Aiton. | Source 202, Nauenberg | |
| H. Jerome Keisler Appears in: Chapter 10 |
1936 to ? | HOW-erd juh-ROHM KYSE-ler | Wisconsin, USA | Elementary Calculus: An Approach Using Infinitesimals (1976), the first calculus textbook built on Robinson's hyperreals | Source 440, Keisler; Source 441, OConnor and Robertson | |
| Roshdi Rashed Appears in: Chapter 3 |
1936 to ? | ROOSH-dee RAA-shid | Egypt / France | Argues that Sharaf al-Din al-Tusi's method rests on an implicit use of the derivative | Source 53, O'Connor | |
| Grabiner Appears in: Chapter 1, Chapter 10, Appendix K |
1938 to ? | GRAY-bin-er | USA | Showed that Cauchy's rigor was built from the eighteenth-century algebra of inequalities, and that the epsilon is the 'e' of erreur. | Source 360, Grabiner; Source 367, Bascelli | |
| Stephen M. Stigler Appears in: Appendix D, Appendix K |
1941 to ? | STEEG-ler | USA | Stated the law of eponymy in 1980 | Source 460, Stigler | |
| Victor J. Katz Appears in: Chapter 2, Chapter 3, Chapter 5, Chapter 10, Appendix G, Appendix K |
1942 to ? | VIK-ter KATS | USA | Wrote the standard short account of how far Islamic and Indian mathematicians got toward calculus, and traced the summation identity from ibn al-Haytham into the Kerala derivations | Source 61, Katz | |
| Seppo Linnainmaa Appears in: Chapter 12, Appendix D |
1945 to ? | SEP-poh LIN-nine-mah | Finland | First published description of the reverse mode of automatic differentiation, in a 1970 master's thesis and a 1976 BIT paper about accumulated rounding error | Source 436, Baydin, Pearlmutter, Radul and Siskind; Source 437, Schmidhuber; Source 438, Griewank | |
| Bottazzini Appears in: Chapter 10, Appendix K |
1947 to ? | bot-taht-TSEE-nee | Italy | Author of The Higher Calculus; argues it was precisely the use of infinitesimals that stopped Cauchy and Abel seeing uniform convergence. | Source 367, Bascelli | |
| Paul Werbos | 1947 to ? | pawl WUR-bohss | USA | 1974 doctoral thesis Beyond Regression, which cast reverse-mode differentiation in formal discrete-time terms; first NN-specific application, 1981 | Source 436, Baydin, Pearlmutter, Radul and Siskind; Source 437, Schmidhuber | |
| Russ | 1947 to ? | RUSS | UK | Translator of Bolzano's 1817 paper (Historia Mathematica 7, 1980) and of The Mathematical Works of Bernard Bolzano (OUP, 2004). | Source 387, Ruch; Source 360, Grabiner | |
| Jan P. Hogendijk Appears in: Chapter 3 |
1955 to ? | yahn HOH-khen-dike | Netherlands | Argues that a different, non-derivative method lies behind al-Tusi's determination of the maximum | Source 53, O'Connor | |
| William Noel | 1965 to ? | WIL-yum noh-EL | United Kingdom / United States | Curator who ran the decade-long Archimedes Palimpsest project and put all its data online free | Source 6, Miller | |
| Reviel Netz Appears in: Chapter 2 |
1968 to ? | reh-vee-EL NETS | Israel / United States | Led the reading of the recovered palimpsest text and published the Method Proposition 14 argument comparing infinite collections | Source 3, Netz; Source 6, Miller | |
| Abigail Quandt | - | AB-ih-gayl KWONT | United States | Spent four years disassembling and stabilising the Archimedes Palimpsest so it could be imaged at all | Source 4; Source 6, Miller | |
| Archibald Pitcairne Appears in: Chapter 6 |
- | AR-chih-bawld pit-KAIRN, also PIT-kairn | Scotland | Friend of Craig and David Gregory whose Solutio problematis de historicis seu inventoribus (Edinburgh, 1688) printed Gregory's reconstruction of Newton's prime theorem on series quadratures | Source 204, Guicciardini | |
| David Gregory Appears in: Chapter 6, Appendix K |
- | DAY-vid GREG-uh-ree | Scotland; Oxford | Scottish acolyte who transcribed Newton manuscripts after his 1694 Cambridge visit, wrote the circulating summary Methodus fluxionum, was shown the Enumeratio in the late 1690s, and printed Newton's 'classical scholia' in his own 1702 book | Source 204, Guicciardini | |
| Edmond Halley Appears in: Chapter 6, Chapter 8, Chapter 9 |
- | Contested: HAL-ee (rhymes with valley) is the form comet astronomers and 89 percent of Halley families use; HAY-lee is common; HAW-lee is the form his biographer Ronan preferred | - | One of the small group of experts allowed to see Newton's mathematical manuscripts; examined the worn De methodis at Cambridge with Raphson in 1691 and was given De quadratura to transcribe in 1695 on the condition that no one else saw it | Source 204, Guicciardini | |
| Evelyn Walker Appears in: Chapter 5, Chapter 7, Appendix G |
- | EV-uh-lin WAW-ker | New York, USA | Professor at Hunter College; made the standard English translation of Leibniz's 1684 and 1686 calculus papers for Smith's Source Book (1929), and documented the originals' printing errors. | Source 232, Leibniz (trans. Walker) | |
| Ioannes Myronas Appears in: Chapter 2 |
- | yoh-HAN-iss my-ROH-nus | Jerusalem (Byzantine) | The scribe who erased Archimedes' Method in 1229 and wrote a prayer book over it - thereby preserving it | Source 4; Source 6, Miller | |
| James Wilson Appears in: Chapter 6, Appendix K |
- | JAYMZ WIL-sun | - | Made a secondary transcript of De methodis from Jones's copy about 1720, now lost, and wrote to Newton in December 1720 reporting that badly copied transcripts of the 1666 and 1671 treatises were circulating in private hands | Source 204, Guicciardini | |
| Jeff Miller | - | JEFF MIL-er | USA | Built and maintained the Earliest Uses of Symbols and Words pages, which have corrected Cajori in dozens of places since 1994 | Source 452, Miller; Source 453, Miller and Aldrich | |
| John Craig Appears in: Chapter 6, Chapter 10, Appendix K |
- | JON KRAYG | Scotland | Scottish mathematician who went to Cambridge after hearing that Wallis meant to publish a summary of Newton's method of squaring curves, transcribed part of De methodis and of the Epistola posterior, and carried the results back to Pitcairne and David Gregory | Source 204, Guicciardini | |
| John Flamsteed | - | - | - | Given a set of notes on algebra by Newton in 1674, one of the earliest documented loans of a Newton mathematical manuscript | Source 204, Guicciardini | |
| John Perry Appears in: Chapter 12 |
- | jon PERR-ee | Britain | Opened the British Association debate of 14 September 1901 that launched the campaign to teach the calculus in ordinary schools | Source 492, Perry | |
| Joseph Raphson Appears in: Chapter 6 |
- | - | - | Examined the original De methodis manuscript at Cambridge with Halley in 1691 and recorded that it was 'very much worn by having been lent out' | Source 204, Guicciardini | |
| Munjala | - | MOON-jaa-luh | India | Gave, around 932 CE, the first correct formula for a planet's true daily motion using the Rcosine as a rate of change | Source 50, Ramasubramanian | |
| Niccolo Guicciardini Appears in: Chapter 6, Chapter 8, Appendix K |
- | nee-koh-LOH gweet-char-DEE-nee | Italy | Established that Newton ran a deliberate scribal publication strategy for his mathematics, and that the withholding followed from a methodological judgment against the 'new analysis' formed in the 1670s | Source 204, Guicciardini | |
| Nicolas Bourbaki Appears in: Chapter 12 |
- | nee-koh-LAH boor-BAH-kee | France | Elements de mathematique (from 1939): rebuilt mathematics in a fixed logical order with no pictures and no history | Source 434, OConnor and Robertson | |
| Richard Swineshead Appears in: Appendix K |
- | SWYNZ-hed | Oxford (England) | Wrote the Liber calculationum (c.1340-50), sixteen treatises of quantitative analysis of change, earning him the single name 'the Calculator' | Source 106, Gale | |
| Robert Wengert | - | WENG-gert | USA | Forward-mode automatic differentiation, 1964; the evaluation trace is still called a Wengert list | Source 436, Baydin, Pearlmutter, Radul and Siskind | |
| Roger Cotes Appears in: Chapter 6, Appendix K |
- | ROJ-er KOHTS (rhymes with coats) | - | Editor of the second edition of the Principia (1713); one of the disciples who had to ask Newton directly how to complete proofs depending on the quadrature of curves, and who made the anti-Cartesian intent of Book 1 Sections 4 and 5 explicit in the index | Source 204, Guicciardini | |
| Sabetai Unguru Appears in: Chapter 2 |
- | sa-BET-eye ung-GOO-roo | Israel / United States | Argued in 1975 that Greek geometry must not be read as algebra in disguise, provoking replies from van der Waerden, Freudenthal and Weil and reframing what it means to ask why the Greeks did not develop calculus | Source 491, Katz | |
| Samuel Horsley Appears in: Chapter 6 |
- | SAM-yoo-ul HORS-lee | - | Editor of Newton's Opera omnia (1779-1785), which rests on the Jones transcript of De methodis and on Wilson's secondary transcript of it rather than on Newton's originals | Source 204, Guicciardini | |
| Speelpenning Appears in: Chapter 12 |
- | bairnt SPAIL-pen-ing | United States (Illinois) | 1980 PhD: the first implementation of reverse mode that was genuinely automatic, transforming programs written in a general-purpose language | Source 436, Baydin, Pearlmutter, Radul and Siskind; Source 438, Griewank | |
| Stephen D. Snobelen Appears in: Appendix K |
- | STEE-vuhn SNOH-buh-luhn | Canada | Established the detailed picture of Newton's concealed anti-Trinitarianism and of the specific strategies he used to survive as a heretic in office. | Source 194, Snobelen | |
| Ted Skopinski Appears in: Chapter 11 |
- | skuh-PIN-skee | Virginia, USA | First author of NASA TN D-233 | Source 423, Skopinski and Johnson; Source 424, OConnor and Robertson | |
| Thomas Pellet | - | - | - | Received an incomplete copy of De methodis from William Jones, an instance of the deliberate practice of passing on curtailed Newton manuscripts | Source 204, Guicciardini |