Eloge: Michael S. Mahoney, 1939–2008Author(s): By Jed Z.   Buchwald ; and D. Graham   BurnettSource: Isis, Vol. 100, No. 3 (September 2009), pp. 623-626Published by: The University of Chicago Press on behalf of The History of Science SocietyStable URL: http://www.jstor.org/stable/10.1086/649137 .

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MICHAEL S. MAHONEY, 1939–2008

Perhaps the clearest testimony to the scholarlyrange and depth of Princeton’s now-lamentedMichael S. Mahoney lies in the dismay of hiscolleagues in the last few years, as they contem-plated his imminent retirement. How to main-tain coverage of his fields? Fretting over thisquestion, the program in history of science thathe did so much to build recently found itselfsketching a five-year plan that involved replac-ing him with no fewer than four new appoint-ments: a historian of mathematics with the abil-ity to handle the course on Greek antiquity, ahistorian of the core problems of the ScientificRevolution, a historian of technology who couldcover the nineteenth-century United States andBritain, and, finally, a historian of the computer-and-media revolution. In his passing we havelost a small department.

Best known for his exacting The Mathemati-cal Career of Pierre de Fermat, 1601–1655(1973; rev. ed., 1994), Mahoney also authored avaluable translation of Descartes’s Le Monde(1979) and saw a suite of his essential essays onseventeenth-century mathematics several timespublished in book form in Japanese (under a title

that would be Englished as Mathematics in His-tory [1982; rev. ed., 2007]). At the time of hisdeath the better part of two manuscripts lay inthe drawers of his book-filled office: a study ofthe mathematical thought of Christiaan Huy-gens, and a long-awaited volume on the historyof computing and software engineering. It is tobe hoped that both these works will yet find theirway into print.

For many years a scroll of old-fashionedtractor-feed computer printout hung over his of-fice door (on the inside, where he could read itfrom his desk), bearing in foot-high letters,birthday-banner style, the chastening motto ofthat towering figure of modern mathematicsCarl Friedrich Gauss: Pauca sed Matura—which Mahoney’s Latinists (he started his careeras a medievalist and continued to prefer to readNewton’s Principia in the original) knew wasgenerally translated “Few, but Ripe,” as in “Nota ton of stuff, but all of it very good.” Onesensed that it hung as a banner strung betweenscholarly pride and quiet self-mortification.

Though of the latter there was little need.Over the course of a forty-year career Mahoneypublished more than sixty articles and bookchapters and many scores of book reviews andlectured on the history of science and technol-ogy from Tokyo and Beijing to Berlin and Lon-don, from Athens to Jerusalem—and to schoolteachers in suburban New Jersey. His intellec-tual reach and pedagogical generosity were fa-bled, and more than one graduate student canrecall his improvisational lunchtime pencil-on-a-napkin reconstructions of the besetting geo-metrical paradoxes of the Pythagoreans, just astwo full generations of undergraduates retaingulp-inducing memories of his drop-this-class-if-you-don’t-want-to-sweat opening lecture inHistory 291, his class on the Scientific Revolu-tion, in which, using a computer program of hisown confection, he demonstrated the intricaciesof the Ptolemaic cosmography, complete withdizzying loops upon loops of epicycles, eccen-tric deferents, and a speckling of equant points.The lesson was twofold: first, history of sciencewas going to require that everyone gird up forproblem sets; second, superseded explanationsof natural phenomena might indeed have beenwrong, but they were finely wrought things,

Isis, 2009, 100:623–626©2009 by The History of Science Society. All rights reserved.0021-1753/2009/10003-0010$10.00

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rigorous and, in context, generally very effec-tive. Upshot? Historical understanding of thesciences would require both hard work and thesympathies of the imagination. If he had put hisown motto up on the wall, it might have beenthat.

Born in New York City on 30 June 1939,Mahoney graduated magna cum laude fromHarvard College in the class of 1960 with adouble concentration in history and science.Mathematics, however, was his first love, andwith the support of a German Foreign ServiceFellowship he spent the next two years in Munich,studying with the celebrated historian of mathe-matics Kurt Vogel, whose late-career appetite forthe computational quirks of Babylonians andEgyptian calendrical calculations rubbed off on theyoung American and left a shimmer. Returning tothe United States to pursue a doctorate in thehistory of science in Charles Gillispie’s newly cre-ated program at Princeton, Mahoney moved awayfrom the archaeo-philological sifting of antiquityand took up the role of mathematics in the rise ofthe new sciences, a topic he would never entirelyput down. His gifts as a scholar and teacherquickly recognized, Mahoney had the good for-tune to be converted from graduate student tomember of the faculty at Princeton, acceding tofull professorship in 1980.

The Princeton program in its early yearswas housed in a small building on WashingtonRoad, where Mahoney, Ted Brown, and TomKuhn had their offices and where graduateseminars were held. Mahoney worked withKuhn as a “preceptor” in Kuhn’s course oflectures on the entire history of science, and itwas during those early years that Mahoneyinaugurated his own courses. He did not dab-ble lightly in early science, and neither werehis students allowed to. Mahoney had, forexample, translated many of Huygens’s pa-pers on the pendulum and on colliding bodies,and his students were expected to work line-by-line through the material, to take it apartand put it back together in ways that revealedthe essential go of the arguments. He expectedhard work and was masterful at guiding dis-cussion in ways that permitted students toshow what they could do. Both of us studiedwith Mahoney—Buchwald in the late 1960s,Burnett in the early 1990s—and throughoutall those years Mahoney’s respect for, andinterest in, his students never changed.

Mahoney’s dissertation had concentrated on thecomplex of changes involved in the emergence ofanalysis during the seventeenth century and on themanifold ways in which the concept of proofevolved throughout that period; from early on he

focused his attentions on one of the most enig-matic mathematicians of the period, Pierre de Fer-mat. When Mahoney’s book on Fermat eventuallytook shape, it had the singular, and at the timeunusual, feature in the history of mathematics ofsetting his subject squarely in the context of theperiod. Instead of mining Fermat’s work for nug-gets of future developments, Mahoney linked itwith great care to the period’s conceptions of thesubject’s central problems and techniques. Fermat,he wrote, “was a French mathematician of the firsttwo-thirds of the seventeenth century. His thought,however original or novel, operated within a rangeof possibilities limited by that time and that place.His odyssey had its boundaries; his drummer beatto a tune of the times.”1

As his research assistant at the time, Buch-wald had the opportunity to learn directly fromMike as he gathered material on Fermat andworked hard to understand the logic behind themathematics of, in his words, that “secretive andtaciturn” man.2 Many times one would enterMike’s study to find him surrounded by metic-ulously drawn diagrams and pages of elaborategeometry and analysis, all done in seventeenth-century fashion. He would occasionally breakfrom his desk to enjoy flying a model plane inwhat were then the cornfields behind the univer-sity. On one occasion the plane disappeared intothe field, never to be found, which remindedMike of the forever-lost pages on which Fermathad reportedly proved his famous theorem. Hisparticular insights came strikingly together in amagisterial piece entitled “The MathematicalRealm of Nature,” in which he allied mathemat-ics with mechanics to show that “as a calculus ofmotion, analytic mechanics made motion a formof machine to be taken apart and reassembled. Inthat calculus, created at the turn of the eigh-teenth century, the new mechanics and the newmathematics met to form a new metaphysics.”3

In the mid-1960s, anyone wanting to use acomputer at Princeton punched FORTRAN pro-grams onto a series of cards and then, having fedthe card stack into a reader, waited for the print-out on the ubiquitous green-striped sheets ofperforated paper. At the time Princeton’s ma-chine was an IBM 7094, which had by today’sstandards an utterly insignificant memory in theform of diminutive magnetic cores equivalent toabout 144K. Mahoney was even then interestedin mechanical computation, and he encouragedstudents to use the machine. In 1969 Princetoninstalled the first time-sharing arrangement,based on the IBM System 360, which allowedboth input and output from remote IBM Selec-tric typewriters. Mahoney had by then recog-nized the revolutionary importance of the new

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procedures, and that summer Buchwald had achance to work with him in exploring its poten-tial.

Despite all this, Mike tended to be self-deprecatory about his own very early engage-ment with computer programming, and he en-joyed joking about how irritating the machinescould be. At a 2004 lecture at the Center forComputing in the Humanities, at King’s Col-lege, London, he told the crowd: “During myfinal year at Harvard in 1959–60, I had a job asa computer programmer for a small electronicsfirm in Boston. It involved writing code for aDatatron 204, soon to become through acquisi-tion the Burroughs 204, a decimally addressed,magnetic drum machine. Programming it meantunderstanding how it worked, since it was justyou and the computer: no operating system, noprogramming support. Six or seven months ofthat persuaded me that computers were not veryinteresting, nor did they seem to me to havemuch of a future. So I abandoned my thoughtsof going into applied mathematics and became ahistorian instead. With foresight like that, it wasprobably a good choice.”4

But the truth was that, despite this puckishanecdote, “mike@princeton.edu” (a handle thatattested to his there-at-the-founding place in thedigital university) never really stopped tinkeringwith computers and the code that makes themrun: long before the World Wide Web existed,he was conducting online discussion sessionsfor his classes by email; he helped configure thefirst workstations for nonscientists at the resi-dential colleges at Princeton; and by 1980 Ma-honey’s own research interests turned directly tothe techno-scientific revolution unfolding allaround him—the dawning of the age of the“personal” computer. Mike was always justifi-ably proud of his ability to talk turkey with thecurrent crop of computing techies on campus,and his enthusiasm for this sort of active en-gagement with technology was more than anavocation; it went to the heart of the questionsthat drove his intellectual life: head and hand,the abstract and the concrete, the mind and themachine. Threading between these hoary antith-eses throughout his career, Mahoney soughtagain and again to understand the means bywhich history’s finest thinkers left the stuff ofthe world behind, only in order to find it again,transformed.

His earliest work on the shift from geometri-cal to algebraic mathematics in the early modernperiod is perhaps the hallmark of this research,since the episode represents one of the mythicalmoments in the history of “abstraction.” More-

over, Mahoney’s later research on the origins ofthe programmable computer can be understood assomething like the obverse of those very first prob-lems to which he turned his attention: if algebraicmathematics had disembodied the world of inkedlines and circles, the world of compass andstraightedge, the history of twentieth-century com-puting amounted to something like the “reincarna-tion” of mathematical operations and their crystal-line logic. A Turing machine is, in the end, not amachine at all, in much the same way that Des-cartes’s hyperbolic lens-grinding machine in LaDioptrique was a fantastic illustration of the ge-ometry of conic sections, but a mechanical fantasy.These slips—from logic, to heuristic, to model, to(if the engineers would cooperate) actual device—preoccupied Mahoney for close to half a centuryand led him to a deep interest in the history oftechnology and handcraft, an interest neverthelessinextricable from his grounding in the history ofmathematics. Huygens’s sea-clock, for instance,sat irresistibly at the nexus of these seeminglydiverse concerns, since its gambit for resolving theconsummately practical problem of the longitudehinged (literally) on a peculiar feature of the geo-metry of the cycloid (which is its own evolute) andrequired materializing the mathematical operationof the “evolution” of a curve by means of brassflanges and little bits of thread. It worked like acharm—but only, alas, on paper. Out of brilliantstories like these, brilliantly told, Mahoney ex-plored the myriad ways that reason has fantasizedits own transcendence and craft has picked up thepieces. The result, as Mahoney taught in decadesof well-attended lectures and intimate graduateseminars, is what we call modernity. To under-stand it, he argued, required rolling up yoursleeves: many scholars have their students over tothe house for tea or supper; only Mike had themover to use his workshop to reconstruct workingmodels of several of the optical devices of Ibn-al-Hazen.

Both of us first encountered the field throughMike’s remarkable lectures. As he once put it toa younger colleague: “the students have a rightto see you think up there”; and to that end hewas sparing about his notes and worked everyyear and every week to steep himself afresh inthe primary sources that were the mainstay ofhis pedagogy. So exhilarating was it to watchhim inhabit lost learning that one of us recallsfeeling as a freshman, scribbling madly in theclosing minutes of the final lecture of History291, a vertiginous collapse of past, present, andfuture redolent of the sibylline climax of GarcıaMarquez’s Hundred Years of Solitude: one felt,for a moment, perched on a fixed seat in Dick-

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inson Hall, that the whole history of thought andaction was collapsing on this very instant; that ifwe were patient for one more moment, the ar-chive would become prophecy. It didn’t, ex-actly; but then again, it did, since both of us hadfound our callings. And we were not alone.

Sadly, now, we are.JED Z. BUCHWALD

Division of the Humanities and SocialSciences

California Institute of TechnologyPasadena, California 91125

D. GRAHAM BURNETT

Department of HistoryPrinceton University

Princeton, New Jersey 08544

NOTES1 M. S. Mahoney, The Mathematical Career of

Pierre de Fermat (Princeton, N.J.: Princeton Univ.Press, 1973), p. x.

2 Ibid.3 M. S. Mahoney, “The Mathematical Realm of

Nature,” in The Cambridge History of Seventeenth-Century Philosophy, ed. Daniel Garber and MichaelAyers (Cambridge: Cambridge Univ. Press, 1998),Vol. 1, pp. 702–755, on pp. 744–745.

4 Cited from the oral version of the presentation“Histories of Computing(s),” delivered 20 March2004 as part of the Digital Scholarship, Digital Cul-ture series; available at http://www.princeton.edu/�mike/articles/histories/kingscch.htm (accessed 31Jan. 2009). A revised version of the piece was subse-quently published under the same title in Interdisci-plinary Science Reviews, 2005, 30:119–135.

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