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The Fields Medal Should Return to Its Roots COMMENT HEALTH Poor artificial lighting GENOMICS Sociology of AI Design robots to OBITUARY Ben Barres, glia puts people, plants and genetics research reveals self-certify as safe for neuroscientist and equality animals at risk p.274 baked-in bias p.278 autonomous work p.281 advocate, remembered p.282 ike Olympic medals and World Cup trophies, the best-known prizes in mathematics come around only every Lfour years. Already, maths departments around the world are buzzing with specula- tion: 2018 is a Fields Medal year. While looking forward to this year’s announcement, I’ve been looking backwards with an even keener interest. In long-over- looked archives, I’ve found details of turning points in the medal’s past that, in my view, KARL NICKEL/OBERWOLFACH PHOTO COLLECTION PHOTO KARL NICKEL/OBERWOLFACH hold lessons for those deliberating whom to recognize in August at the 2018 Inter- national Congress of Mathematicians in Rio de Janeiro in Brazil, and beyond. Since the late 1960s, the Fields Medal has been popularly compared to the Nobel prize, which has no category for mathematics1. In fact, the two are very different in their proce- dures, criteria, remuneration and much else. Notably, the Nobel is typically given to senior figures, often decades after the contribution being honoured. By contrast, Fields medal- lists are at an age at which, in most sciences, a promising career would just be taking off. This idea of giving a top prize to rising stars who — by brilliance, luck and circum- stance — happen to have made a major mark when relatively young is an accident of history. It is not a reflection of any special connection between maths and youth — a myth unsupported by the data2,3. As some mathematicians have long recognized4, this accident has been to mathematics’ detriment. It reinforces biases within the discipline and in the public’s attitudes about mathemati- Olga Ladyzhenskaya was on the Fields Medal shortlist in 1958. cians’ work, career pathways and intellectual and social values. All 56 winners so far have been phenomenal mathematicians, but such biases have contributed to 55 of them being male, most being from the United States and The Fields Medal Europe and most working on a collection of research topics that are arguably unrepre- sentative of the discipline as a whole. When it began in the 1930s, the Fields should return to Medal had very different goals. It was rooted more in smoothing over international conflict than in celebrating outstanding scholars. In fact, early committees delib- its roots erately avoided trying to identify the best young mathematicians and sought to pro- Forgotten records of mathematics’ best-known mote relatively unrecognized individuals. As I demonstrate here, they used the medal prize hold lessons for the future of the discipline, to shape their discipline’s future, not just to argues historian Michael Barany. judge its past and present. ©2018 Mac millan Publishers Li mited, part of Spri nger Nature. All ri18ght sJANUARYreserved. 2018 | VOL 553 | NATURE | 271 COMMENT As the mathematics profession grew organizers’ discussions, years later, over what mostly through letters sent to Bohr, who and spread, the number of mathemati- to do with these leftover funds. summarized the key points in letters he sent cians and the variety of their settings made Fields forced the issue from his death- back. The committee conducted most of it harder to agree on who met the vague bed in 1932, endowing two medals to be these exchanges in the second half of 1949, standard of being promising, but not a star. awarded at each ICM. The 1932 ICM in agreeing on the two winners that December. In 1966, the Fields Medal committee opted Zurich appointed a committee to select the The letters suggest that Bohr entered the for the current compromise of consider- 1936 medallists, but left no instructions as to process with a strong opinion about who ing all mathematicians under the age of 40. how the group should proceed. Instead, early should win one of the medals: the French Instead of celebrity being a disqualification, committees were guided by a memorandum mathematician Laurent Schwartz, who it became almost a prerequisite. that Fields wrote shortly before his death, had blown Bohr away with an exciting new I think that the Fields Medal should return titled ‘International Medals for Outstand- theory at a 1947 conference6. The Second to its roots. Advanced mathematics shapes ing Discoveries in Mathematics’. World War meant that Schwartz’s career our world in more ways than ever, the dis- Most of the memorandum is procedural: had got off to an especially rocky start: he cipline is larger and more diverse, and its how to handle the funds, appoint a commit- was Jewish and a Trotskyist, and spent part demographic issues and institutional chal- tee, communicate its decision, design the of the French Vichy regime in hiding using lenges are more urgent. The Fields Medal medal and so on. In a false name. His long-awaited textbook had plays a big part in defining what and who fact, Fields wrote, the “Fields still not appeared by the end of 1949, and matters in mathematics. committee “should be stipulated there were few major new results to show. The committee should leverage this role left as free as possible” that the medal Bohr saw in Schwartz a charismatic leader by awarding medals on the basis of what to decide winners. To should not be of mathematics who could offer new con- mathematics can and should be, not just minimize national named after nections between pure and applied fields. what happens to rise fastest and shine bright- rivalry, Fields stipu- any person or Schwartz’s theory did not have quite the est under entrenched norms and structures. lated that the medal place.” revolutionary effects Bohr predicted, but, by By challenging themselves to ask every four should not be named promoting it with a Fields Medal, Bohr made years which unrecognized mathematics after any person or a decisive intervention oriented towards his and mathematicians deserve a spotlight, place, and never intended for it to be named discipline’s future. the prizegivers could assume a more active after himself. His most famous instruction, The best way to ensure that Schwartz won, responsibility for their discipline’s future. later used to justify an age limit, was that the Bohr determined, was to ally with Marston awards should be both “in recognition of Morse of the Institute for Advanced Study in BORN OF CONFLICT work already done” and “an encouragement Princeton, who in turn was promoting his The Fields Medal emerged from a time of for further achievement”. But in context, this Norwegian colleague, Atle Selberg. The path deep conflict in international mathematics instruction had a different purpose: “to avoid to convincing the rest of the committee was that shaped the conceptions of its purpose. invidious comparisons” among factious not straightforward, and their debates reveal Its chief proponent was John Charles Fields, national groups over who deserved to win. a great deal about how the members thought a Canadian mathematician who spent his The first medals were awarded in 1936, to about the Fields Medal. early career in a fin de siècle European math- mathematicians Lars Ahlfors from Finland Committee members started talking ematical community that was just beginning and Jesse Douglas from the United States. about criteria such as age and fields of study, to conceive of the field as an international The Second World War delayed the next even before suggesting nominees. Most endeavour5. medals until 1950. They have been given thought that focusing on specific branches The first International Congress of every four years since. of mathematics was inadvisable. They enter- Mathematicians (ICM) took place in 1897 tained a range of potential age considera- in Zurich, Switzerland, followed by ICMs BLOOD AND TEARS tions, from an upper limit of 30 to a general in Paris in 1900, Heidelberg in Germany in The Fields Medal selection process is sup- principle that nominees should have made 1904, Rome in 1908 and Cambridge, UK, in posed to be secret, but mathematicians are their mark in mathematics some time since 1912. The First World War derailed plans human. They gossip and, luckily for histori- the previous ICM in 1936. Bohr cryptically for a 1916 ICM in Stockholm, and threw ans, occasionally neglect to guard confiden- suggested that a cut-off of 42 “would be a mathematicians into turmoil. tial documents. Especially for the early years rather natural limit of age”. When the dust settled, aggrieved research- of the Fields Medal, before the International By the time the first set of nominees was ers from France and Belgium took the reins Mathematical Union became more formally in, Bohr’s cut-off seemed a lot less arbitrary. and insisted that Germans and their war- involved in the process, such ephemera may It became clear that the leading threat to time allies had no part in new international well be the only extant records. Bohr’s designs for Schwartz was another endeavours, congresses or otherwise. They One of the 1936 medallists, Ahlfors, French mathematician, André Weil, who planned the first postwar meeting for 1920 served on the committee to select the 1950 turned 43 in May 1949. Everyone, Bohr in Strasbourg, a city just repatriated to winners. His copy of the committee’s corre- and Morse included, agreed that Weil was France after half a century of German rule. spondence made its way into a mass of docu- the more accomplished mathematician. In Strasbourg, the US delegation won ments connected with the 1950 ICM, largely But Bohr used the question of age to try to the right to host the next ICM, but when hosted by Ahlfors’s department at Harvard ensure that he didn’t win.
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