Why Are There So Few Women Mathematicians?

How a corrosive culture keeps women out of leadership positions on math

JANE C. HU NOV 4, 2016 – Atlantic

As soon as mathematician Chad Topaz ripped the plastic off his copy of the American Mathematical Society’s magazine Notices, he was disappointed. Staring back at him from the cover were the faces of 13 of his fellow mathematicians—all of them men, and the majority of them white.  “Highlighting all this maleness and whiteness—what is the message that is being sent to the membership?” he wondered. Continue reading

Tributes paid to ‘shining light’ Maryam Mirzakhani


There is a classic geometric problem, put forward by Ernst Strauss in the 1950s, called the Illumination problem.  In it, he asked if a room with mirrored walls can always be illuminated by a single point light source, allowing for the repeated reflection of light off the mirrored walls.  Or in other words, can there be a room shape constructed which would leave any point in darkness?

Maryam Mirzakhani devoted her life to solving equations such us these and her brilliant and innovative work in abstract mathematics is being used to shed light on some long-standing physics problems to do with ricocheting and diffusion of light, billiards, wind and other entities.  Her findings are expected to have many uses in science, sports and other fields for years to come.

There was a quiet and orderly rush in the direction of the lecture hall on Tuesday morning as tributes were about to be paid to the first ever female winner of the Fields Medal (received at the ICM in Seoul in 2014), who passed away from cancer in July of 2017.  She left her husband Jan Vondrak, also a professor at Stanford, and young daughter Anahita.

The hall was lead in tribute and a minute’s silence, by Turkish mathematician Betul Tanbay, who recalled the illumination problem and compared her late colleague to the candle itself, lighting a path for others to follow.  “Maryam showed forever that excellence is not a matter of gender or geography,” she added, “Maths is a universal truth that is available to us all.”

Maryam was born in Tehran in 1977 and considered herself lucky to have finished junior school at the same time as the Iran/Iraq war ended.  Had it not, the world may have been forever deprived of her genius.

The moment she arrived at Sharif University as a young mathematics student, it was clear she was destined for greatness.  “I haven´t met anyone in Iran like Maryam,”  said Professor Saieed Akbari, who taught her a number of courses and tutored the Iranian Math Olympiad teams.  “She was unique, very brilliant.  When I taught her linear algebra, I gave her a problem which was very difficult to solve in 3 dimensions.  Within one week she came back to me with the solution in every dimension!  Another time I gave her an open problem with no solution and offered a ten dollar reward without telling the team that there was no solution. Three days later she came back with it solved!”  In both instances, the findings of this young math prodigy were published as papers.

As well as being precociously talented, Maryam was a humble individual, shunning the limelight and deflecting her success.  “She told me she had excellent parents, was lucky enough to go to a good school and have a group of brilliant friends. And all of these people helped her win the prize.”  Professor Akbari added.

Maryam later became a professor of mathematics at Stanford University where her research topics included Teichmüller theory, hyperbolic geometry, ergodic theory and symplectic geometry.  When she was awarded the Fields Medal, her work in “the dynamics and geometry of Reimann surfaces and their moduli spaces” was cited as being stand-out.

Doctor Ashraf Daneshkhah of the Women’s Committee at the Iranian Mathematical Society told me that Maryam has “inspired many women in Iran to go into mathematics.”  And her compatriot was a shining example, “very polite and quiet, always thinking rather than talking.”

Doctor Ashraf was here to present a proposal that Maryam’s birthday – May 12th – be recognized and supported by the World Meeting for Women in Mathematics as the Women in Mathematics Day. The date will be celebrated every year inside the mathematical community, encouraging females from all over the world to advance their achievements in the field.

Female Inventors

I just read this article from  that has been recently published in Interesting Engineering, I hope you also enjoy reading it:

Female Inventors and Their Inventions That Changed the World and Impacted the History In a Revolutionary Way

Female inventors, scientists, and engineers have discovered countless revolutionary and life-changing inventions that have caused unprecedented breakthroughs in the history of the world.

You will find whole the story here

for the second time an Iranian won a Fields Medal!

As IMPA reported at 1st august 2018:

“Researchers from Germany, India, Iran and Italy take home the 2018 Fields Medal”

the whole story:

“Four notable and promising researchers from four different countries – Germany, India, Iran, and Italy – are the winners of the most important international award in mathematics, the Fields Medal. Delivered for the first time in 1936, the medal is recognition for works of excellence and an incentive for new outstanding achievements.

Awarded every four years at the world’s largest mathematics event – the International Congress of Mathematicians (ICM) – the medal will be given this year to Peter Scholze, Akshay Venkatesh, Caucher Birkar, and Alessi Fegalli at ICM’s opening ceremony on August 1st, at Riocentro.

Founded by the Canadian mathematician John Charles Fields to celebrate outstanding achievements, the Fields Medal has already been awarded to 56 scholars of the most diverse nationalities, among them, Brazilian Fields laureate Artur Avila, an extraordinary researcher from IMPA, awarded in 2014 in South Korea. Due to its importance and prestige, the medal is often likened to a Nobel Prize of Mathematics.

The winners of the Fields medal are selected by a group of renowned specialists nominated by the Executive Committee of the International Mathematical Union (IMU), which organize the ICMs. Every four years, between two and four researchers under the age of 40 are chosen. Since 2006, a cash prize of 15 thousand Canadian dollars accompanies the medal.

Meet the winners of the Fields Medal 2018:

for the second time an Iranian won a Fields Medal!

 Fields awards ceremony 2018, showing medal winners Peter Scholze, Alessio Figalli, Caucher Birkar and Akshay Venkatesh. Photograph: Fabio Motta/Courtesy IMC 2018

Akshay Venkatesh

Conquering the greatest honor among the world’s mathematicians before the age of 40 is a notable accomplishment, although the life of Akshay Venkatesh is already marked with precocious feats. Born in New Delhi, India in 1981, and raised in Australia, at age 12 he became a medalist at the International Mathematical Olympiad. From there, he dived into world of mathematics, starting a promising career. When he began his bachelor’s degree in Mathematics and Physics at the University of Western Australia, he was a 13-year-old boy.

At 20, Venkatesh finished his PhD at Princeton University and soon became an instructor at C.L.E. Moore, at the Massachusetts Institute of Technology (MIT), a prestigious position offered to recent graduates in the area of ​​Pure Mathematics, previously occupied by prominent figures such as the American John Nash (1928-1915). Upon leaving in 2004, he became a Clay Research Fellow and was appointed associate professor at the Courant Institute of Mathematical Sciences at New York University.

He became a professor at Stanford University at the age of 27, and as of this year is a faculty member at the Institute for Advanced Study (IAS).

Venkatesh has his feet in Number Theory – an area that deals with abstract issues and had no known application until the arrival of cryptography in the late 1970s – but roves with ease through related topics, such as Theory of Representation, Ergodic Theory, and Automorphic Forms. Armed with a meticulous, investigative and creative approach to research, detecting impressive connections between diverse areas, his contributions have been fundamental to several fields of research in Mathematics. It is no wonder that his work has been recognized by several distinguished awards such as Ostrowisk (2017), Infosys (2016), SASTRA Ramanujan (2008) and Salem (2007).

Previously a guest speaker at the 2010 ICM, Venkatesh has been invited back to speak in Rio this August.

Alessio Figalli

Born in Naples, Italy on April 2, 1984, Alessio Figalli belatedly discovered an interest in science. Until high school, his only concern was playing football. The training for the International Mathematical Olympiad (IMO) awakened his interest in the subject and, upon joining the Scuola Normale Superiore di Pisa, chose Mathematics.

Figalli completed his PhD in 2007 at the École Normale Supérieure de Lyon in France, with the guidance of Fields Medal laureate Cédric Villani. He has worked at the French National Center for Scientific Research, École Polytechnique, the University of Texas in the USA and ETH Zürich in Switzerland. A specialist in calculating variations and partial differential equations, he was invited to speak at the 2014 ICM in Seoul. He has won several awards, including: Peccot-Vimont (2011), EMS (2012), Cours Peccot (2012), Stampacchia Medal (2015) and Feltrinelli (2017).

Caucher Birkar

Caucher Birkar’s dedication to the winding and multidimensional world of algebraic geometry, with its ellipses, lemniscates, Cassini ovals, among so many other forms defined by equations, granted him the Philip Leverhulme prize in 2010 for exceptional scholars whose greatest achievement is yet to come. Given the substantial contributions of Birkar to the field, that prize was a prophecy: after eight years, the Cambridge University researcher joins the select group of Fields Medal winners at the age of 40.

Birkar, who just this year received recognition for his work as one of the London Mathematical Society Prize winners, was born in 1978 in Marivan, a Kurdish province in Iran bordering Iraq with about 200,000 inhabitants. His curiosity was awakened by algebraic geometry, the same interest that, in that same region, centuries earlier, had attracted the attention of Omar Khayyam (1048-1131) and Sharaf al-Din al-Tusi (1135-1213).

After graduating in Mathematics from Tehran University, Birkar went to live in the United Kingdom, where he became a British citizen. In 2004, he completed his PhD at the University of Nottingham with the thesis “Topics in modern algebraic geometry”. Throughout his trajectory, birational geometry has stood out as his main area of interest. He has devoted himself to the fundamental aspects of key problems in modern mathematics – such as minimal models, Fano varieties, and singularities. His theories have solved long-standing conjectures.

In 2010, the year in which he was awarded by the Foundation Sciences Mathématiques de Paris, Birkar wrote, alongside Paolo Cascini (Imperial College London), Christopher Hacon (University of Utah) and James McKernan (University of California, San Diego), an article called “Existence of minimal models for varieties of general log type” that revolutionized the field. The article earned the quartet the AMS Moore Prize in 2016.

Peter Scholze

Peter Scholze was born in Dresden, Germany on December 11, 1987. Only 30 years old, he is already considered by the scientific community as one of the most influential mathematicians in the world.

In 2012, at age 24, he became a full professor at the University of Bonn, Germany. Scholze impresses his colleagues with the intellectual ability he has shown since was a teenager, when he won four medals – three gold and one silver – at the International Mathematical Olympiad (IMO).

The mathematician completed his university graduate and masters in record time – five semesters – and gained notoriety at the age of 22, when he simplified a complex mathematical proof of numbers theory from 288 to 37 pages.

A specialist in arithmetic algebraic geometry, he stands out for his ability to understand the nature of mathematical phenomena and to simplify them during presentations.

At age 16, still a student at the Heinrich-Hertz-Gymnasium – a school with a strong scientific focus – Scholze decided to study Andrew Wiles’ solution to Fermat’s Last Theorem. Faced with the complexity of the result, he realized that he was on the right track in choosing Mathematics as a profession.

He was a guest speaker at ICM 2014 in Seoul, South Korea, and will be a plenary member this year at the Rio de Janeiro Congress.

Scholze has been repeatedly recognized for his contributions to ​​arithmetic algebraic geometry. He collects major mathematics awards, such as EMS (2016), Leibniz (2016), Fermat (2015), Ostrowski (2015), Cole (2015), Clay Research 2014), SASTRA Ramanujan (2013), Prix and Cours Peccot (2012) and, finally, the Fields Medal (2018).”

Reference: IMPA

You can also find some more information from the 1st issue of the Guardian:

for the second time an Iranian won a fields medal

Fields medals 2018 winners (from L to R): Caucher Birkar, Alessio Figalli, Akshay Venkatesh, Peter Scholze. Photograph: Handout

Former refugee among winners of Fields medal – the ‘Nobel prize for maths’

An Kurdish man who came to Britain as a refugee after fleeing conflict two decades ago is one of four men who have been awarded the Fields medal, considered the equivalent of a Nobel prize for mathematics.

The winners of the prize, presented at the International Congress of the International Mathematical Union in Rio de Janeiro, have been announced as Prof Caucher Birkar, 40, from Cambridge University, Prof Akshay Venkatesh, 36, an Australian based at Princeton and Stanford in the US, Prof Alessio Figalli, 34, from ETH in Zurich and Prof Peter Scholze, 30, from Bonn University.

The Fields medal is perhaps the most famous mathematical award. It was first awarded in 1936 and since 1950 has been presented every four years to up to four mathematicians who are under 40. As well as the medal, each recipient receives prize money of 15,000 Canadian dollars (£8,750). With all the prizes this year going to men, the late Maryam Mirzakhani remains the only woman to have received the accolade.

Birkar was born in Marivan in Iran – a Kurdish city heavily affected by the Iran-Iraq war of the 1980s – and studied mathematics at the University of Tehran before coming to the UK in 2000. After a year, he was granted refugee status, became a British citizen and began a PhD.

“When I was in school it was a chaotic period, there was the war between Iran and Iraq and the economic situation was pretty bad,” said Birkar. “My parents are farmers, so I spent a huge amount of time actually doing farming. In many ways it was not the ideal place for a kid to get interested in something like mathematics.”

Birkar says it was his brother who at an early age introduced him to more advanced mathematical techniques.

Prof Ivan Fesenko of the University of Nottingham, one of Birkar’s PhD supervisors, told the Guardian how Birkar, who initially spoke very little English, came to study with him.

“The Home Office sent him to live in Nottingham while they were processing his application for asylum status,” said Fesenko. “He came to me because he was interested in research work related to my general areas.”

Birkar’s talent, says Fesenko, quickly became apparent as he began his PhD. “I thought I should give him some problem – if he solves it, then this will be his PhD. Typically a PhD lasts three or four years. I gave him a problem and he solved it in three months,” said Fesenko.

“He is very, very smart; you start to talk with him and you recognise that he can read your thoughts several steps ahead. But he never uses this to his advantage, he is very, very respectful and he gently helps people to develop further,” said Fesenko.

As with many of the winners of the Fields medal, Birkar’s research is in areas of mathematics that can seem incomprehensible to a lay audience. His citation for the award says he won the medal “for his proof of the boundedness of fano varieties and for contributions to the minimal model program.”

Prof Paolo Cascini of Imperial College London has worked with Birkar. He said that in simple terms Birkar’s work focused on classifying geometrical shapes and describing their building blocks.

Birkar said he hoped the news may “put a little smile on the lips” of the world’s 40 million Kurds.

The youngest for the four winners, Germany’s Peter Scholze, became a professor at the age of just 24, and has been described by previous award committees as “already one of the most influential mathematicians in the world.”

Among his achievements, Scholze invented the theory of perfectoid spaces – which are noted in his citation for the Fields medal, and have been described as a class of fractal structures allowing problems to be moved from one number system to another, making them easier to solve.

“Geometry is the study of space and shape,” said Kevin Buzzard of Imperial College London. “One technique that geometers have introduced is the idea of studying a complicated space by mapping a simpler space onto it. For example, a line is a simpler object than a circle. But if you imagine wrapping a line up into a spring shape and compressing the spring, you have found a way of mapping a line into a circle. Geometers might use this technique to analyse questions about circles, by turning them into perhaps more complex questions about lines.”

Perfectoid spaces, he says, turns this logic on its head. “The counterintuitive idea introduced by Scholze is that to study a geometric object, you might instead want to find a mapping from a space which is so grotesque and twisted that in some sense it cannot be twisted up any more. The result is that instead of ending up having to solve complicated questions about simple objects, you have to solve simple questions about extremely complicated objects.”

The Italian winner, Figalliworks in the field of optimal transport, which has its roots in the research of 18th-century mathematician Gaspard Monge, who studied where to send material dug from the ground for use in construction so that the transport costs are as low as possible.

Venkatesh becomes only the second Australian to win the prestigious medal, after Terence Tao in 2006.Venkatesh was recognised for his use of dynamics theory, which studies the equations of moving objects to solve problems in number theory, which is the study of whole numbers, integers and prime numbers.

Venkatesh grew up in Perth and at age 13 became the youngest person to study at the University of Western Australia. He earned first class honours in pure mathematics aged 16 before studying at Princeton.

At UWA, he went straight into second-year maths courses after he proved he could write the exam papers for all the first year subjects he had never taken.

His work also uses representation theory, which represents abstract algebra in terms of more easily-understood linear algebra, and topology theory, which studies the properties of structures that are deformed through stretching or twisting, like a Mobius strip.

Receiving his award on Wednesday, he said: “A lot of the time when you do math, you’re stuck, but at the same time there are all these moments where you feel privileged that you get to work with it.

“You have this sensation of transcendence, you feel like you’ve been part of something really meaningful.”

One of his early mentors, Prof Cheryl Praeger, who has known Venkatesh since he was 12, and supervised his honours thesis when he was 15, said he was always “extraordinary”.

“At our first meeting, I was speaking with Akshay’s mother Svetha, while Akshay was sitting at a table in my office reading my blackboard which contained fragments from a supervision of one of my PhD students.

“At Akshay’s request I explained what the problem was. He coped with quite a lot of detail and I found that he could easily grasp the essence of the research.”

Reference: The Guardian


The Fields Medal should return to its roots

Like Olympic medals and World Cup trophies, the best-known prizes in mathematics come around only every four years. Already, maths departments around the world are buzzing with speculation: 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-overlooked archives, I’ve found details of turning points in the medal’s past that, in my view, hold lessons for those deliberating whom to recognize in August at the 2018 International 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 procedures, criteria, remuneration and much else. Notably, the Nobel is typically given to senior figures, often decades after the contribution being honoured. By contrast, Fields medallists are at an age at which, in most sciences, a promising career would just be taking off.

When it began in the 1930s, the Fields Medal had very different goals. It was rooted more in smoothing over international conflict than in celebrating outstanding scholars. In fact, early committees deliberately avoided trying to identify the best young mathematicians and sought to promote relatively unrecognized individuals. As I demonstrate here, they used the medal to shape their discipline’s future, not just to judge its past and present.

As the mathematics profession grew and spread, the number of mathematicians and the variety of their settings made it harder to agree on who met the vague standard of being promising, but not a star. In 1966, the Fields Medal committee opted for the current compromise of considering all mathematicians under the age of 40. Instead of celebrity being a disqualification, it became almost a prerequisite.

I think that the Fields Medal should return to its roots. Advanced mathematics shapes our world in more ways than ever, the discipline is larger and more diverse, and its demographic issues and institutional challenges are more urgent. The Fields Medal plays a big part in defining what and who matters in mathematics.

The committee should leverage this role by awarding medals on the basis of what mathematics can and should be, not just what happens to rise fastest and shine brightest under entrenched norms and structures. By challenging themselves to ask every four years which unrecognized mathematics and mathematicians deserve a spotlight, the prizegivers could assume a more active responsibility for their discipline’s future.

Born of conflict

The Fields Medal emerged from a time of deep conflict in international mathematics that shaped the conceptions of its purpose. Its chief proponent was John Charles Fields, a Canadian mathematician who spent his early career in a fin de siècle European mathematical community that was just beginning to conceive of the field as an international endeavour5.

The first International Congress of Mathematicians (ICM) took place in 1897 in Zurich, Switzerland, followed by ICMs in Paris in 1900, Heidelberg in Germany in 1904, Rome in 1908 and Cambridge, UK, in 1912. The First World War derailed plans for a 1916 ICM in Stockholm, and threw mathematicians into turmoil.

When the dust settled, aggrieved researchers from France and Belgium took the reins and insisted that Germans and their wartime allies had no part in new international endeavours, congresses or otherwise. They planned the first postwar meeting for 1920 in Strasbourg, a city just repatriated to France after half a century of German rule.

In Strasbourg, the US delegation won the right to host the next ICM, but when its members returned home to start fundraising, they found that the rule of German exclusion dissuaded many potential supporters. Fields took the chance to bring the ICM to Canada instead. In terms of international participation, the 1924 Toronto congress was disastrous, but it finished with a modest financial surplus. The idea for an international medal emerged in the organizers’ discussions, years later, over what to do with these leftover funds.

Fields forced the issue from his deathbed in 1932, endowing two medals to be awarded at each ICM. The 1932 ICM in Zurich appointed a committee to select the 1936 medallists, but left no instructions as to how the group should proceed. Instead, early committees were guided by a memorandum that Fields wrote shortly before his death, titled ‘International Medals for Outstanding Discoveries in Mathematics’.

Most of the memorandum is procedural: how to handle the funds, appoint a committee, communicate its decision, design the medal and so on. In fact, Fields wrote, the committee “should be left as free as possible” to decide winners. To minimize national rivalry, Fields stipulated that the medal should not be named after any person or place, and never intended for it to be named after himself. His most famous instruction, later used to justify an age limit, was that the awards should be both “in recognition of work already done” and “an encouragement for further achievement”. But in context, this instruction had a different purpose: “to avoid invidious comparisons” among factious national groups over who deserved to win.

The first medals were awarded in 1936, to mathematicians Lars Ahlfors from Finland and Jesse Douglas from the United States. The Second World War delayed the next medals until 1950. They have been given every four years since.

Blood and tears

The Fields Medal selection process is supposed to be secret, but mathematicians are human. They gossip and, luckily for historians, occasionally neglect to guard confidential documents. Especially for the early years of the Fields Medal, before the International Mathematical Union became more formally involved in the process, such ephemera may well be the only extant records.

One of the 1936 medallists, Ahlfors, served on the committee to select the 1950 winners. His copy of the committee’s correspondence made its way into a mass of documents connected with the 1950 ICM, largely hosted by Ahlfors’s department at Harvard University in Cambridge, Massachusetts; these are now in the university’s archives.

The 1950 Fields Medal committee had broad international membership. Its chair, Harald Bohr (younger brother of the physicist Niels), was based in Denmark. Other members hailed from Cambridge, UK, Princeton in New Jersey, Paris, Warsaw and Bombay. They communicated mostly through letters sent to Bohr, who summarized the key points in letters he sent back. The committee conducted most of these exchanges in the second half of 1949, agreeing on the two winners that December.

The letters suggest that Bohr entered the process with a strong opinion about who should win one of the medals: the French mathematician Laurent Schwartz, who had blown Bohr away with an exciting new theory at a 1947 conference6. The Second World War meant that Schwartz’s career had got off to an especially rocky start: he was Jewish and a Trotskyist, and spent part of the French Vichy regime in hiding using a false name. His long-awaited textbook had still not appeared by the end of 1949, and there were few major new results to show.

Bohr saw in Schwartz a charismatic leader of mathematics who could offer new connections between pure and applied fields. Schwartz’s theory did not have quite the revolutionary effects Bohr predicted, but, by promoting it with a Fields Medal, Bohr made a decisive intervention oriented towards his discipline’s future.

The best way to ensure that Schwartz won, Bohr determined, was to ally with Marston Morse of the Institute for Advanced Study in Princeton, who in turn was promoting his Norwegian colleague, Atle Selberg. The path to convincing the rest of the committee was not straightforward, and their debates reveal a great deal about how the members thought about the Fields Medal.

Committee members started talking about criteria such as age and fields of study, even before suggesting nominees. Most thought that focusing on specific branches of mathematics was inadvisable. They entertained a range of potential age considerations, from an upper limit of 30 to a general principle that nominees should have made their mark in mathematics some time since the previous ICM in 1936. Bohr cryptically suggested that a cut-off of 42 “would be a rather natural limit of age”.

André Weil

The nomination of French mathematician André Weil (left) divided the 1950 Fields Medal committee.Credit: MFO/Oberwolfach Photo Collection

By the time the first set of nominees was in, Bohr’s cut-off seemed a lot less arbitrary. It became clear that the leading threat to Bohr’s designs for Schwartz was another French mathematician, André Weil, who turned 43 in May 1949. Everyone, Bohr and Morse included, agreed that Weil was the more accomplished mathematician. But Bohr used the question of age to try to ensure that he didn’t win.

As chair, Bohr had some control over the narrative, frequently alluding to members’ views that “young” mathematicians should be favoured while framing Schwartz as the prime example of youth. He asserted that Weil was already “too generally recognized” and drew attention to Ahlfors’s contention that to give a medal to Weil would be “maybe even disastrous” because “it would make the impression that the Committee has tried to designate the greatest mathematical genius.”

Their primary objective was to avoid international conflict and invidious comparisons. If they could deny having tried to select the best, they couldn’t be accused of having snubbed someone better.

But Weil wouldn’t go away. Committee member Damodar Kosambi thought it would be “ridiculous” to deny him a medal — a comment Bohr gossiped about to a Danish colleague but did not share with the committee. Member William Hodge worried “whether we might be shirking our duty” if Weil did not win. Even Ahlfors argued that they should expand the award to four recipients so that they could include Weil. Bohr wrote again to his Danish confidant that “it will require blood and tears” to seal the deal for Schwartz and Selberg.

Bohr prevailed by cutting the debate short. He argued that Weil would open a floodgate to considering prominent older mathematicians, and asked for an up or down vote on the pair of Schwartz and Selberg. Finally, at the awards ceremony at the 1950 ICM, Bohr praised Schwartz for being recognized and eagerly followed by a younger generation of mathematicians — the very attributes he had used to exclude Weil.

Further encouragement

Another file from the Harvard archives shows that the 1950 deliberations reflected broader attitudes towards the medal, not just one zealous chair’s tactics. Harvard mathematician Oscar Zariski kept a selection of letters from his service on the 1958 committee in his private collection.

Zariski’s committee was chaired by mathematician Heinz Hopf of the Swiss Federal Institute of Technology in Zurich. Its first round of nominations produced 38 names. Friedrich Hirzebruch was the clear favourite, proposed by five of the committee members.

Hopf began by crossing off the list the two oldest nominees, Lars Gårding and Lipman Bers. His next move proved that it was not age per se that was the real disqualifying factor, but prior recognition: he ruled out Hirzebruch and one other who, having recently taken up professorships at prestigious institutions, “did not need further encouragement”. Nobody on the committee seems to have batted an eyelid.

A sweeping expedient

By 1966, the adjudication of which young mathematicians were good but not too good had become testing. That year, committee chair Georges de Rham adopted a firm age limit of 40, the smallest round number that covered the ages of all the previous Fields recipients.

Suddenly, mathematicians who would previously have been considered too accomplished were eligible. Grothendieck, presumably ruled out as too well-known in 1962, was offered the medal in 1966, but boycotted its presentation for political reasons.

The 1966 cohort contained another politically active mathematician, Stephen Smale. He went to accept his medal in Moscow rather than testify before the US House Un-American Activities Committee about his activism against the Vietnam War. Colleagues’ efforts to defend the move were repeated across major media outlets, and the ‘Nobel prize of mathematics’ moniker was born.

This coincidence — comparing the Fields Medal to a higher-profile prize at the same time that a rule change allowed the medallists to be much more advanced — had a lasting impact in mathematics and on the award’s public image. It radically rewrote the medal’s purpose, divorcing it from the original goal of international reconciliation and embracing precisely the kinds of judgement Fields thought would only reinforce rivalry.

Any method of singling out a handful of honorees from a vast discipline will have shortcomings and controversies. Social and structural circumstances affect who has the opportunity to advance in the discipline at all stages, from primary school to the professoriate. Selection committees themselves need to be diverse and attuned to the complex values and roles of mathematics in society.

But, however flawed the processes were before 1966, they forced a committee of elite mathematicians to think hard about their discipline’s future. The committees used the medal as a redistributive tool, to give a boost to those who they felt did not already have every advantage but were doing important work nonetheless.

Our current understanding of the social impact of mathematics and of barriers to diversity within it is decidedly different to that of mathematicians in the mid-twentieth century. If committees today were given the same licence to define the award that early committees enjoyed, they could focus on mathematicians who have backgrounds and identities that are under-represented in the discipline’s elite. They could promote areas of study on the basis of the good they do in the world, beyond just the difficult theorems they produce.

In my view, the medal’s history is an invitation for mathematicians today to think creatively about the future, and about what they could say collectively with their most famous award.

Reference: Nature.com

Mathématiques, l'explosion continue

La brochure « Mathématiques, l’explosion continue », conçue par la Fondation Sciences Mathématiques de Paris (FSMP), la Société Française de Statistiques(SFdS), la Société de Mathématiques Appliquées et Industrielles (SMAI) et la Société Mathématique de France (SMF), a été réalisée grâce au soutien financier de Cap’Maths.
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