Tag: John Nash

Ramanujan, Nash, Turing, Mirzakhani

From a short review of a new documentary about the life and work of the Iranian mathematician Maryam Mirzakhani, September 9, 2022:

While there are other movies about real-life mathematicians such as Nash, Ramanujan and Turing, the special abilities of these individuals are often depicted as making them eccentric in their private lives. In contrast, Mirzakhani lived a “normal” life, was married with a child and simply loved math. I want people to know that mathematicians like her also exist.

…

The documentary powerfully conveys the attitude that there’s nothing women can’t do simply because they’re women, which makes it well worth watching from the perspective of diversity and gender.

This is well and good. I haven’t yet watched the documentary but will at the first opportunity. This said, the review raises a curious point about the impression that films, documentaries, etc. have created about John Nash, Srinivasa Ramanujan and Alan Turing. The reviewer, Prof. Yukari Ito of the Kavli Institute in Japan, has written that they have given us the impression that being a great mathematician requires one to be eccentric, or that contributing to mathematics at the highest level demands the sort of transcendental brilliance that a human mind may never fully comprehend. Ramanujan exemplified this sort of work by setting forth a very large number of axioms in number theory without specifying the steps in between the first principles and the final thing. When he asked, he said a goddess was working through him. It may well be that Ramanujan’s biggest contribution to the idea of mathematics was his incomprehensible mind. However, the stories of Nash and Turing are significantly different. Unlike Ramanujan, they both had formal training in mathematics that allowed them to think more clearly about their respective domains, and neither man attributed their work to any sort of divine intervention. They were eccentric men, sure, but unlike Prof. Ito, I prefer to think that they were distinguished by an exceptionalism that also attends to Maryam Mirzaklhani.

Specifically, Turing and Nash led normal lives too, in that they had families, they had homes and they had to work with the same quotidian constraints as many others of their generation (presumably minus misogyny, racism, etc. because they were white men). Sure, they were oddities in their respective social milieus, but I don’t believe that lends itself to the impression that mathematics and eccentricism are linked, at least in the cases of Nash and Turing. Nash was ill (he later developed schizophrenia) and Turing was gay well before the UK accepted homosexuality. It applies perfectly in Ramanujan’s case, of course. But by lumping the three men together, I fear that Prof. Ito’s review misidentifies the real nature of Mirzakhani’s achievement: not that she leads a ‘normal’ life but that she is a woman, and a woman from Iran. This is also what I meant by the exceptionalism that attends to Mirzakhani. Consider who the subjects of our films and documentaries are. Ramanujan, Nash and Turing had films made about them because they were eccentric – and Mirzakhani doesn’t escape this sampling bias as much as confirms it. There is a documentary about her because she hails from a country where women don’t have many of the rights that their counterparts in most other parts of the world enjoy, and because she was the first woman to be awarded the Fields Medal. There are several male and female mathematicians, and in fact mathematicians of other genders, who are perfectly brilliant as well as lead perfectly normal lives (in Prof. Ito’s definition). It’s just that their experiences may not make for a good movie. In fact, it may well be that what most people consider ‘normal’ hasn’t ever been the subject of a movie about a good mathematician.

The structural issues that Prof. Ito overlooks also include a significant part of what allowed the men she mentioned to be successful – the division of labour in society, within their homes, where as men they were free to focus on their work without contributing to helping their partners run the house or attending to any kind of tedious administrative work at their places of employment. This is as much an indictment of patriarchy as that attitude among prestigious institutes that continues to this day – that brilliant men’s ‘eccentricities’ should be excused so that they can keep bringing in the grants, the citations and the awards. Mirzakhani was not normal. I’m not familiar with her story (I really need to watch the documentary) but I’m certain that she had more barriers in her way to achieve the level of success that she did. That in turn elevates her achievements in a sad way, and might also inspire others to think that mathematics stands to benefit through more than just mathematical contributions. After all, aren’t we paying attention to Mirzakhani herself because of the Fields Medal committee’s disgraceful dismissal of women’s contributions for eight decades?

Remembering John Nash, mathematician who unlocked game theory for economics

The Wire
May 25, 2015

The economist and Nobel Laureate Robert Solow once said, “It wasn’t until Nash that game theory came alive for economists.” He was speaking of the work of John Forbes Nash, Jr., a mathematician whose 27-page PhD thesis from 1949 transformed a chapter in mathematics from a novel idea to a powerful tool in economics, business and political science.

At the time, Nash was only 21, his age a telltale mark of genius that had accompanied and would accompany him for the rest of his life.

That life was brought to a tragic close on May 23 when his wife Alicia Nash and he were killed in a car-accident at the New Jersey Turnpike. He was 86 and she was 82; they are survived by two children.

Alicia (née Larde) met Nash when she took an advanced calculus class from him at the Massachusetts Institute of Technology in the mid-1950s. He had received his PhD in 1950 from Princeton University, spent some time as an instructor there and as a consultant at the Rand Corporation, and had moved to MIT in 1951 determined to take on the biggest problems in mathematics.

Between then and 1959, Nash made a name for himself as possibly one of the greatest mathematicians since Carl Friedrich Gauss. He solved what was until then believed to be an unsolvable problem in geometry dating from the 19th century. He worked on a cryptography machine he’d invented while at Rand and tried to get the NSA to use it. He worked with the Canadian-American mathematician Louis Nirenberg to develop non-linear partial differential equations (in recognition, the duo was awarded the coveted Abel Prize in 2015).

He made significant advances in the field of number theory and analysis that – in the eyes of other mathematicians – easily overshadowed his work from the previous decade. After Nash was awarded the Nobel Prize for economics in 1994 for transforming the field of game theory, the joke was that he’d won the prize for his most trivial work.

In 1957, Nash took a break from the Institute for Advanced Studies in Princeton, during which he married Alicia. In 1958, she became pregnant with John Charles Martin Nash. Then, in 1959, misfortune struck when Nash was diagnosed with paranoid schizophrenia. The illness would transform him, his work and the community of his peers in the next 20 years far beyond putting a dent in his professional career – even as it exposed the superhuman commitments of those who stood by him.

This group included his family, his friends at Princeton and MIT, and the Princeton community at large, even as Nash was as good as dead for the world outside.

His colleagues were no longer able to understand his work. He stopped publishing papers after 1958. He was committed to psychiatric hospitals many times but treatment didn’t help. Psychoanalysis was still in vogue in the 1950s and 1960s – while it’s been discredited now, its unsurprising inability to get through to Nash ground at people’s hopes. In these trying times, Alicia Nash became a great source of support.

Although the couple had divorced in 1963, he continued to write her strange letters – while roaming around Europe, while absconding from Princeton to Roanoke (West Virginia), while convinced that the American government was spying on him.

She later let him live in her house along with their son, paying the bills by working as a computer programmer. Many believe that his eventual remission – in the 1980s – had been the work of Alicia. She had firmly believed that he would feel better if he could live in a quiet, friendly environment, occasionally bumping into old friends, walking familiar walkways in peace. Princeton afforded him just these things.

The remission was considered miraculous because it was wholly unexpected. The intensity of Nash’s affliction was exacerbated by the genius tag, by how much of Nash’s brilliance the world was being deprived of. And the deprivation in turn served to intensify the sensation of loss, drawing out each day that he was unable to make sense when he spoke, when he worked. John Moore, a mathematician and friend of the Nashes, thought they could have been his most productive years.

After journalist Sylvia Nasar’s book A Beautiful Mind, and then an Academy-Award-winning movie based on it, his story became a part of popular culture – but the man himself withdrew from society. Ron Howard, who directed the movie, mentions in a 2002 interview that Nash couldn’t remember large chunks of his life from the 1970s.

While mood disorders like depression strike far more people – and are these days almost commonplace – schizophrenia is more ruthless and debilitating. Even as scientists think it has a firm neurological basis, a perfect cure is yet to be invented because schizophrenia damages a victim’s mind as much as her/his ability to process social stimuli.

In Nash’s case, his family and friends among the professors of Princeton and MIT protected him from succumbing to his own demons – the voices in his head, the ebb of reason, the tendency to isolate himself, that are altogether often the first step toward suicide in people less cared for. Moreover, Nash’s own work played a role in his illness. He was convinced for a time that a new global government was on the horizon, a probable outcome in game theory that his work had made possible, and tried to give up his American citizenship. As a result, his re-emergence from the two decades of mental torture were as much about escaping the vile grip of irrationality and paranoia as much as regaining a sense of certainty in the face of his mathematics’ enchanting possibilities.

A Beautiful Mind closes with Nash’s peers at Princeton learning of his being awarded the Nobel in 1994, and walking up to his table to congratulate him. On screen, Russell Crowe smiles the smile of a simple man, a certain man, revealing nothing of the once-brazen virtuosity that had him dashing into classrooms at Princeton just to scribble equations on the boards, dismissing his colleagues’ work, rearing to have a go at the next big thing in science. By then, that brilliance lay firmly trapped within John Nash’s beautiful but unsettled mind. With his death, and that of Alicia, that mind will now always be known and remembered by the brilliant body of work it produced.