Tag: Alan Turing

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?

Two of Alan Turing’s WW-II papers are now in the public domain

The Wire
May 21, 2015

A scientific paper written by Alan Turing, the brilliant computer scientist who cracked the Enigma code during the Second World War and bolstered Britain’s war efforts, was recently declassified by the British government and uploaded to the arXiv pre-print server. The paper’s entitled ‘The Applications of Probability to Cryptography’. It has Turing bringing to bear a style of reasoning that is absent in today’s statistics-heavy technical literature. It is both didactic and meticulous, and provides great insight into how Turing explored the cryptographic problems he was confronted with.

Consider:

When the whole evidence about some event is taken into account it may be extremely difficult to estimate the probability of the event, even very approximately, and it may be better to form an estimate based on a part of the evidence, so that the probability may be more easily calculated. This happens in cryptography in a very obvious way. The whole evidence when we are trying to solve a cipher is the complete traffic, and the events in question are the different possible keys, and functions of the keys. Unless the traffic is very small indeed the theoretical answer to the problem “What are the probabilities of the various keys? ” will be of the form “ The key . . . has a probability differing almost imperceptibly from 1 (certainty) and the other keys are virtually impossible”. But a direct attempt to determine these probabilities would obviously not be a practical method.

Here and there, he also admits he’s making guesses – some quite in the air and others not so much – of the sort that are inadmissible in the modern era of scientific publishing, where demands on researchers to be exact have driven many to fabricate results and fake conclusions. At one point, Turing writes, “This judgement is not entirely a guess; some rather insecure mathematical reasoning has gone into it”, prompting the popular statistician Andrew Gelman to quip on his blog: “He’s so goddamn reasonable. He’s everything I aspire to.”

The paper was uploaded to arXiv on May 18 together with another called ‘The Statistics of Repetitions’, both accompanied by editor’s notes that focused on what it was like to prepare manuscripts “at a time when typographical errors were corrected by hand, and mathematical expression handwritten into spaces left in the text”. The papers can be found hereand here.

Alan Turing’s claims to fame are many, ranging from deciphering the Enigma code used by the Nazis for encrypted communication, to defining the hypothetical Turing machine that’s influential in studies of computing, to predicting oscillating chemical reactions that were observed about a decade later. He was also gay at a time when homosexuality was a crime in the UK, and was chemically castrated when he refused to be sent to prison for fear he’d have to discontinue his work. He died of cyanide poisoning in 1954, barely 42 years old. In 2009, then British Prime Minister Gordon Brown issued an apology for the way Turing had been treated in his lifetime. Queen Elizabeth II pardoned him posthumously in 2013.

Most recently, he was brought to life in the blockbuster movie ‘The Imitation Game’ (2014), where he was played by Benedict Cumberbatch.