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Akshay Venkatesh: Australian wins Fields Medal


Akshay Venkatesh: Australian wins Fields Medal

I am delighted to see that an Australian, Akshay Venkatesh, is one of the four winners of this year’s Fields Medal. It is hard to underestimate the significance of this award to an Australian and the way in which one hopes it will reflect on Australian mathematics. The Fields Medal is the Nobel Prize of mathematics. I do not know why a discipline as fundamental to the good of humanity as mathematics does not have a Nobel Prize. The Fields Medal is awarded to up to four mathematicians every four years and only to mathematicians under the age of 40. Last year I set myself the sad task of writing in these columns an obituary for Maryam Mirzakhani who was one of the 2014 winners. Several of my mathematical heroes have been awarded the Fields Medal over the years. You have probably heard of none of them, but they include René Them (who worked on Catastrophe Theory and informed my post-graduate work), Paul Cohen (whose work, like Venkatesh’s, was related to the foundations of mathematics) and Grigori Perelman (who proved something called the Poincaré conjecture and who declined the Fields Medal).


Above: Akshay Venkatesh (source)

Akshay Venkatesh is 36, was born in New Delhi and is currently teaching at Stanford University. He graduated from the University of Western Australia when he was but 16. I found his home page which was brief and to the point, as well as being out of date, as you would expect from a mathematician whose capabilities are immense. Like Albert Einstein and Kurt Gödel, he may not have time for the mundanity of the world. I reproduce the page below. I am sure you will be interested in the number theory seminar; the last one was on 21 May 2018 and was about “Producing Surjective Arboreal Galois Representations”. I expect you wish you hadn’t asked. There are many, and I cannot say I am one of them, who are waiting for his forthcoming paper “Derived Galois Deformation Rings”. I mention this because the title refers to Galois whose story is one of the strangest and saddest stories in the history of mathematics. But I will write of Galois another day.


Venkatesh is the second Australian to be honoured with a Fields Medal. The first was Terence Tao who won the medal in 2006 and whose work is not unrelated to Grigori Perelman. To those of us who inhabit (in my case but peripherally), the mathematical world. Tao has an Erdös number of 2. Paul Erdös (1913 – 1996) was a very influential Hungarian mathematician who had no fixed abode but travelled the world collaborating with others while sleeping on their sofas. The Erdös number describes the ‘collaborative distance’ between Erdös and another person, as measured by authorship of mathematical papers. For example, If Alice collaborates with Paul Erdös on one paper, and with Bob on another, but Bob never collaborates with Erdös himself, then Alice is given an Erdös number of 1 and Bob is given an Erdös number of 2, as he is two steps from Erdös. Mathematicians are strange people.

Given Erdös has been dead these twenty years the average Erdös number across all mathematicians and over time is, as we mathematicians would say, monotonically increasing (that means that it’s always going up, it never stays constant or decreases). You can read Paul Hoffman’s “The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth” which is a biography of Erdös. If you are even remotely interested in mathematics, then this read would be worth the effort. You don’t need any (or much) mathematical capability to read it. Venkatesh met Erdös when he was 10 and in 2009 read a paper on the “Geometry of Numbers” at the 11th Erdös Symposium at the University of Florida. I cannot discover Venkatesh’s but I have no doubt that he knows what it is.

I know that you are wondering why you should be in the least bit interested in Akshay Venkatesh’s brilliant achievement. The citation for his award tells us that he has been awarded the Fields “for his synthesis of analytic number theory, homogeneous dynamics, topology, and representation theory, which has resolved long-standing problems in areas such as the equidistribution of arithmetic objects.” Now you do not need to worry if you do not understand any of this. Few mathematicians would claim that they do; certainly, I do not know anything about representation theory. It may not have been invented when I was studying Pure Mathematics. His research relates to something called number theory. Number theory is concerned with the study of the integers (whole numbers) and is frequently called the “queen of mathematics.” Of course, one of the most important topics within number theory has to do with the prime numbers (those numbers that are divisible only by themselves and 1 like 3, 17 and 31,957). Prime numbers are important because the security of your data on the internet depends upon very large prime numbers.

There is a short write-up, by Allyn Jackson of the American Mathematical Society, of the reasons why Venkatesh won this year’s medal. Jackson says, “Even in a subject requiring such breadth, Akshay Venkatesh stands out for the startlingly original way he has connected number theory problems to deep results in other areas. Far from using them as ‘black boxes’ to crank out solutions, Venkatesh brings fresh insights to the results and highlights their unexpected connections to number theory. In this way he has made striking advances in number theory while also greatly enriching other branches of mathematics.”

There is, of course, an Australian Mathematical Society. This august body has the most tedious and unimaginative website in the history of the Internet. Quite how it would inspire anyone to pursue a career or interest in mathematics is beyond me. Yet there is nary a mention of Venkatesh on their homepage. Shame on them. We should be proud to number Akshay Venkatesh among Australians even if the Australian Mathematical Society is not.

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