Thursday, November 20, 2008

Geometry of numbers

Georgy Feodosevich Voronoy (or Voronoi), a Russian mathemetician of Ukrainian descent, died 100 years ago today, aged only 40. To celebrate his centenary, Ukraine has issued a special coin. However, there isn’t much information about him on the internet in English, but what there is, is partly derived from a diary he kept.

Voronoy studied at St Petersburg University, where he was a student of Andrey Markov, another celebrated mathemetician. In 1894, he became professor at the University of Warsaw, and in 1897 put forward a doctoral thesis on continuous fractions. He is best known for developing theories on the so-called Voronoi tessellation.

Only a small amount of information about Voronoy is available on the internet in English, and it seems to come mostly from The St. Petersburg School of Number Theory by Boris Nikolaevich Delone and Robert G. Burns, first published in Russian in 1947 (the English translation is viewable on Googlebooks). And the authors’ brief biography of him partly relies on a diary he kept.

While still at St Petersburg, he studied a particularly hard maths problem, and wrote in his diary: ‘I myself have lost hope of ever solving this problem’. And in equally self-doubting mode, he wrote: ‘The pure mathematics lectures captivate me more and more. I prefer Professor Sokhotsky’s lectures in the special course on higher algebra to all the others. . . The main thing that concerns me is whether I have enough talent.’

There is one more Voronoy diary entry quoted in The St Petersburg School of Number Theory; it’s from 1904, when he was already suffering severely from gallstones:

‘I am making great progress with the question under study [indefinite quadratic forms]; however, at the same time my health is becoming worse and worse. Yesterday I had for the first time a clear idea of the algorithm in the theory of forms I am investigating, but also suffered a strong attack of bilious colic which prevented me from working in the evening and from sleeping the whole night. I am so afraid that the results of my enduring efforts, obtained with such difficulty, will perish along with me.’

He died a few years later on 20 November 1908, but, the book’s authors say, ‘the depth and importance of [his] spacious works is such that they have had a profound influence on modern number theory. Voronoi was in fact the cofounder, along with Minkowski, of the geometry of numbers’.

This year, Wikipedia’s short article on Voronoy notes, Ukraine has released a special coin to commemorate his centenary.

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