Tuesday, November 20, 2018

Refuge in numbers

‘As for me the mind comes ahead always and everywhere. And the worldly wisdom, known from books, is saying that mind and love can scarcely be reconciled. That is what makes me fear sometimes that Olia probably will not be happy with me. As for me, I shall probably always take refuge in Mathematics.’ This is taken from the diaries of Georgy Feodosevich Voronoy (or Voronoi), a Russian mathematician of Ukrainian descent born 150 years ago today.

Voronoy studied at St Petersburg University, where he was a student of Andrey Markov, another celebrated mathemetician. In 1891, he married Olia, and they would have six children (although one died in childbirth). 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. He died in November 1908, and in 1918 the Ukraine government
 released special coins to commemorate the centenary.

Wikipedia has a small amount of information about Voronoy; a little more is available, partly thanks to diaries, in published books freely available online.

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) contains a brief biography of Voronoy. The 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’. 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 further Voronoy diary entry, from 1904, quoted in The St Petersburg School of Number Theory: ‘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.’

There are more substantial extracts from 
Voronoy’s diaries to be found in Life and Times of Georgy Voronoi by Halyna Syta and Rien van de Weygaert, a 30-page monograph free to download from ResearchGate. The authors explain that Voronoy’s children saved their father’s manuscripts - including mathematical notebooks and diaries - and that they are now held by the National Library of Ukraine’s institute of manuscripts. Here are a couple of extracts from the monograph that refer to and quote from Voronoy’s diaries, as well as one dated diary extract.

‘It says something about the personality of Georgy Voronoi that in these student years he confided his doubts to his diary. Fortunately, this diary has been partially preserved. Along with his descriptions of everyday experiences and events, it is a sincere self-confession of a young man. It discloses his character, his inner world, the process of his creative growth and self-consciousness. The author is active and sensitive and cannot remain indifferent to the events around him. He also tries to help when necessary. At times he is hot-tempered, for which he later expresses regret. He states “I am merrily gazing at God’s world and to everything I touch I submit myself with rapture”. Georgy aims “to reach everything by heart, and not just by intellect” and tries to look at himself from the outside. In this, he displays a rather low self-esteem, while also trying to grasp his own feelings and inclinations: “What am I after all? I am fond of playing cards. I do not have any noble pride. That is, if I am mocked I do not get angry and do not quarrel with the offender. I feel my weakness in front of the powerful of this world”.’

‘Recollections about his acquaintance and the development of his relations with Olia Krytska occupy a particular place in the diary. Georgy writes so sincerely about his feelings, with such virtue and temperament - (events are almost ignored, only his feelings are recorded) - that these pages read like a real novel. He determined once and forever for himself that his destiny was in Bohdany, but he concealed his feelings for the time being because he had no financial basis for his own family. His father insisted on this decision. Such a vagueness in relations brought him many sufferings, but he patiently waited for his hour and did not permit any other passion to find the way to his heart. In 1889, on the eve of his departure, Georgy wrote about his last visit to Bohdany:

”Once more I am writing down my last visit to Krytskis... I am mounting the horse, once more saying goodbye to everybody, that is the end to everything which filled my life during the four months and which will cause me to behave stern and cool during the whole stretch of the Petersburg year. Only mathematics as a bright star is shining afore me, in it I trust all my hopes... The experience of the last year has strengthened my endurance, and my creative eagerness, suppressed before, is bursting into action, and I am certain that Petersburg will bring me much that is new in this respect. So goodbye, Olia, goodbye, Zhuravka! Till the new spring I shall cover myself with my armour. And, as if dreaming I shall see this summer, which gave me so much strength and health and those grains of happiness, which I know I shall so often experience when reading my diary in Petersburg, picking them from those talks with Olia, which I wrote down, along with everything which so often made my heart beat.”

31 December 1890
‘True to the old custom, today, on the eve of New Year, I cast a glance at how I have lived through and deeply felt the Old Year. The first thing which I gladly note and which has become a harbinger of my future happiness is: Olia loves me. I know it now for certain! How happy I am! So long I had been silently suffering from doubts, and at last it has been clarified, and I have already become Olia’s fiancĂ©! ...

Yes, now I know well that Olia loves me, but nevertheless lasting doubts and expectations have brought some bitterness. I seem to have become hardened in my permanent solitude. Ever growing passion for Mathematics has developed in me an egotism of no small degree. I am afraid I cannot feel strongly and surrender fully to my feelings.

As for me the mind comes ahead always and everywhere. And the worldly wisdom, known from books, is saying that mind and love can scarcely be reconciled. That is what makes me fear sometimes that Olia probably will not be happy with me. As for me, I shall probably always take refuge in Mathematics.’

This article is a substantially revised version of one first published 10 years ago on 20 November 2008.

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