- To: mathgroup at smc.vnet.net
- Subject: [mg110162] Vladmir Arnold
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Sat, 5 Jun 2010 07:31:19 -0400 (EDT)
I just heard sad news. It is not directly related to Mathematica but it will be probably of interest to at leas some users of this forum. Vladmir Igorevich Arnold, one of the greatest mathematicians of the modern era died on Thursday in France. I have always regarded him as a kind of personal hero and not just for his mathematical work so I felt compelled to write this brief note just for the MathGroup. Arnold, contributions to mathematics are too numerous to list here (even if I were competent to do so) but probably most famous one is the so called Kolmogorov=96Arnold=96Moser theorem (KAM) , which Arnold also used to extend Poincare's work on the stability of elliptical orbit in the three body problem. Arnold's start of his mathematical career was spectacular: before his 20th birthday he was already famous after solving Hilbert's Thirteenth problem. Arnold was the recipient of numerous international prizes but also among the greatest mathematicians never to have been awarded the Field's Medal. In fact such an award was proposed in 1974 but the proposal was met with strong opposition from the Soviet mathematical establishment and was dropped - soon after than Arnold passed the age of 40 making him ineligible for the prize. In addition to being a mathematical genius, Arnold possessed numerous other talents and wide interests. He was a marvellously entertaining writer with highly idiosyncratic views on numerous subjects, including history (and not just of mathematics). His book "Hyugens and Barrow, Newton and Hooke" is a gem: as far as I know there is nothing else quite like it. But what is perhaps most relevant to this forum are Arnold's outspoken views on the nature and philosophy of mathematics (which I have already quoted here in the past). Arnold was a passionate opponent of the highly abstract approach to mathematics characteristic of the French Buorbaki school, which emphasised rigour at the expense of intuition. Arnold's view was exactly the opposite and he was fond of repeating his famous definition of mathematics: mathematics is a part of physics and like physics it is an experimental science, the main difference being that in physics experiments usually cost millions of dollars while in mathematics units of roubles. While one might quibble with the last part of this statement (for most of us here the cost of mathematical experiments is roughly equal to the cost of Mathematica) I think the sentiment behind it would find a lot of support here.