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MathGroup Archive 2010

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Vladmir Arnold

  • 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.




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