NetNews Usenet Archive 1992 #19/NN_1992_19.iso/spool/sci/math/10791

Text File | 1992-09-01 | 1.8 KB | 49 lines

Newsgroups: sci.math
Path: sparky!uunet!cis.ohio-state.edu!pacific.mps.ohio-state.edu!zaphod.mps.ohio-state.edu!menudo.uh.edu!sugar!claird
From: [e-mail] (Cameron Laird)
Subject: Re: Kolmogorov's theorem
Organization: NeoSoft Communications Services -- [phone]
Date: Tue, 01 Sep 1992 14:23:42 GMT
Message-ID: <[e-mail]>
References: <[e-mail]> <[e-mail]>
Lines: 38

In article <[e-mail]> [e-mail] writes:
            .
            .
            .
>Every continuous multivariate real function can be represented as a depth-4
>composition of continuous one-variate functions and sum. This result of
>Kolmogorov and his student Arnold solves the 13-th Hilbert problem.
>
> A.N.Kolmogorov. Soviet Math. Doklady (DAN SSSR) 108(2), 1956.
> V.I.Arnold. Same 114(4), 1957.
> A.N.Kolmogorov. Same 114(5), 1957.

Can someone "explain" Kolmogorov, in a few
words, or perhaps point me to a biography
(I'd be happy to read a Russian one, if I
can get my hands on it)?  He was, of course,
one of the big, big thinkers of our century,
but I haven't yet succeeded in getting a
handle on his work.  I run into him in so
many areas ...  Hilbert, for example, was
at least as universal in his work, but I can
at least begin to summarize his work by
noting that he posed and solved problems,
often those which arise in calculating
solutions to integral equations.  What were
Kolmogorov's themes?

This is perhaps a good place to point out
that, along with everything else he wrote,
Kolmogorov was also a success popularizer.
It's been some time since I read anything
of his in this category, but I remember them
as charming.
--

Cameron Laird
[e-mail] ([e-mail])    [phone]
[e-mail] ([e-mail])      [phone]