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# A great russian mathematician Vladimir Arnold died on 3rd of June, 2010 in Paris

Fri, 2010-06-04 08:40 - gregk

Vladimir Arnold died on 3rd of June 2010 in Paris, just 9 days before his 73rd birthday.

I am sure many mechanicians know him by **his books**, such as

- "Catastrophe Theory",
- "Topological Methods in Hydrodynamics",
- "Mathematical Methods of Classical Mechanics" (classics)
- "Ordinary Differential Equations"(classics)
- "Arnold's Problems" (A brain-twister)
- and many others (librarything.org, amazon.com).

Arnold's web page

Arnold's **bioghraphy** at Wikipedia in

**Interviews** with Arnold in English:

Arnold's **lecture** on "Teaching mathematics".

R.I.P.

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## Comments

## An immense loss for mathematics and mechanics

In many of his books he introduces modern methods into mechanics. He is not only a great pure mathematician but cares about the application. Respect to the Moscow school.

R. I .P.

## Re. V. I. Arnold

I don't think I am qualified to comment on his work---the gap between the mathematical abilities being so huge.

But it so happens that while a student at UAB in early 1990s, I had read some of his more conceptual articles on the catastrophe theory, and as you might expect, had come out with a great impression. I can't articulate it well, but let me say that his writing was very special, very different. That's what I distinctly remember thinking.

Later on, while doing my recent PhD, when I was thinking of the diffusion equation and searching all the prior literature to see if the ideas (good/bad) that I was toying with had been mentioned in the same manner earlier, and still was not getting anywhere, I decided to end my search by looking up Arnold. It's rare for a mathematician to be so vigorously physical in his thinking, as he was. So rare, in fact, that I privately said to myself that if Arnold hasn't written on the topic, then I need no look no further---no one else could possibly have (or they will let me know once I publish).

People are happy to cite their Erdos numbers; I am happy to mention here that I could cite Arnold's "Lectures on Partial Differential Equations" [^] in my PhD thesis.

R.I.P.

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[E&OE]

## Field Medal, catastrophe theory, fracture, stability

In 1974 the Soviet Union opposed Professor Arnold's award of the Fields

Medal, the foremost recognition in work in mathematics that is often

compared to the Nobel Prize, making him one of the most prominent

mathematicians to never receive the prize.

In these respects, he reminds me of another russian mathematician. In 2006, Grigori Perelman, credited with proving the

Poincaré conjecture, refused his Fields

Medal[3]

and did not attend the congress.[12]

Regarding mechanics, he is mostly known for

catastrophe theorywhich is abranch of bifurcation theory in the study of dynamical systems; it is also a particular special case of

more general singularity theory in geometry.

Its application to stability and fracture in mechanics perhaps is best described here . It was very qualitative however, and it has remained such, so far. So there is room to improve for the followers of this great mathematician.

Michele Ciavarella, Politecnico di BARI - Italy, Rector's delegate.

http://poliba.academia.edu/micheleciavarella

Editor, Italian Science Debate, www.sciencedebate.it

Associate Editor, Ferrari Millechili Journal, http://imechanica.org/node/7878