Around Arnold's side

 

Let's us start.

Arnold  recalled : French science  has always been different from science  to other countries. Montaigne claimed that in France '' in one's work nobody should understand a word, otherwise it would be possible to say that one did not discover anything new ".In France all references in predecessors were  considered inappropriate, references to foreigners authors (since Montaigne's time) were especially blameworthy.Futhermore, Arnold added the description of French mathematics given by Abel is surprisingly exact  even now " Everyone wants to teach and nobody wants to learn anything new, each is an expert in a narrow field (it could be the theory of elasticity, celestial mrchanics; or number theory) and is not interested in anything outside of this field "

And Arnold to talk: The hospitality of French colleagues was so warm that they invited me to tale part in a Bourbaki Congress.When I said that I do not sympathize with this sect, they explained that they consider me as a " Moscou Bourbanist", which was wrong because for me exemples are much more important to general statements, and I prefer induction to deduction. We should therefore not be surprised that Arnold states the following :

The are two principal ways  to  formulate mathematical assertions ( problems, conjectures, theorems,....) Russian and French. The Russian way is  to choose the most simple and specific case ( so that nobody could  simplify the formulation preserving the main  point).The french way is to generalize the statement as far as nobody could generaize it further. 

 To illustrate how detached we were from the rest  of world at the time. I should  mention a curious incident. A remark found in the collection of translated papers "Fibre Bundles" that the idea of expressing a special sequence by rectangles consisting of groups,where the consecutive differentials act by generalized knight moves, is due to E.B.DYnkin ( so that the corresponding figures in the notes.to the translation are called Dynkin's diagramms ). When I was in France in 1965, I asked  Serre whether he knew of this improvment to the theory. Serre couldn't stop laughing. How else could one made calculations with spectral sequence ? To be fair , in French publications there were no diagramms (indispensable to the reader) - probably to make the theory incomprehensible to the uninitiated (but more likely due to typically careless French user-unfriendlliess).

 

 However, the environment did matter,and the Paris Seminar did not rise to the place its Moscow prototype occupîed in the mathematical world. The composition was different, the Parisian mathematical community did not reveal such acute interest in what was going on there, who knows what else went wrong ....Vladmir Igorvich Arnold  (V.I.A) having a very dominant and assertive personnality, felt the difference in the atmosphere and understandably grew more and more bitter about " the Western style" of doing mathematics. His criticism ( very often more than well deserved) took forms which, apparently, many of his French colleagues had deemeed offensve: for instance, he would never miss opportunity to stress the fact that a certain problem, on which a respectable (and strong) French professor worked with only partial success, was " completed solved " by some young Moscow prodigy undergraduate. Both completeness of solution  and the role Arnold himself could play in reaching it was conveniently  stretched to produce infurating effects. Another  sad  (in my view) crusade  V.I.A. launched about that time was against  what he called  "Bourbakism" and "pure mathematics" While the opposition to the formal axiomatic exposition of mathematical results was always  characteristic of Arnold's trademark style (as I already mentioned ), he gradually went overboard  with ridiculing what he  considered formalismand unnecessary abstractions. The mere  names  of Bourbaki and Hardy became anathema for Arnold and the logical construction of solid foundations  for futur building ( the trademark Boubaki style) became the subject of ridicule more and more frequently. He went as far as to claim on several occasions that " there is no mathematics, only a branch of Physics " . Clearly,  he did not mean those things litterally, being himself  a most subtle mathematician, but the chorus of jingoists  of all stripes  cheered those provocative  statements much to the chagrin of genuine mathematical community.  (By Sergei YAKOVENKO)

to be continued ......

 

Prof David A.Johnson

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