4 ms·

So much of this article strikes me as utterly ridiculous. To start with, even if someone where to believe that mathematics was only of value in its application

So much of this article strikes me as utterly ridiculous. To start with, even if someone where to believe that mathematics was only of value in its application, it would still be ridiculous to say that it was a part of physics and worthless beyond physics. From there it seems to focus on denegrating the value of pure and axiomatic mathematics focusing almost purely on the need to keep mathematics tied to physics.

carterschonwald 17y ago
VI Arnold has authored some of the best expositional texts on mathematical physics and differential equations on the planet, even if he's being hyperbolic, there is still insight to be gained from his work
TriinT 17y ago
Arnold's article is highly satirical. If I wrote such an article, it would be, indeed, utterly ridiculous. Arnold is such a great mathematician that he has earned the right to poke fun at his own field. His books on differential equations and classical mechanics are simply the best. Moreover, Arnold is more of a geometer than an analyst. His article is also a not-so-subtle attack on the French fanatics (i.e., "bourbakists"), who tried to axiomatize all math and remove any geometrical and intuitive aspects from it. On the value of pure and axiomatic mathematics, I would like to quote Jacques Hadamard (who was french!): "The object of mathematical rigor is to sanction and legitimize the conquests of intuition, and there was never any other object for it." Rigor should follow intuition, not vice versa.
- onedognight 17y ago
  > His books on differential equations and classical mechanics are simply the best. I'm partial to his Topological Methods in Hydrodynamics myself. In case you're a "school child" interested in mathematics, the lecture he mentioned, The Abel theorem in problems, was just recently translated into english by Sujit Nair. http://www.cds.caltech.edu/~nair/abel.pdf http://www.cds.caltech.edu/~nair/abel.pdf
  - TriinT 17y ago
    Thanks for the wonderful URL. Yes, I am a "school child" indeed, albeit a bit older (i.e., I am a grad student ;-)
- timwiseman 17y ago
  Ah, perhaps it is because I am not familiar with him that I completely missed the satire. I had taken it to be quite literal.

carterschonwald 17y ago

VI Arnold has authored some of the best expositional texts on mathematical physics and differential equations on the planet, even if he's being hyperbolic, there is still insight to be gained from his work

TriinT 17y ago

Arnold's article is highly satirical. If I wrote such an article, it would be, indeed, utterly ridiculous. Arnold is such a great mathematician that he has earned the right to poke fun at his own field. His books on differential equations and classical mechanics are simply the best. Moreover, Arnold is more of a geometer than an analyst. His article is also a not-so-subtle attack on the French fanatics (i.e., "bourbakists"), who tried to axiomatize all math and remove any geometrical and intuitive aspects from it. On the value of pure and axiomatic mathematics, I would like to quote Jacques Hadamard (who was french!): "The object of mathematical rigor is to sanction and legitimize the conquests of intuition, and there was never any other object for it." Rigor should follow intuition, not vice versa.

onedognight 17y ago
> His books on differential equations and classical mechanics are simply the best. I'm partial to his Topological Methods in Hydrodynamics myself. In case you're a "school child" interested in mathematics, the lecture he mentioned, The Abel theorem in problems, was just recently translated into english by Sujit Nair. http://www.cds.caltech.edu/~nair/abel.pdf http://www.cds.caltech.edu/~nair/abel.pdf
- TriinT 17y ago
  Thanks for the wonderful URL. Yes, I am a "school child" indeed, albeit a bit older (i.e., I am a grad student ;-)
timwiseman 17y ago
Ah, perhaps it is because I am not familiar with him that I completely missed the satire. I had taken it to be quite literal.