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In the preface to his book "Lectures On Partial Differential Equations" Arnold writes:

The effort to destroy this unnecessary scholastic pseudoscience is a natural and proper reaction of society) to the irresponsible and self-destructive aggressiveness of the super-pure mathematicians educated in the spirit of Hardy and Bourbaki.

I think this quote is very unfair towards Hardy. As far as I know he was not agressive and his book "Mathematician's Apology", it is written in a rather defensive manner. He writes his personal opinion about mathematics and never states that this is the only way that mathematics should be studied.

On the other hand there have been some Bourbakists who tried really agressively to enforce their opinion and style on all of mathematics.

Arnold didn't like Hardy, this is not a secret (for example, see this question https://hsm.stackexchange.com/questions/13614/does-arnold-say-that-hardy-is-responsible-for-ramanujans-untimely-death).

Question. Did Arnold really have any objective reason to put Hardy and Bourbakists on the same level? Or was this quote motivated by Arnold's personal dislike for Hardy?

Tyrell
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    Hardy was eccentric and opinionated. According to C. P. Snow, in the foreword to the Apology, Hardy had quite a few friends who thought kindly of him. Snow also says that Hardy was painfully shy, a condition that can be misread for arrogance. Hardy made his distaste for "applied" mathematics known, but expressed deep appreciation for mathematical physics. I believe I would have found Hardy outrageous but delightful. But, outspoken, opinionated people do tend to make enemies. Such is life. – Chris Leary Jun 30 '22 at 15:15
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    What does "objective" mean in this context? Are you asking if Hardy had done some objectively measurable harm to math and math education? Or, maybe, you are asking if Hardy expressed views that Arnold found to be harmful and abhorrent. (The existence of such expressions of view is objectively verifiable.) – Moishe Kohan Jun 30 '22 at 15:55
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    This looks like a question for [hsm.se], not for this site. – Federico Poloni Jun 30 '22 at 22:02
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    Hardy's "Mathematician's Apology", when published in Russian, astounded me with the poverty of the arguments. Looking at the title, the reader might expect a coherent explanation of why mathematics is useful and why it should be studied, but Hardy makes only one clear argument - that mathematics is not used for war. This is amazing, firstly, because this is not true, and, secondly, because that is all that came to Hardy's mind. From this essay, I concluded that Hardy, at least, was not a diversified person. – Sergei Akbarov Jul 01 '22 at 05:00
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    This often happens among mathematicians, when a person is good in some area of ​​his own, but becomes incompetent as soon as he goes beyond it (and what is most amazing, he doesn't feel that something is wrong). Arnold himself often demonstrates this quality, in particular when he criticises other mathematicians, for example, Bourbaki and Hardy, and I see this as a manifestation of the general crisis of modern science: now educational institutions produce robots, not humans. In my opinion, this is what should be discussed in situations like this. – Sergei Akbarov Jul 01 '22 at 05:01
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    I don't want to get into the finer points of this discussion, but there is a distinction between arguing that the motivation of Pure Mathematics is not its application ( though many Pure Mathematicians might dispute that anyway) and taking pride in the view that Pure Mathematics is "useless". The most famous quote of Hardy on the matter is open to the latter interpretation, and, as such, it has probably done a disservice to the public perception of Pure Mathematicians, since it is widely quoted. – Geoff Robinson Jul 01 '22 at 13:51
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    Honestly, I do not think that speculating about Arnold's supposed prejudices can be useful in any way. Let's stick to the evidence. – Francesco Polizzi Jul 01 '22 at 17:59

1 Answers1

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This comment by Arnold has been criticized by others, I quote from a book review:

Prof. Arnold is extremely passionate in expressing his philosophical ideas on mathematics and returns to these themes repeatedly throughout the book. Sympathetic as we might be to some of his points of view, we do not find it constructive to take extreme positions such as the ones advocated by Prof. Arnold. As an example, perhaps it is time to re-evaluate our own perceptions about Hardy's contribution. He considered himself a pure mathematician with seemingly no interest in applications. But much of his work in analysis even at the time was applicable, and the Hardy-Weinberg test is still used in counting red blood cells, of which Hardy himself was aware.

Hardy's efforts to bring rigor to mathematics in Britain are viewed positively, see the discussion at Unrigorous British mathematics prior to G.H. Hardy

Carlo Beenakker
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