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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?

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    $\begingroup$ 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. $\endgroup$
    – Chris Leary
    Jun 30, 2022 at 15:15
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    $\begingroup$ This looks like a question for History of Science and Mathematics, not for this site. $\endgroup$
    – Federico Poloni
    Jun 30, 2022 at 22:02
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    $\begingroup$ 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. $\endgroup$
    – Sergei Akbarov
    Jul 1, 2022 at 5:00
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    $\begingroup$ 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. $\endgroup$
    – Geoff Robinson
    Jul 1, 2022 at 13:51
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    $\begingroup$ Honestly, I do not think that speculating about Arnold's supposed prejudices can be useful in any way. Let's stick to the evidence. $\endgroup$
    – Francesco Polizzi
    Jul 1, 2022 at 17:59

1 Answer 1

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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

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    $\begingroup$ Some of the answers to that other MO question, e.g., by David Chow and Calvin Khor, give quotes in which Hardy strongly criticizes other mathematicians' work as "little more than nonsense" and "fundamental incompetence." The criticisms may be deserved, but they surely exhibit some of the "aggressiveness" that Arnold claimed. $\endgroup$
    – Timothy Chow
    Jul 1, 2022 at 0:18
  • $\begingroup$ fixed link, thanks. $\endgroup$
    – Carlo Beenakker
    Jul 1, 2022 at 10:23

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