# Are there well-known mathematicians who shared Arnold's view about mathematics as natural science?

V. I. Arnold asserted that mathematics is a natural science: "Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap." V.I. Arnold: "On teaching mathematics" (1997)

This opinion is rare. Many mathematicians will oppose, in particular pure mathematicians. But is it solitary?

Are there famous mathematicians who have shared in written form Arnold's view that mathematics is a natural science?

• This opinion is not rare. It was common until the beginning of 19th century, for example it was explicitly expressed by Fourier. And many mathematicians still hold it. – Alexandre Eremenko Jun 12 '17 at 14:36
• @Alexandre Eremenko: Can you provide quotes? Of course most interesting would be contemporary mathematicians. When I have seen discussions about Arnold's provocative statement, I have never met a supporter (except myself). – Otto Jun 12 '17 at 16:39
• As I am also a supporter, you already have $\geq 2$, besides Arnold. Now, most mathematicians do not make such general statements in print, because they are busy proving theorems. So next time I see this expressed in print, I will inform you. Meanwhile you may read the Introduction to Fourier's Analytic Theory of Heat. – Alexandre Eremenko Jun 12 '17 at 18:42
• I am not sure if you are looking for the uses of this specific language, or sympathy to the view. Many would say that there are obvious similarities and dissimilarities between mathematics and natural sciences, so this is about drawing an imaginary line. Here is Magidin putting them on the same side of it. See also the 1990-s debate over the Glimme-Jaffe's manifesto on mathematics vs physics, with many big names participating. – Conifold Jun 12 '17 at 23:49
• @Conifold: I am looking for sympathy to this view. I often encountered strict refusal and even the opinion that mathematics is not a science at all because sciences have to be experimentally falsifyable. Mathematics and natural sciences are often housed within a common faculty. On the other hand much of modern mathematics is certainly without any connection to a science. – Otto Jun 13 '17 at 10:40

## 2 Answers

Newton is a dubious example here, but it is well known that in the preface of his Principia he asserted (p.xiii):

geometry is a founded on mechanical practice and is nothing but that part of universal mechanics which accurately proposes and demonstrates the art of measuring.

Leaving aside the etymology harking back to 'measuring', for Newton geometry is mathematics, as he disliked cartesianism and its algebraic approach.

Before the XXth.c most of mathematics has been done by natural scientists-physicists; Imre Lakatos, who was a philosopher, proposed in his Proofs and refutations the view that mathematics is just like any other science; later Quinn and Jaffe outlined the idea that mathematics is theoretical and makes hypotheses, for which proofs are offered and so it functions as a natural science.

An explicit statement has been given by Kronecker:

Mathematics is a natural science – not better, not more complete, and not simpler the phenomena can be described than mathematically.

"About the notion of number in mathematics", Public lecture in summer semester 1891 at Berlin – Kronecker's last lecture. "Sur le concept de nombre en mathematique" Retranscrit et commenté par Jacqueline Boniface et Norbert Schappacher: Revue d'histoire des mathématiques 7 (2001).