Recently, a teacher of mine stated that, since the institutional division between philosophy and other fields of academic enquiry, especially the natural sciences, happened somewhere along the 19th century, thinkers that we now regard as mathematicians (like Euler and Gauss) did not think of themselves primarily as mathematicians, but as philosophers. I know that the work of such thinkers was considerably less specialized back then but, even so, is what my teacher claiming true? Citations from the mathematicians/philosophers naming themselves one or the other way would be particularly helpful.
Did thinkers we now regard as mathematicians call themselves philosophers prior to the 19th century?
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4$\begingroup$ This is certainly not true for 17-18 century. Newton, Bernoullis, Euler, Lagrange and Gauss called themselves mathematicians. Another thing is that Physics was called "natural philosophy", so a physicist could be a "natural philosopher". For example Newton was both a mathematician and a natural philosopher. His principal work is called Mathematical foundations of natural philosophy. $\endgroup$– Alexandre EremenkoCommented May 23, 2022 at 12:58
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2$\begingroup$ The loose use of the term "philosopher", such as (1) The Lives of the French, Italian and German Philosophers, Late Members of the Royal Academy of Science in Paris... by M. de Fontenelle, John Chamberlayne, 1717, which includes Bernoulli, L'Hopital and other mathematicians, or (2) Newton's reference to unnamed "philosophers" (sic) in his preface to his Principia, may explain your teacher's impression. The term "philosophy" was then allowed to comprise a wider range of fields than it is today, at least in relation to the work of academic Departments of Philosophy. $\endgroup$– Michael E2Commented May 24, 2022 at 18:41
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$\begingroup$ Related $\endgroup$– sdsCommented May 31, 2022 at 16:24
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Your teacher is simply wrong. Most major fields of academia were regarded as a specialized area of interest for millennia, originating formally and most significantly in ancient Greece.
Archimedes, for example, made a clear distinction in his writing (I wish I could give the exact citation for you) between applied and pure mathematics (although they didn't use those terms).The applied regarding his work in physics, and the pure in mathematics.
Even the more niche field of logic was well-defined enough to be its own study by the 13th to 14th century, with medieval scholars specifically referring to themselves as logicians.
Pythagoras, the main individual responsible for the distinction between pure and applied math as well as the beginnings of Greek philosophy, spoke clearly about the fact that philosophy and pure mathematics were separate fields of thought, and it was his cult's, the Pythagoreans', purpose to integrate them into a mathematical worldview.
In Eastern thought, primarily China and India, there was also a clear distinction made between a society's architects and its sages. Lao-tzu and the Buddha certainly weren't considered in the same regard as a mathematician.
The examples feel endless. It is human nature to label, categorize, and distinct things, and our fields of thought and study are no different. To posit that this wasn't the case until recent - that all pre-19th century scholars simply called themselves philosophers, is preposterous.
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1$\begingroup$ I've often encountered terms like arithmetician and geometrician and algebraist in older literature. The links I've given are for the 1700-1800 date range. They can easily be changed to 1800-1900 if more results are desired. $\endgroup$ Commented May 23, 2022 at 16:04