Preface

This was a response to a question on Quora: According to Wikipedia and Encyclopædia Britannica Sir Isaac Newton is both a physicist and mathematician. Is that claim true?

Introduction

Another Quora contributor, Diptarka Hait, has argued that it is better to think of Newton as the ‘last great magician’ rather than either physicist or mathematician. Given the power of Newton’s mind and, as Hait observed, the truth that Newton approached nature as a unity, there is much to the thought that Newton was a magician (read Hait’s contribution for the sense in which ‘magician’ is being used). Certainly, this may be said of Newton and other intellects who may express the result of thought in terms of reason but whose sources of thought seen beyond the reach of reason alone (and perhaps the rest of us).

Comment on editing history

This ‘second edition’ is substantially the same as the first but has been edited for improvements and the addition of headings.

Brief answer

I am going to argue that Newton was both mathematician and physicist (this does not negate ‘Newton as magician’).

The question may be seen as suggesting that an individual cannot be both mathematician and physicist. That would of course not be true. One can be a poet and a philosopher. One can be a physicist and a mathematician. When two avocations are not exclusive one can be both of them. And this is true even in our era of specialization. It was more likely to obtain in Newton’s time--a time that was still the beginning of modern science.

In Newton’s case it was true that he was ‘multi-disciplinary’. I elaborate below in the longer answer.

An interesting aspect of the question is whether a given activity is or can be simultaneously mathematical and physical--perhaps this is the sense of the question. I will address this issue later, after the ‘long answer’.

Long answer

As mathematician he invented and established much of calculus, he proved the binomial theorem, he was a master of Euclidean Geometry and the mathematics of his time. As physicist he was the foremost developer of the science of optics of his time (he proved many optical theorems, he built the first reflecting telescope, and he espoused the corpuscular theory of light which was abandoned later and then equivocally resuscitated with quantum theory). His major achievement in physics was of course his theory of mechanics which integrated a fundamental understanding of the laws of mechanics, a philosophy of space and time (one that we no longer accept), and the theory of universal gravitation (replaced by Einstein’s). Though we no longer accept Newton’s mechanics or philosophy as fundamental, it was an immense advance and unification for his time--it was the first comprehensive physical theory that could and did predict so many phenomena in so many realms that it became regarded as necessarily true.

Newton wrote at a time when and in a way that mathematics and physics were not yet fully separated. His physics was occasion to develop the calculus and his calculus supported development of his physics (it is remarkable that this is reflected in the title of his work The Mathematical Principles of Natural Philosophy in which he depended much on techniques of geometry rather than calculus--apparently he felt that that approach would be better accepted than calculus: Newton probably knew that the foundations of calculus were shaky; in fact firm foundation would not be formulated till the nineteenth century).

Of course the claim in the question can be true--even today with specialization one can be both physicist and mathematician. But regarding Newton it is true: he was a physicist using mathematics and a mathematician developing the mathematics he needed for his physics. This sets him apart from most physicists of our time. Einstein turned to collaborators for the calculus of tensors upon which his formulation of the General Theory of Relativity depends. This is of course not a mark against Einstein and modern physicists--the specialization of today is the result of the advances that require years of training / practice to get up to speed in either physics or mathematics. It is remarkable, by the way, that Paul Dirac created much of the mathematics needed for his work in quantum mechanics. Even today one can be both mathematician and physicist. Another example is Ed Witten, one of the leading researchers in string theory and other fields of theoretical physics. His work has significantly impacted pure mathematics (Wikipedia: Edward Witten) and he is so far the only physicist to have received the Fields Medal of the International Mathematical Union.

Can an endeavor be simultaneously mathematics and physics?

This brings me to an issue that was not asked by the questioner but still bears on the question--are science and mathematics truly distinct? I once attended a lecture by a mathematician who referred to mathematics as a science. How can that be? Is it not true that mathematics is abstract and that we create it as much as discover it? In the beginning of course mathematics was a science--the early theories of number and of geometry must have been theories of concrete things but then, in Euclid, the abstract approach to mathematics arose. Mathematics became, perhaps, the theories of form rather than of the concrete. But to what does mathematics refer--what are these forms and where do they reside? Or is mathematics simply abstract and has no essential object even while it may apply to many objects? Gödel was a Platonist--he held that mathematics is about mathematical objects which reside in some ideal world or space but not in our concrete world.

Many modern mathematicians are Platonist with regard to mathematics. Why? It is because of the sense that even if mathematics is abstract, there is a sense of the inevitability of mathematics. Mathematicians may err in proof and interpretation. However, once a field of mathematics or theorem is established it appears inevitably and essentially true. The theorem of Pythagoras--how could it not be true? Of course we know that there are alternate geometries in which it is not true (and in non metric geometries it is neither true nor false)--but that is where interpretation comes in. The theorem is and will always remain true of certain forms.

So what is being said is that the sense in which mathematics is a science is that its systems are sciences of abstract worlds.

Imagine, however, that the universe is the realization of all possibility. In that case all concepts that (a) agree known facts in the limited domain of the empirical and (b) are logically consistent are realized as objects. Why? It is because regarding all possibility, logic--which may now be seen as including fact in which premise and conclusion coincide--is the only constraint. Therefore, since logic is inherent in the structure of mathematics, the mathematical systems must have objects in the universe. Therefore, under the possibility hypothesis, the systems of mathematics have interpretations as sciences of the abstract just as the natural and social sciences are sciences of the concrete.

Thus the diversion is pertinent to the question because we now see a sense in which physics (science generally) and mathematics are not fundamentally distinct.

Postscript

Can anything more be said of the ‘possibility hypothesis’? For an answer see the essay The way of being at my site http://www.horizons-2000.org. This essay has a tentative proof of the possibility hypothesis (but is much more and includes motivation, interpretation, significance, and consequences regarding the possibility hypothesis that I have named the fundamental principle of metaphysics).