Quotes

Paul Davies 

The astronomer James Jeans once proclaimed that God is a mathematician. His pithy phrase expresses in metaphorical terms an article of faith adopted by almost all scientists today. The belief that the underlying order of the world can be expressed in mathematical form lies at the very heart of science, and is rarely questioned.

The Matter Myth P. Davies & J. Gribbin p.140 / Simon & Schuster 1992

Paul Dirac 

Paul Dirac: [re: The successful Schrödinger equation] Schrödinger got this equation by pure thought, looking for some beautiful generalisation of deBroglies ideas, and not by keeping to the experimental development of the subject in the way Heisenberg did. ... I think that there is a moral to this story, namely that it is more important to have beauty in one's equations than to have them fit experiment. If Schrödinger had been more confident of his work, he could have published it some months earlier, and he could have published a more accurate equation. It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one's work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further development of the theory.

The evolution of the physicist's picture of nature p.46 Sci. American 208 May 1963

Albert Einstein 

… an enigma presents itself which in all ages has agitated inquiring minds. How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things.

Geometry and Experience address by Albert Einstein (1921), expanded (Prussian Academy of Sciences, Jan 27th)

Richard Feynman 

I find it quite amazing that it is possible to predict what will happen by mathematics, which is simply following rules which really have nothing to do with what is going on in the original thing.

...

One of the most important things in this 'guess - compute consequences - compare with experiment' business is to know when you are right. It is possible to know when you are right way ahead of checking all the consequences. You can recognise truth by its beauty and simplicity. ... When you get it right, it is obvious that it is right ... because usually what happens is that more comes out than goes in.

The Character of Physical Law p.171 / BBC 1965, Penguin 1992

Galileo Galilei 

Wrote to a friend, Castelli:

I believe that the intention of Holy [Scripture] was to persuade men of the truths necessary for salvation such as neither science nor any other means could render credible, but only the voice of the Holy Spirit. But I do not think it necessary to believe that the same God who gave our senses, our speech, our intellect, would have put aside the use of these, to teach us instead such things as with their help we could find out for ourselves, particularly in the case of these sciences of which there is not the smallest mention in the Scriptures; and, above all, astronomy, of which so little notice is taken that the names of none of the planets are mentioned. Surely if the intention of the sacred scribes had been to teach the people astronomy, they would not have passed over the subject so completely.

Galileo's Daughter Dava Sobel quoted p.65 / Fourth Estate Ltd. 1999

Werner Heisenberg 

p.56. [recalling initially dull maths lessons] The thought that mathematics somehow corresponded to the structures of our experience struck me as remarkably strange and exciting

p.61. [recalling discovering QM correct predictions of the H atom] When the first terms seemed to accord with the energy principle, I became rather excited...I had the feeling that, through the surface of atomic phenomena, I was looking at a strangely beautiful interior, and felt almost giddy at the thought that I now had to probe this wealth of mathematical structures nature had so generously spread out before me.

p.68 [recalled comment to Einstein re: matrix mechanics]: "… the mere fact that we could never have arrived at these forms by ourselves, that they were revealed to us by nature, suggests strongly that they must be part of reality itself, not just of our thoughts about reality ... I frankly admit that I am strongly attracted by the simplicity and beauty of the mathematical schemes with which nature presents us. You must have felt this, too: the almost frightening simplicity and wholeness of the relationships which nature suddenly spreads out before us and for which none of us was in the least prepared."

The Physicists Conception of Nature * / G. Allen & Unwin London 1971

Johannes Kepler 

Thanks be to Thee, O Lord our Creator, who hast granted me visions of beauty in Thy creation, and with the work of these Thy hands I give Thee praise. Lo, I have completed the work to which Thou hast bestowed upon me; I have proclaimed the splendour of Thy work unto those who will read these proofs, in as much as I, in the limitations of my mind, have been able to grasp them.

Cosmic Mystery / Mysterium Cosmographicum, Chapter IV (quoted in W. Heisenberg - The Physicists Conception of Nature *)

The wisdom of the Lord is infinite; so also are His glory and His power. 

Ye heavens, sing His praises! Sun, moon, and planets glorify Him in your ineffable language! 

Celestial harmonies, all ye who comprehend His marvellous works, praise Him.

And thou, my soul, praise thy Creator! 

It is by Him and in Him that all exists. 

That which we know best is comprised in Him, as well as in our vain science. 

To Him be praise, honour, and glory throughout eternity.

The Harmony of the World 1619.

James Clerk Maxwell 

Teach me so thy works to read

that my faith new strength accruing

may from world to world proceed

wisdom's faithful search pursuing

till thy truth my mind imbuing

I proclaim the eternal creed

oft the glorious theme renewing

God our Lord is God indeed

James Clerk Maxwell: A Biography quoted I. Tolstoy p.160 / Canongate, 1981

Roger Penrose 

p.126 [re: structures such as the Mandelbrot Set] ... there are things in mathematics for which the term 'discovery' is indeed much more appropriate than 'invention' ... These are the cases where much more comes out of the structure than is put into it in the first place. One may take the view that in such cases the mathematicians have stumbled upon 'works of God.'

p.197. List of superb theories (and accuracies):

Euclidean geometry (1 in 1,000,000,000)

Statics

Newtonian mechanics (1 in 10,000,000)

Maxwell's electromagnetic theory (valid for sub-atomic particles and galaxies)

Special and general relativity (1 in 100,000,000,000,000)

Quantum theory (no observed errors@1989)

Quantum electrodynamics (1 in 1,000,000,000)

[and perhaps Darwinian natural selection]

p.556. It is hard for me to believe, as some have tried to maintain, that such SUPERB theories could have arisen merely by some random natural selection of ideas leaving only the good ones as survivors. The good ones are simply much too good ... There must, indeed, be some deep underlying reason for the accord between mathematics and physics, i.e. between 'Plato's world' and the physical world.

The Emperor's New Mind / Vintage 1989

Max Planck 

[S]cience demands ... the believing spirit. Anybody who has been seriously engaged in scientific work of any kind realizes that over the entrance to the gates of the temple of science are written the words: Ye must have faith. It is a quality the scientists cannot dispense with. The man who handles a bulk of results obtained from an experimental process must have an imaginative picture of the law that he is pursuing. He must embody this in an imaginary hypothesis. The reasoning faculties alone will not help forward a step ... This imaginative vision and faith in the ultimate success are indispensable. The pure rationalist has no place here.

Where is Science Going? p.214 / Allen & Unwin 1933

John Polkinghorne 

[S]ome of the most beautiful patterns thought up by the mathematicians are found actually to occur in the structure of the world around us. ... Paul Dirac invented ... quantum field theory ... I can't believe Dirac's ability to invent that theory, or Einstein's ability to invent the general theory of relativity, is a sort of spin-off from our ancestors having to dodge sabre-toothed tigers. It seems to me that something much more profound, much more mysterious is going on.

Hockerill Lecture London November 1992 abridged extract / Church Times 4th Dec. 1992

Eugene Wigner 

The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and ... there is no rational explanation for it.

… it is hard to believe that our reasoning power was brought, by Darwin's process of natural selection, to the perfection which it seems to possess.

Newton's law ... a monumental example of a law, … simple to the mathematician, which has proved accurate beyond all reasonable expectation.

The miracle occurred only when matrix mechanics was applied to problems for which Heisenberg's calculating rules were meaningless. H's rules presupposed that [they] could not be applied to cases [such as He with 2 electrons].

Nevertheless, the calculation of the lowest energy level of He [1960] agree with the experimental data within the accuracy of ... 1 part in 10 million. Surely in this case we 'got something out' of the equations that we did not put in.

… we do not know why our theories work so well.

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will extend, for better or for worse, to our pleasure even though perhaps also to our bafflement, to wide branches of learning.

The Unreasonable Effectiveness of Mathematics in the Natural Sciences Comm. Pure & Appl. Maths. xiii 1-14 1960

Further information at History of Mathematics archive, University of St. Andrews:

https://mathshistory.st-andrews.ac.uk/Biographies/Davies_Paul

https://mathshistory.st-andrews.ac.uk/Biographies/Dirac

https://mathshistory.st-andrews.ac.uk/Biographies/Einstein

https://mathshistory.st-andrews.ac.uk/Biographies/Feynman

https://mathshistory.st-andrews.ac.uk/Biographies/Kepler

https://mathshistory.st-andrews.ac.uk/Biographies/Galileo

https://mathshistory.st-andrews.ac.uk/Biographies/Heisenberg

https://mathshistory.st-andrews.ac.uk/Biographies/Maxwell

https://mathshistory.st-andrews.ac.uk/Biographies/Penrose

https://mathshistory.st-andrews.ac.uk/Biographies/Planck

https://mathshistory.st-andrews.ac.uk/Biographies/Polkinghorne

https://mathshistory.st-andrews.ac.uk/Biographies/Wigner