Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another p… - William Rowan Hamilton
" "Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true … If our hypothesis is about anything, and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.
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About William Rowan Hamilton
Sir William Rowan Hamilton (4 August 1805 – 2 September 1865) was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His studies of mechanical and optical systems led him to discover new mathematical concepts and techniques. His greatest contribution is perhaps the reformulation of Newtonian mechanics, now called Hamiltonian mechanics. This work has proven central to the modern study of classical field theories such as electromagnetism, and to the development of quantum mechanics. In mathematics, he is perhaps best known for his discovery of quaternions.
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Sir William Rowan Hamilton
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Hamilton Mathematics Institute
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Additional quotes by William Rowan Hamilton
I would myself say that the purely imaginary objects are the only realities, the ὂντως ὂντα [truest things], in regard to which the corresponding physical objects are as the shadows in the cave; and it is only by means of them that we are able to deny the existence of a corresponding physical object; and if there is no conception of straightness, then it is meaningless to deny the conception of a perfectly straight line.
There is a temptingly simple explanation for the fact that science is mathematical in nature: it is because we give the name of science to those areas of intellectual inquiry that yield to mathematical analysis. ...Science ...deals with precisely those subjects amenable to quantitative analysis, and that is why mathematics is the appropriate language... The puzzle becomes a tautology: mathematics is the language of science because we reserve the name "science" for anything that mathematics can handle. If it's not mathematical, to some degree at least, it isn't really science.
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Now comes the Einstein–Podolsky–Rosen entangled state. Now I see faces, people saying, "Oh..?" Don't worry! When you go to the concert, you don't need to be able to read the music, to enjoy the music. ...So here... [are] equations. It's a pleasure for my colleague physicists. If you can't read the equation, listen to me. I'm not going to sing, but... listen to the words... the words are... a way of describing the equations, and you don't need to know the mathematics...
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