William Rowan Hamilton Quotes

Irish mathematician and astronomer (1805-1865)

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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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Alternative Names: Sir William Rowan Hamilton • Hamilton Mathematics Institute • Hamilton

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In the pure mathematics, we contemplate absolute truths, which existed in the Divine Mind before the morning stars sang together, and which will continue to exist there, when the last of their radiant host shall have fallen from heaven.

The mathematician may be compared to a designer of garments, who is utterly oblivious of the creatures whom his garments may fit. ...The conic sections, invented in an attempt to solve the problem of doubling the altar of an oracle, ended by becoming the orbits followed by the planets... The imaginary magnitudes invented by Cardan and Bombelli describe... the characteristic features of alternating currents. The absolute differential calculus, which originated as a fantasy of Reimann, became the mathematical model for the theory of Relativity. And the matrices which were a complete abstraction in the days of Cayley and Sylvester appear admirably adapted to the... quantum of the atom.

Mathematics became an experimental subject. Individuals could follow previously intractable problems by simply watching what happened when they were programmed into a personal computer. ...The PC revolution has made science more visual and more immediate ...by creating films of imaginary experiences of mathematical worlds. ...Words are no longer enough.

The more advanced the sciences have become, the more they have tended to enter the domain of mathematics, which is a sort of center towards which they converge. We can judge of the perfection to which a science has come by the facility, more or less great, with which it may be approached by calculation.

I maintain that in every special natural doctrine only so much science proper is to be met with as mathematics; for... science proper, especially of nature, requires a pure portion, lying at the foundation of the empirical, and based upon à priori knowledge of natural things. ...the conception should be constructed. But the cognition of the reason through construction of conceptions is mathematical. A pure philosophy of nature in general, namely, one that only investigates what constitutes a nature in general, may thus be possible without mathematics; but a pure doctrine of nature respecting determinate natural things (corporeal doctrine and mental doctrine), is only possible by means of mathematics; and as in every natural doctrine only so much science proper is to be met with therein as there is cognition à priori, a doctrine of nature can only contain so much science proper as there is in it of applied mathematics.

Between the philosopher's attitude towards the issue of reality and that of the mathematician there is this essential difference: for the philosopher the issue is paramount; the mathematician's love for reality is purely platonic.

It's a lonely profession.

Mathematics is the source of a wicked intellect that, while making man the lord of the earth, also makes him the slave of the machine.

It might have been beans, successful hunts, or victories in battle, but, for millennia, people were using maths to describe things - counting them, measuring them, dividing them up.

I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."

A marveilous newtrality have these things mathematicall and also a strange participation between things supernaturall, imortall, intellectuall, simple and indivisible, and things naturall, mortall, sensible, compounded and divisible.

In doing mathematics, I express something personal. It is a source of joy to know that, despite this personal aspect, the fruit of my work can be of interest to other mathematicians.

You don’t need anybody’s permission to be a great mathematician!

Theorems often tell us complex truths about the simple things, but only rarely tell us simple truths about the complex ones. To believe otherwise is wishful thinking or "mathematics envy."

What has philosophy got to do with measuring anything? It's the mathematicians you have to trust, and they measure the skies like we measure a field.