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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Susan: What is algebra exactly; is it those three-cornered things?
Phoebe: It is x minus y equals z plus y and things like that. And all the time you are saying they are equal, you feel in your heart, why should they be.

Numbers exist only in our minds. There is no physical entity that is number 1. If there were, 1 would be in a place of honor in some great museum of science, and past it would file a steady stream of mathematicians gazing at 1 in wonder and awe.

So, nat'ralists observe, a flea
Hath smaller fleas that on him prey,
And these have smaller still to bite 'em
And so proceed ad infinitum.

Something more than impeccable logic is required in mathematics. An expert logician will not necessarily be a passable mathematician for all his skill in logic, any more than a scholarly prosodist will be a respectable poet for all his mastery of meter.

As to your Newton, I confess I do not understand his void and his gravity; I admit he has demonstrated the movement of the heavenly bodies with more exactitude than his forerunners; but you will admit it is an absurdity to maintain the existence of Nothing.

Number is the ruler of forms and ideas, and the cause of gods and daemons.

I enjoy being surprised by mathematics and its intrinsic difficulty. The moment I enjoy best is when the pieces of the puzzle fall into one coherent whole.

Sometime, in the future that is knocking at our door, we shall have to retrain ourselves or our children to properly tell the truth. The exercise will be particularly painful in mathematics. The enrapturing discoveries of our field systematically conceal, like footprints erased in sand, the analogical train of thought that is the authentic life of mathematics. Shocking as it may be to the conservative logician, the day will come when currently vague concepts such as motivation and purpose will be made formal and accepted as constituents of a revamped logic, where they will at last be alloted the equal status they deserve, side-by-side with axioms and theorems. Until that day, however, the truths of mathematics will make only fleeting appearances, like shameful confessions whispered to a priest, to a psychiatrist, or to a wife.

If a 'religion' is defined to be a system of ideas that contains unprovable statements, then Gödel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one.

Any author who uses mathematics should always express in ordinary language the meaning of the assumptions he admits, as well as the significance of the results obtained. The more abstract his theory, the more imperative this obligation. In fact, mathematics are and can only be a tool to explore reality. In this exploration, mathematics do not constitute an end in itself, they are and can only be a means.

Mathematics, in an earlier view, is the science of space and quantity; in a later view, it is the science of pattern and deductive structure. Since the Greeks, mathematics is also the science of the infinite.

The Koch Curve - Triangles outside triangles outside triangles ad infinitum the Koch curve goes, it's infinitely infinitesimal, this self-similarity shows. A length too long to measure, an area too small to see, what else can this contradiction be, behold fractal geometry.

<math>10^{50}</math> is a long way from infinity.

A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.

Mathematical methods present... two advantages. Their terminology is precise and concentrated, in a fashion which ordinary language cannot afford to adopt. Further, the symbols which result from their employment have implications which, when brought to light, yield new knowledge. This is deductively reached, but it is none the less new knowledge. With greater precision than is usual, ordinary language may be made to do some, if not a great deal, of this work for which mathematical methods are alone quite appropriate. If ordinary language can do part of it an advantage may be gained. The difficulty that attends mathematical symbolism is the accompanying tendency to take the symbol as exhaustively descriptive of reality. Now it is not so descriptive. It always embodies an abstraction. It accordingly leads to the use of metaphors which are inadequate and generally untrue. It is only qualification by descriptive language of a wider range that can keep this tendency in check.