William Rowan Hamilton Quotes

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.

An equation means nothing to me unless it expresses a thought of God.

Mathematics is universal. But very little else is.

Dialectical mathematics is a rigorously logical science, where statements are either true or false, and where objects with specified properties either do or do not exist. Algorithmic mathematics is a tool for solving problems. Here we are concerned not only with the existence of a mathematical object, but also with the credentials of its existence. Dialectical mathematics is an intellectual game played according to rules about which there is a high degree of consensus. The rules of the game of algorithmic mathematics may vary according to the urgency of the problem on hand. We never could have put a man on the moon if we had insisted that the trajectories should be computed with dialectic rigor. The rules may also vary according to the computing equipment available. Dialectic mathematics invites contemplation. Algorithmic mathematics invites action. Dialectic mathematics generates insight. Algorithmic mathematics generates results.

Mathematics is the bold luxury of pure reason, one of the few that remain today.

Where there is life there is a pattern, and where there is a pattern there is mathematics. Once that germ of rationality and order exists to turn a chaos into a cosmos, then so does mathematics. There could not be a non-mathematical Universe containing living observers.

If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics.

It's magic," the chief cook concluded, in awe.
"No, not magic," the ship's doctor replied. "It's much more. It's mathematics.

One of the best ways to sharpen your brain, and to develop intelligence, is to study mathematics. It challenges and strengthens your mind in a way that very few other things do. It’s like going to the gym -- but for your brain!

In universities, mathematics is taught mainly to men who are going to teach mathematics to men who are going to teach mathematics to.... Sometimes, it is true, there is an escape from this treadmill. Archimedes used mathematics to kill Romans, Galileo to improve the Grand Duke of Tuscany's artillery, modern physicists (grown more ambitious) to exterminate the human race. It is usually on this account that the study of mathematics is commended to the general public as worthy of State support.

My earliest mathematical memory is my father explaining to me the theorem that three angles in a triangle add up to 180 degrees. The idea that something could be proved to be always true was very appealing to me.

I was an atheist, finding no reason to postulate the existence of any truths outside of mathematics, physics and chemistry. But then I went to medical school, and encountered life and death issues at the bedsides of my patients. Challenged by one of those patients, who asked "What do you believe, doctor?", I began searching for answers.

A narrative of the decisive epochs in the development of mathematics was wanted. ...Numerous professionals... know from hard experience what mathematical invention means. ...Whoever has himself attempted to advance mathematics is inclined to be more skeptical than the average spectator toward any alleged anticipation of notable progress. ...often what looks like an anticipation ...was not even aimed in the right direction. ...when at length progress started; it proceeded along lines totally different from those which, in retrospect, it 'should' have followed.

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.

Mathematics may be universal in a nonpersonal sense, but whether it can appeal to all people and be understood by all people is another question.