A mathematician is a device for turning coffee into theorems.

For a smart material to be able to send out a more complex signal it needs to be nonlinear. If you hit a tuning fork twice as hard it will ring twice as loud but still at the same frequency. That's a linear response. If you hit a person twice as hard they're unlikely just to shout twice as loud. That property lets you learn more about the person than the tuning fork.

The fraction of life can be increased in value not so much By increasing your numerator as by lessening your denominator. Nay, unless my Algebra deceives me, unity itself divided by zero will give infinity.

In the company of friends, writers can discuss their books, economists the state of the economy, lawyers their latest cases, and businessmen their latest acquisitions, but mathematicians cannot discuss their mathematics at all. And the more profound their work, the less understandable it is.

The mathematical life of a mathematician is short. Work rarely improves after the age of twenty-five or thirty. If little has been accomplished by then, little will ever be accomplished.

Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere.

Mathematics, the non-empirical science par excellence ... the science of sciences, delivering the key to those laws of nature and the universe which are concealed by appearances.

The so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things.

About Thomas Hobbes He was 40 years old before he looked on geometry which happened accidentally. Being in a gentleman's library, Euclid's Elements lay open, and 'twas the 47 El. libri I' Pythagoras' Theorem. He read the proposition 'By God', sayd he, 'this is impossible' So he reads the demonstration of it, which referred him back to such a proposition which proposition he read. That referred him back to another, which he also read. Et sic deinceps, that at last he was demonstratively convinced of that truth. This made him in love with geometry.

How happy the lot of the mathematician. He is judged solely by his peers, and the standard is so high that no colleague or rival can ever win a reputation he does not deserve.

The good Christian should beware of mathematicians, and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell.

For the things of this world cannot be made known without a knowledge of mathematics.

In the mathematics I can report no deficience, except that it be that men do not sufficiently understand the excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For if the wit be too dull, they sharpen it if too wandering, they fix it if too inherent in the sense, they abstract it. So that as tennis is a game of no use in itself, but of great use in respect it maketh a quick eye and a body ready to put itself into all postures so in the mathematics, that use which is collateral and intervenient is no less worthy than that which is principal and intended.

What is algebra exactly is it those three-cornered things

The longer mathematics lives the more abstract and therefore, possibly also the more practical it becomes.

Einstein is an analytical mathematician seeking to give a physical interpretation to the conclusions of his mathematical process. In this he is hampered by a load of contradictory and absurd assumptions of the school that he follows, which throws him in to all manner of difficulty. Einstein has such a faculty for embracing both sides of a contradiction that one would have to be of the same frame of mind to follow his thought, it is so peculiarly his own. The whole Relativity theory is as easy to follow as the path of a bat in the air at night.

The different branches of Arithmetic Ambition, Distraction, Uglification, and Derision.

I continued to do arithmetic with my father, passing proudly through fractions to decimals. I eventually arrived at the point where so many cows ate so much grass, and tanks filled with water in so many hours I found it quite enthralling.

'I think you're begging the question,' said Haydock, 'and I can see looming ahead one of those terrible exercises in probability where six men have white hats and six men have black hats and you have to work it out by mathematics how likely it is that the hats will get mixed up and in what proportion. If you start thinking about things like that, you would go round the bend. Let me assure you of that'

I had a feeling once about Mathematics that I saw it all. Depth beyond depth was revealed to me the Byss and Abyss. I saw as one might see the transit of Venus or even the Lord Mayor's Show a quantity passing through infinity and changing its sign from plus to minus. I saw exactly why it happened and why the tergiversation was inevitable but it was after dinner and I let it go.

Don't talk to me of your Archimedes' lever. He was an absentminded person with a mathematical imagination. Mathematics commands all my respect, but I have no use for engines. Give me the right word and the right accent and I will move the world.

Mathematics is written for mathematicians.

... it is interesting to note that the original problem that started my research is still outstanding - namely the problem of planning or scheduling dynamically over time, particularly planning dynamically under uncertainty. If such a problem could be successfully solved it could eventually through better planning contribute to the well-being and stability of the world.

Mathematics seems to endow one with something like a new sense.

Mathematics is the tool specially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field.

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