mathematics

• Every true mathematician sees mathematics everywhere—in a child's swing or a pendulum, in the outline shape of a tree and that of its leaves, in the clouds

  — Kathleen Ollerenshaw

• He who refuses to do arithmetic is doomed to talk nonsense.

  — John McCarthy

• The PC revolution has made science more visual and more immediate ...by creating films of imaginary experiences of mathematical worlds.

  — John D. Barrow

• Probability plays a central role in many fields, from quantum mechanics to information theory, and even older fields use probability now that the presence of "noise" is officially admitted. The newer aspects of many fields start with the admission of uncertainty.

  — Richard Hamming

• Mathematics is not just a language. Mathematics is a language plus reasoning.

  — Richard Feynman

• You cannot read mathematics superficially; the inescapable abstraction always has an element of self-torture in it, and the one to whom this self-torture is joy is the mathematician.

  — Rózsa Péter

• The only thing I am interested in using mathematics for is to have a good time and to help others do the same.

  — Paul Lockhart

• What one searches for in the algebraic art are the relations which lead from the known to the unknown

  — Omar Khayyám

• If you think about it long enough, you'll see that it's obvious.

  — Saul Gorn

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

  — Robert Musil

• The point, being indivisible, occupies no space. That which occupies no space is nothing. The limiting surface of one thing is the beginning of another.

  — Leonardo da Vinci

• Any progress in the theory of partial differential equations must also bring about a progress in Mechanics.

  — Carl Gustav Jacob Jacobi

• How many theorems in geometry which have seemed at first impracticable are in time successfully worked out!

  — Archimedes

• So far, all of reality seems to be described by exquisite, elegant mathematical equations. We can’t stop now – it’s got to be beautiful all the way down!

  — Katie Mack

• Nothing is that which fills no space.

  — Leonardo da Vinci

• There are times when I feel like I'm in a big forest and don't know where I'm going. But then somehow I come to the top of a hill and can see everything more clearly. When that happens, it's really exciting.

  — Maryam Mirzakhani

• There is scarcely any one who states purely arithmetical questions, scarcely any who understands them. Is this not because arithmetic has been treated up to this time geometrically rather than arithmetically?

  — Pierre de Fermat

• Mathematical and physiological researches have shown that the space of experience is simply an actual case of many conceivable cases, about whose peculiar properties experience alone can instruct us.

  — Ernst Mach

• There is no other Royal path which leads to geometry.

  — Euclid

• Mathematics in general is fundamentally the science of self-evident things.

  — Felix Klein