Quotes About Mathematics

Mathematics is not a deductive science - that's a cliche. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.

A partir de estas definiciones, Spinoza procede por medio de pruebas euclidianas a construir un sistema determinista e irrefutable que abarca todo el universo.

JOY goes against the foundations of mathematics: it multiplies when we divide.

Any argument where one supposes an arbitrary choice to be made an uncountably infinite number of times ...[is] outside the domain of mathematics.

Arithmetic has a very great and elevating effect, compelling the soul to reason about abstract number, and rebelling against the introduction of visible or tngible objects into the argument.

An ounce of algebra is worth a ton of verbal argument.

Geometry is the art of correct reasoning from incorrectly drawn figures.

Mathematics is an art of human understanding.

Every education system on Earth has the same hierarchy of subjects: at the top are mathematics and languages, then the humanities, and the bottom are the arts.

Mathematics is really an art, not a science.

A mathematical point is the most indivisble and unique thing which art can present.

Our thoughts, our language, are always at a distance from whatever they're trying to describe. We have other kinds of languages, like mathematics, like music, like art, but there's always that gap.

It can be argued that the mathematics behind these images [of the orbit diagram for quadratic functions and the Mandelbrot set] is even prettier than the pictures themselves.

I guess I can put two and two together." "Sometimes the answer's four," I said, "and sometimes it's twenty-two.

It is in the world of things and places, times and troubles and turbid processes, that mathematics is not so much applied as illustrated.

If the calculus is much like a cathedral, its construction the work of centuries, it remained until the nineteenth century a cathedral suspiciously suspended in midair, the thing simply hanging there, with no one absolutely convinced that one day the gorgeous and elaborate structure would not come crashing down and fracture in a thousand pieces.

Alan Turing appears to be becoming a symbol of the shift towards computing, not least because of his attitude of open-minded defiance of convention and conventional thinking. Not only did he conceptualise the modern computer – imagining a simple machine that could use different programmes – but he put his thinking into practice in the great code breaking struggle with the Nazis in World War II, and followed it up with pioneering early work in the mathematics of biology and chaos.

While reading a book about the construction of the Panama Canal, I came across an anecdote about the project's chief engineer, whose math teacher used to say, "If you have five minutes to solve a problem, use the first three to figure out how you're going to do it.

The core accounting equation A = L + E can be dissolved and reshuffled into everything from E = A - L to beyond.

that traversing an infinite number of dimensionless mathematical points is not obviously paradoxical in the way that traversing an infinite number of physical-space points is.

Respecting infinite sets, for example, Intuitionism is rabidly anti-Cantor and Formalism staunchly pro-Cantor, even though both Formalism and Intuitionism are anti-Plato and Cantor is a diehard Platonist. Which, migrainous or not, means we're back to metaphysics: the modern wrangle over math's procedures is ultimately a dispute over the ontological status of math entities.

It was the Greeks who turned math into an abstract system, a special symbolic language that allows people not just to describe the concrete world but to account for its deepest patterns and laws.

Cantor's discovery that lines, planes, cubes, and polytopes were all equivalent as sets of points goes a long way toward explaining why set theory was such a revolutionary development for math-revolutionary in theory and practice both.

To make a long story short, Cantorian set theory helps unify and clarify math in the sense that all mathematical entities can now be understood as fundamentally the same kind of thing-a set.