Quotes About Mathematics

I am not a mathematician, but I was aware that for centuries, mathematics was considered the queen of the sciences because it claimed certainty. It was grounded on some fundamental certainties - axioms - that led to others.

Imagine life without any algorithms at all, you wouldn't be able to do anything. This is already completely encompassing. We have a habit of over-trusting what mathematics or computer scientists tell us to do, without questioning it, too much faith in the magical power of analysis.

I didn't know what kinds of questions to ask in mathematics. In physics, I could see there were things that were known and things that weren't.

There's actually an awful lot of mathematics that goes into designing a railway, keeping it running, making sure everything runs optimally. Every time you need something to be optimal there's going to be some mathematics at play.

I read one or two other books which gave me a background in mathematics other than logic.

There is no royal road to geometry.

Projective geometry is all geometry.

Geometry was the first exciting course I remember.

I think about all of my students who were math-phobic, who didn't believe they could learn math, who didn't understand, who didn't think they were smart enough, and by the end, they understood that they already had the gifts, and my job was to help them access them, and I believe that.

This is a global fight to get the right people in the right place and we're talking about people with PhDs in engineering, computer science, mathematics.

Mathematics would certainly have not come into existence if one had known from the beginning that there was in nature no exactly straight line, no actual circle, no absolute magnitude.

Intersections of lines, for example, remain intersections, and the hole in a torus (doughnut) cannot be transformed away. Thus a doughnut may be transformed topologically into a coffee cup (the hole turning into a handle) but never into a pancake. Topology, then, is really a mathematics of relationships, of unchangeable, or "invariant," patterns.

The conclusion is that the physical theory and the mathematical theory of science are valid methods but not valid philosophies. Facts need interpretation the physical theory forgets that it has no such principles of interpretation with its own bosom.

The physical method becomes a philosophy when it asserts there is no higher knowledge than the empirical knowledge of scientific phenomena. The mathematical method becomes a philosophy when it asserts that some higher knowledge is needed to explain scientific facts, and that higher knowledge is mathematics.

The first part, or the Æsthetics, which has nothing in common with art, disengages the a priori forms of sensible knowledge, namely, the forms of space and time, which furnish mathematics with their object. Æsthetics thus divorced mathematics from reality, for it makes the condition of mathematics not the real, but a mental form of space and time.

Even in the realm of pure mathematics, the mathematician may use any set of symbols he desires within any given region of space-time; he may even go so far as to maintain that any one set of symbols fits the scheme as well as any other, but to erect this method into a philosophy and confuse independence of any one special meaning with independence of all meaning is unjustified and unwarranted.

The mathematical method is disinterested in the efficient cause and the final cause or the goodness of a thing and it should not be so disinterested.

Do mathematics have a relation to reality or are they only a mathematical symbol?

And, believe me, if I were again beginning my studies, I should follow the advice of Plato and start with mathematics.

Mathematics is the language with which God has written the universe.

Philosophy is written in that great book which ever lies before our eyes — I mean the universe — but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.

Philosophy is written in this all-encompassing book that is constantly open to our eyes, that is the universe; but it cannot be understood unless one first learns to understand the language and knows the characters in which it is written. It is written in mathematical language, and its characters are triangles, circles, and other geometrical figures; without these it is humanly impossible to understand a word of it, and one wanders in a dark labyrinth.

La matematica è l'alfabeto nel quale Dio ha scritto l'universo.

Mathematics is the alphabet with which God has written the universe.