A Quote by L. E. J. Brouwer

Beyond the natural numbers, addition, multiplication, and mathematical induction are intuitively clear.

L. E. J. Brouwer

Quote Topics

Addition Beyond Clear Mathematical Multiplication Natural Numbers

Quote Author

L. E. J. Brouwer
Dutch - Mathematician
February 27, 1881 - December 2, 1966

... in going over the history of all the inventions for which history could be obtained it became more and more clear that in addition to training and in addition to extensive knowledge, a natural quality of mind was also necessary.

Reginald Fessenden

What a mathematical proof actually does is show that certain conclusions, such as the irrationality of , follow from certain premises, such as the principle of mathematical induction. The validity of these premises is an entirely independent matter which can safely be left to philosophers.

Timothy Gowers

An old French mathematician said: "A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street." This clearness and ease of comprehension, here insisted on for a mathematical theory, I should still more demand for a mathematical problem if it is to be perfect; for what is clear and easily comprehended attracts, the complicated repels us.

David Hilbert

With four? Doing a little... Addition? Multiplication?

Veronica Roth

The kind of knowledge which is supported only by observations and is not yet proved must be carefully distinguished from the truth; it is gained by induction, as we usually say. Yet we have seen cases in which mere induction led to error. Therefore, we should take great care not to accept as true such properties of the numbers which we have discovered by observation and which are supported by induction alone. Indeed, we should use such a discovery as an opportunity to investigate more exactly the properties discovered and to prove or disprove them; in both cases we may learn something useful.

Leonhard Euler

Life isn't just addition and subtraction. There's also the accumulation, the multiplication, of loss, of failure.

Julian Barnes

There is no division nor subtraction in the heart-arithmetic of a good mother. There are only addition and multiplication.

Bess Streeter Aldrich

In the Middle Age, in Germany, if you wanted to learn addition and multiplication, you could go to any university. But if you wanted to learn division, you could only do it in one place, Heidelberg. This makes sense, since in my theory with Vladimir Retakh and Robert Wilson, addition and multiplications are cheap, but division is expensive.

Israel Gelfand

It is time, therefore, to abandon the superstition that natural science cannot be regarded as logically respectable until philosophers have solved the problem of induction. The problem of induction is, roughly speaking, the problem of finding a way to prove that certain empirical generalizations which are derived from past experience will hold good also in the future.

A.J. Ayer

The world looks like a multiplication-table, or a mathematical equation, which, turn it how you will, balances itself.

Ralph Waldo Emerson

I will calmly wait for my induction to the Baseball Hall of Fame. Don't I have the numbers to be inducted?

Sammy Sosa

All the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers.

James C. Maxwell

The mathematical phenomenon always develops out of simple arithmetic, so useful in everyday life, out of numbers, those weapons of the gods: the gods are there, behind the wall, at play with numbers.

Le Corbusier

The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work-that is, correctly to describe phenomena from a reasonably wide area.