Quotes by Hermann Weyl

Hermann Weyl

… numbers have neither substance, nor meaning, nor qualities. They are nothing but marks, and all that is in them we have put into them by the simple rule of straight succession.

Numbers

Simple

Simplicity

A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details.

Principles

Simple

Simplicity

Before one can generalize, formalize, and axiomatize, there must be a mathematical substance.

Mathematical

Mathematics

Substance

Besides language and music, it [mathematics] is one of the primary manifestations of the free creative power of the human mind, and it is the universal organ for world understanding through theoretical construction. Mathematics must therefore remain an essential element of the knowledge and abilities which we have to teach, of the culture we have to transmit, to the next generation.

Creative

Math

Teaching

Besides language and music, mathematics is one of the primary manifestations of the free creative power of the human mind.

Creative

Math

Mind

But it seems an irony of creation that man’s mind knows how to handle things the better the farther removed they are from the center of his existence. Thus we are cleverest where knowledge matters least.

Matter

Men

Mind

For mathematics, even to the logical forms in which it moves, is entirely dependent on the concept of natural number.

Moving

Natural

Numbers

God exists because arithmetic is consistent – the Devil exists because we can’t prove it!

Faith

God

Hope

In geometric and physical applications, it always turns out that a quantity is characterized not only by its tensor order, but also by symmetry.

Geometry

Order

Physics

It is impossible to discuss realism in logic without drawing in the empirical sciences… A truly realistic mathematics should be conceived, in line with physics, as a branch of the theoretical construction of the one real world and should adopt the same sober and cautious attitude toward hypothetic extensions of its foundation as is exhibited by physics.

Attitude

Drawing

Real

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Achievement

Art

Attitude

Beauty

Book

Brilliant

Cold

Construction

Couple

Creative

Decades

Decision

Discovery

Doctrine

Drawing

Effort

Essence

Faith

Fog

Forever

Geometry

Glory

God

Greek

Heaven

Hope

Ideas

Imagination

Infinite

Lasts

Long

Math

Mathematical

Mathematics

Matter

Men

Mind

Moving

Natural

Numbers

Order

Our Generation

Physics

Practice

Principles

Quality

Real

Reality

Science

Simple

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Quotes by Hermann Weyl

Hermann Weyl

… numbers have neither substance, nor meaning, nor qualities. They are nothing but marks, and all that is in them we have put into them by the simple rule of straight succession.

A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details.

Before one can generalize, formalize, and axiomatize, there must be a mathematical substance.

Besides language and music, mathematics is one of the primary manifestations of the free creative power of the human mind.

But it seems an irony of creation that man’s mind knows how to handle things the better the farther removed they are from the center of his existence. Thus we are cleverest where knowledge matters least.

For mathematics, even to the logical forms in which it moves, is entirely dependent on the concept of natural number.

God exists because arithmetic is consistent – the Devil exists because we can’t prove it!

In geometric and physical applications, it always turns out that a quantity is characterized not only by its tensor order, but also by symmetry.

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