Quotes on Mathematical

The research worker, in his efforts to express the fundamental laws of Nature in mathematical form, should strive mainly for mathematical beauty. He should take simplicity into consideration in a subordinate way to beauty ... It often happens that the requirements of simplicity and beauty are the same, but where they clash, the latter must take precedence.

Prayers for the condemned man will be offered on an adding machine. Numbers constitute the only universal language.

One factor that has remained constant through all the twists and turns of the history of physical science is the decisive importance of the mathematical imagination.

If we possessed a thorough knowledge of all the parts of the seed of any animal (e.g. man), we could from that alone, be reasons entirely mathematical and certain, deduce the whole conformation and figure of each of its members, and, conversely if we knew several peculiarities of this conformation, we would from those deduce the nature of its seed.

Geometry enlightens the intellect and sets one's mind right. All of its proofs are very clear and orderly. It is hardly possible for errors to enter into geometrical reasoning, because it is well arranged and orderly. Thus, the mind that constantly applies itself to geometry is not likely to fall into error. In this convenient way, the person who knows geometry acquires intelligence.

When we ask for advice, we are usually looking for an accomplice.

The world needs heroes and it's better they be harmless men like me than villains like Hitler

The temptation to believe that the Universe is the product of some sort of design, a manifestation of subtle aesthetic and mathematical judgment, is overwhelming. The belief that there is "something behind it all" is one that I personally share with, I suspect, a majority of physicists.

The core of science is not a mathematical modeling--it is intellectual honesty. It is a willingness to have our certainties about the world constrained by good evidence and good argument.

We must admit with humility that, while number is purely a product of our minds, space has a reality outside our minds, so that we cannot completely prescribe its properties a priori.

To a person of analytical ability, perceptive enough to realise that mathematical equipment was a powerful sword in economics, the world of economics was his or her oyster in 1935. The terrain was strewn with beautiful theorems begging to be picked up and arranged in unified order.

It is the first duty of a hypothesis to be intelligible.

The whole is more than the sum of its parts.

Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.

The apex of mathematical achievement occurs when two or more fields which were thought to be entirely unrelated turn out to be closely intertwined. Mathematicians have never decided whether they should feel excited or upset by such events.

First, it is necessary to study the facts, to multiply the number of observations, and then later to search for formulas that connect them so as thus to discern the particular laws governing a certain class of phenomena. In general, it is not until after these particular laws have been established that one can expect to discover and articulate the more general laws that complete theories by bringing a multitude of apparently very diverse phenomena together under a single governing principle.

One cannot really argue with a mathematical theorem.

I protest against the use of infinite magnitude ..., which is never permissible in mathematics.

Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them.

Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.

There still remain three studies suitable for free man. Arithmetic is one of them.