Quotes on Mathematical

Mathematics is a more powerful instrument of knowledge than any other that has been bequeathed to us by human agency.

Naturally, we are inclined to be so mathematical and calculating that we look upon uncertainty as a bad thing...Certainty is the mark of the common-sense life. To be certain of God means that we are uncertain in all our ways, we do not know what a day may bring forth. This is generally said with a sigh of sadness; it should rather be an expression of breathless expectation.

Mathematics as a science, commenced when first someone, probably a Greek, proved propositions about "any" things or about "some" things, without specifications of definite particular things.

To emphasize only the beautiful seems to me to be like a mathematical system that only concerns itself with positive numbers.

His epitaph: Who, by vigor of mind almost divine, the motions and figures of the planets, the paths of comets, and the tides of the seas first demonstrated.

Thou shalt not answer questionnaires Or quizzes upon world affairs, Nor with compliance Take any test. Thou shalt not sit with statisticians nor commit A social science.

In the 1940s, economics started getting highly mathematical. It was basically because economists weren't smart enough to write down models of real behavior that they started writing down models of highly rational behavior - and they kind of forgot about humans.

My suggestion is that at each state the proper order of operation of the mind requires an overall grasp of what is generally known, not only in formal logical, mathematical terms, but also intuitively, in images, feelings, poetic usage of language, etc.

In all affairs it's a healthy thing now and then to hang a question mark on the things you have long taken for granted.

The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It's like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design.

An expert is a man who has made all the mistakes which can be made, in a narrow field.

What I love about cooking is that after a hard day, there is something comforting about the fact that if you melt butter and add flour and then hot stock, it will get thick! It's a sure thing! It's a sure thing in a world where nothing is sure; it has a mathematical certainty in a world where those of us who long for some kind of certainty are forced to settle for crossword puzzles.

...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.

'When I use a word,' Humpty Dumpty said in rather a scornful tone, 'it means just what I choose it to mean - neither more nor less.'

The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.

For me, I guess the main motivation is the satisfaction of finally understanding some tricky mathematical concept or phenomenon and then explaining it to others.

Look somewhere else for someone who can follow you in your researches about numbers. For my part, I confess that they are far beyond me, and I am competent only to admire them.

It is generally believed that our science is empirical and that we draw our concepts and our mathematical constructs from the empirical data. If this were the whole truth, we should, when entering into a new field, introduce only such quantities as can directly be observed, and formulate natural laws only by means of these quantities.

One cannot inquire into the foundations and nature of mathematics without delving into the question of the operations by which the mathematical activity of the mind is conducted. If one failed to take that into account, then one would be left studying only the language in which mathematics is represented rather than the essence of mathematics.

Those who are accustomed to judge by feeling do not understand the process of reasoning, because they want to comprehend at a glance and are not used to seeking for first principles. Those, on the other hand, who are accustomed to reason from first principles do not understand matters of feeling at all, because they look for first principles and are unable to comprehend at a glance.

It is quite clear that beauty does depend on one's culture and upbringing for certain kinds of beauty, pictures, literature, poetry and so on...But mathematical beauty is of a rather different kind. I should say perhaps it is of a completely different kind and transcends these personal factors. It is the same in all countries and at all periods of time.