It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences.
I chose to deal with the science of cryptography. Cryptography began in mathematics. Codes were developed, even from Caesar's time, based on number theory and mathematical principles. I decided to use those principles and designed a work that is encoded.
I was a mathematician by nature, and still am - I just knew I didn't want to be a mathematician. So I decided not to take any mathematics courses.
The problem is that no ethical system has ever achieved consensus. Ethical systems are completely unlike mathematics or science. This is a source of concern.
Now being in such grace and favor by reason I learned him some points of geometry and understanding of the art of mathematics with other things, I pleased him so that what I said he would not contrary.
In my schooling through high school, I excelled mainly in chemistry, physics and mathematics.
In Libya, I did well at school because I was clever. In Egyptian public school, I got the highest marks for the basest of reasons. And in the American school, I struggled. Everything - mathematics, the sciences, pottery, swimming - had to be conducted in a language I hardly knew and that was neither spoken in the streets nor at home.
An early fascination with higher mathematics at the university level blossomed into speculative thinking that could provide a basis for dealing with economic issues.
I finally reached the conclusion that mathematics was the study I was best fitted to follow, though I did not clearly see in what way I should turn the subject to account.
My interest in the sciences started with mathematics in the very beginning, and later with chemistry in early high school and the proverbial home chemistry set.
I was on the mathematics faculty at M.I.T. from 1951 through until I resigned in the spring of 1959.
Being exposed to theory, stimulated by a basic love of concepts and mathematics, was a marvelous experience.
I had an excellent math and physics teacher in high school named T.C. Patel, and in the university, I had truly dedicated professors in both physics and mathematics who gave me a sound foundation with which to pursue graduate studies.
I can do lightning mathematics quicker than somebody can do them on a calculator.
Logic and mathematics are nothing but specialised linguistic structures.
What affected me most profoundly was the realization that the sciences of cryptography and mathematics are very elegant, pure sciences. I found that the ends for which these pure sciences are used are less elegant.
When I was a college student at Yale, I was studying physics and mathematics and was absolutely intent on becoming a theoretical physicist.
If I were again beginning my studies, I would follow the advice of Plato and start with mathematics.
All science requires mathematics. The knowledge of mathematical things is almost innate in us. This is the easiest of sciences, a fact which is obvious in that no one's brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.
If indeed, as Hilbert asserted, mathematics is a meaningless game played with meaningless marks on paper, the only mathematical experience to which we can refer is the making of marks on paper.
The object of pure physics is the unfolding of the laws of the intelligible world; the object of pure mathematics that of unfolding the laws of human intelligence.
Consequently he who wishes to attain to human perfection, must therefore first study Logic, next the various branches of Mathematics in their proper order, then Physics, and lastly Metaphysics.
Reading music is something that's inherently hateful to me. It makes music like mathematics.
Well, some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve.
Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
From the ages of five to twelve, I attended the Saint Laurence O'Toole elementary school in Lawrence, a city next to Methuen, and was taught by sisters of the Catholic order of Notre Dame de Namour. I enjoyed all my subjects there. I do not remember ever learning any science, except for mathematics.
Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.
The most painful thing about mathematics is how far away you are from being able to use it after you have learned it.
The longer mathematics lives the more abstract - and therefore, possibly also the more practical - it becomes.
Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.
The Theory of Groups is a branch of mathematics in which one does something to something and then compares the result with the result obtained from doing the same thing to something else, or something else to the same thing.
Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.
If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability.
All mathematics is is a language that is well tuned, finely honed, to describe patterns; be it patterns in a star, which has five points that are regularly arranged, be it patterns in numbers like 2, 4, 6, 8, 10 that follow very regular progression.
I grew up in Adelaide, Australia. No one in my family had finished high school, and I was smart at mathematics, so I became an academic and got my Ph.D. in computer science at Stanford. I didn't set out to be a businessperson.
In mathematics the art of proposing a question must be held of higher value than solving it.
