A Quote by Stanislaw Ulam
In many cases, mathematics is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from external affairs. Some practice it as if using a drug.
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When the world is mad, a mathematician may find in mathematics an incomparable anodyne. For mathematics is, of all the arts and sciences, the most austere and the most remote, and a mathematician should be of all men the one who can most easily take refuge where, as Bertrand Russell says, "one at least of our nobler impulses can best escape from the dreary exile of the actual world."
Pathology has made us acquainted with a great number of states in which the boundary lines between the ego and the external world become uncertain or in which they are actually drawn incorrectly. There are cases in which parts of a person's own body, even portions of his own mental life - his perceptions, thoughts and feelings -, appear alien to him and as not belonging to his ego; there are other cases in which he ascribes to the external world things that clearly originate in his own ego and that ought to be acknowledged by it.
The man who accepts Western values absolutely, finds his creative faculties becoming so warped and stunted that he is almost completely dependent on external satisfactions, and the moment he becomes frustrated in his search for these, he begins to develop neurotic symptoms, to feel that life is not worth living, and, in chronic cases, to take his own life.
If a mathematician wishes to disparage the work of one of his colleagues, say, A, the most effective method he finds for doing this is to ask where the results can be applied. The hard pressed man, with his back against the wall, finally unearths the researches of another mathematician B as the locus of the application of his own results. If next B is plagued with a similar question, he will refer to another mathematician C. After a few steps of this kind we find ourselves referred back to the researches of A, and in this way the chain closes.
The Islamic world is suffering not only because of external oppression but also because of the loss of its own dignity, of its own heritage, of its own practice of Islam, of its weakening of its own ethics, and many things which are internal to Islam not just external.
On foundations we believe in the reality of mathematics, but of course, when philosophers attack us with their paradoxes, we rush to hide behind formalism and say 'mathematics is just a combination of meaningless symbols,'... Finally we are left in peace to go back to our mathematics and do it as we have always done, with the feeling each mathematician has that he is working with something real. The sensation is probably an illusion, but it is very convenient.
We're going to show great heart. DACA is a very, very difficult subjects, one of the most difficult. You have these incredible kids in many cases, not in all cases, in some of the cases they are gang members and drug dealers, too. But you have some absolutely incredible kids, I would say mostly. They were brought here in such a way, it's a very, very tough subject.
People that are that good at motivating and inspiring are rare. In many cases, you wish it was parents, and in many cases it is, but in a lot of cases it happens outside the family as well - or, in some cases, only.
When the mathematician says that such and such a proposition is true of one thing, it may be interesting, and it is surely safe. But when he tries to extend his proposition to everything, though it is much more interesting, it is also much more dangerous. In the transition from one to all, from the specific to the general, mathematics has made its greatest progress, and suffered its most serious setbacks, of which the logical paradoxes constitute the most important part. For, if mathematics is to advance securely and confidently, it must first set its affairs in order at home.
To criticize mathematics for its abstraction is to miss the point entirely. Abstraction is what makes mathematics work. If you concentrate too closely on too limited an application of a mathematical idea, you rob the mathematician of his most important tools: analogy, generality, and simplicity. Mathematics is the ultimate in technology transfer.
I don't think that everyone should become a mathematician, but I do believe that many students don't give mathematics a real chance. I did poorly in math for a couple of years in middle school; I was just not interested in thinking about it. I can see that without being excited mathematics can look pointless and cold. The beauty of mathematics only shows itself to more patient followers.
May not music be described as the mathematics of the sense, mathematics as music of the reason? The musician feels mathematics, the mathematician thinks music: music the dream, mathematics the working life.
It is indubitable that a 50-year-old mathematician knows the mathematics he learned at 20 or 30, but has only notions, often rather vague, of the mathematics of his epoch, i.e. the period of time when he is 50.
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 future seems a little gloomy! Go to bed early, sleep well, eat moderately at breakfast; the future looks brighter. The world's outlook may not have changed, but our capacity for dealing with it has. Happiness, or unhappiness, depends to some extent on external conditions, but also, and in most cases chiefly, on our own physical and mental powers. Some people would be discontented in Paradise, others ... are cheerful in a graveyard.
The desire to explore thus marks out the mathematician. This is one of the forces making for the growth of mathematics. The mathematician enjoys what he already knows; he is eager for more knowledge.
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