Norbert Wiener (Ex- Prodigy & I am a Mathematician)
When Pythagoras discovered the theorem of the right triangle, he sacrificed a hundred oxen; since then, whenever a new truth is unveiled, all oxen tremble.(Also Ludwig Borne)
Epur si muove – And yet it does move(Galileo)
When I returned to Cambridge as a mature mathematician after working with engineers for years, Hardy used to claim that the engineering phraseology of much of my mathematical work was a humbug, and that I had employed it to curry favor with my engineering friends at Massachusetts Institute of Technology. He thought I was really a pure mathematician in disguise, and that these other aspects of my work were superficial. This, is fact has not been the case. The very same ideas that may be employed in that Limbo of the Sages known as number theory are potent tools in the study of the telegraph and the telephone and the radio. No matter how innocent he may be in his inner soul and in his motivation, the effective mathematician is likely to be a powerful factor in changing the face of the society. Thus he is really dangerous as a potential armorer of the new scientific war of the future. He may hate this, but he does less than his full duty if he does not face these facts.
I found the Cambridge environment far more sympathetic to me than I had foung that of harvard. Cambridge was devoted to the intellect. The pretense of lack of interest in intellectual matters which had been a sine qua non of life of respectable Harvard scholar was only a convention and an interesting game at Cambridge, where the point was to qwork as hard as you could in private while pretending to exhibit a superiors indifference. Furthermore, Harvard has always been hated the eccentric and the individual, while, as I have said, in Cambridge eccentricity is so highly valued that those who do not really possess it are forced to assume it for the sake of appearances.
Mathematics is too arduous and uninviting a field to appeal to those to whom it does not give great rewards. These rewards are of exactly the same character as those of the artist. To see a difficult uncompromising material take living shape and meaning is to be Pygmalion, whether the material is stone or hard, stone-like logic. To see meaning and understanding come where there has been no meaning and no understanding is to share the work of a demiurge. No amount of technical correctness and no amount of labour can replace this creative moment, whether in the life of a mathematician or of a painter or musician. Bound up with it is a judgment of values, quite parallel to the judgment of values that belongs to the painter or the musician. Neither the artist nor the mathematician may be able to tell you what constitutes the difference between a significant piece of work and an inflated trifle; but if he is not able to recognise this in his own heart, he is no artist and no mathematician.
We surmised that life was to be such a nightmare as Kafka has since described, form which one awakes only to become aware that the nightmare is real, or from which one awakes into an even worse nightmare.
This, together with Fermat’s last theorem and the demonstration of Riemann’s hypothesis concerning the Zeta function, is one of the perennial puzzlers of mathematics. Every mathematician who is worth his salt has broken a lance on atleast one of them. I have tried solving all three, and each time my supposed proof has crumpled into fool’s gold in my hands. I do not regret my attempts, for it is only by trying problems that exceed his powers that the mathematician can ever learn how to use these powers to their full extent.
If I am to speak Spanish effectively, I must think in Spanish and I cannot be tempted to translate out of an English phrase book. I must say the sort of things that a Spanish-speaking person would say, and these are never precisely the same as those which an English- speaking person would say.
All true research is a gamble, and the payoff is anything but prompt. A fellowship is a longterm investment in a man, not a sight draft or paper collectible twelve months from issue. Creativity cannot be hurried, and Clio takes her time in Handing out the awards.
It was at M.I.T. too that my ever- growing interest in the physical aspects of mathematics began to take definite shape. The school buildings overlook the River Charles and command a never changing skyline of such beauty. The moods of the waters of the river were always delightful to watch. To me, as a mathematician and a physicist, they had another meaning as well. How could one bring to a mathematical regularity the study of the mass of ever shifting ripples and waves, for was not the highest destiny of mathematics the discovery of order among disorder? At one time the waves ran high, flecked with patches of foam, while at another they were barely noticeable ripples. Sometimes the lengths of the waves were to be measured in inches, and again they might be many yards long. What descriptive language could I use that would portray these clearly visible facts without involving me in the inextricable complexity of a complete description of the water surface?
To understand the Brownian motion, let us imagine a pushball in a field in which a crowd is milling around. Various people in the crowd will run into the pushball and will move it about. Some will push in one direction and some in another, and the balance of pushes is likely to be tolerably even. Nevertheless, notwithstanding these balanced pushes, the fact remains that they are pushes by individual people and that their balance will be only approximate. Thus, in the course of time, the ball will wander about the field like the drunken man whom we have already mentioned and we shall have a certain irregular motion in which what happens in the future will have very little to do with what has happened in the past.
The stir that a paper makes depends not only on its inner merits but on the interested of the other workers in the fields… At any rate, I was too committed to this field to accept the mandates of the new fashion.
I categorically deny this cold and rigid concept of mathematics. A piece of mathematics may have the virtues of logic and rigor yet, in the technical opinion of the trained observer, it may be insensitive and purely formal. To other mathematicians, the task of the mathematician is to use a rigid and demanding medium to express a new and significant vision of some aspects of the universe; to express apercus which reveals something new and something exciting. If his medium is strict and confining, so are in fact the media of all creative artists. The counterpoint of the musician does not interfere with his perceptivity, nor is a poet less free because his language has a grammar or his sonnets a form. To be free to do anything whatever is to be free to do nothing.
In the early years of the alternating current, there was a battle royal between the Westinghouse people who owned the alternating current inventions, and the General Electric and Edison people, who had invested heavily in direct-current engineering. Thus quarrel had one of its consequences the fact that New York State decided to execute criminals by alternating current. This was the result of a deal put through by legislature in order to give a bad name to the supposedly more dangerous alternating current and to make people unwilling to have this introduced into their houses.
I did not realise at that time how carefully many professors conserve problems for their own graduate students and how sharply they regard proprietary rights in new problems. I had been used to freer atmosphere of England…
…was Swift’s famous jingle:
So, Naturalists observe, a flea
Hath smaller fleas that on him prey;
And these have smaller still to bite’em;
And so proceed ad infinitum.
It has been well said that the modern physicist is a quantum theorist on Monday, Wednesday, and Friday and a student of gravitational relativity theory on Tuesday, Thursday, and Saturday. On Sunday the physicist is neither, but is praying to his God that someone, preferably himself, will find the reconciliation between the two views.
(Koebe)On one occasion, when he had visited Da Vinci’s horribly mutilated painting of the Last Supper, he is supposed to have said: “How sad! This painting will pass away, while my theorem concerning the uniformisation of analytic functions will endure forever.”
During the Christmas vacation. Paley did a little skiing in the Adirondacks with an Irish friend who, I think was another Commonwealth fellow, and after skiing was over they continued to Montreal. I believe they almost wrecked their car in Adirondacks, and they got entangled with a group of New York gangsters who had moved to Montreal during prohibition. Paley came home to Boston rather thrilled than chastened.
Hadamard told us a delightful story about his own youth, when he felt a certain disfavour form his more conservative colleagues because of his kinship with the wife of Colonel Dreyfus. With the Dreyfus affair exciting all France to great emotional heights, everyone was either an ardent Dreyfusard or an ardent anti- Dreyfusard. Among the latter was the great mathematician Hermite, who was to examine the young Handamard for his doctorate. Hadamard approached this occasion with fear and trembling, and this embarrassment was not relieved when the old gentleman said to him, “M. Hadamard, you are a traitor!”Hadamard fumbled something in confusion, and Hermite went on to say, “You have deserted geometry for analysis”
We are running upstream against a great torrent of disorganisation, which tends to reduce everything to the heat-death of equilibrium and sameness… Like the Red Queen, we cannot stay where we are without running as fast as we can.
We are fighting for a definitive victory in the indefinite future. It is the greatest possible victory to be, to continue to be, and to have been.
Communication is the cement of society. Society does not consist merely in a multiplicity of individuals, meeting only in personal strife and for the sake of procreation, but in an intimate interplay of these individuals in a larger organism.
The limiting case of the great scientific institution, by which we may test the soundness of the principles on which it acts, is the writing shop of the monkeys and the typewriter which, in the course of the ages, will almost certainly succeed in making every possible combination of the letters of the alphabet and the words in the dictionary. To say that the monkey’s work will contain the works of Shakespeare has no other sense than to say that a black of marble will contain a statue of Michelangelo.