Mejor, hablemos del tiempo

porque como me tires de la lengua…

Nothing I have ever done is of the slightest practical use

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En La música de los números primos el matemático G. H. Hardy, a través de sus colaboraciones con Littlewood y también con Ramanujan, juega un papel bastante importante como hilo conductor de la historia a principios del siglo XX. Y como hacen varias referencias a su libro Apología de un matemático, al final decidí leermelo.

No es de extrañar que me haya gustado más la introducción de C. P. Snow que el texto de Hardy en sí (además, vienen a ser de una longitud similar), ya que Snow cuenta un montón de batallitas tanto matemáticas (muchas empleadas luego por Marcus du Sautoy en su libro) como personales:

Hardy, always inept about introducing a conversation, said, probably without a greeting, and certainly as his first remark: ‘I thought the number of my taxi cab was 1729. It seemed to me rather a dull number.’ To which Ramanujan replied: ‘No, Hardy! No, Hardy! It is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways.’

1729 = 13 + 123 = 103 + 93

Por el contrario, el texto en defensa del trabajo de matemático, aunque está bien, es bastante más seco y tampoco me parece ninguna maravilla. Sobre todo, he echado en falta más hincapié en torno a la idea de universalidad de las matemáticas:

A chair or a star is not in the least like what it seems to be; the more we think of it, the fuzzier its outilines become in the haze of sensation which surrounds it; but ‘2’ or ‘317’ has nothing to do with sensation, and its properties stand out the more clearly the more closely we scrutinize it. It may be that modern physics fits best into some framework of idealistic philosophy — I do not believe it, but there are eminent physicists who say so. Pure mathematics, on the other hand, seems to me a rock on which all idealism founders: 317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way.

El caso es que Hardy deja bien claro que las matemáticas no necesitan defensa alguna. Veamos entonces el matemático en sí. Ya nos advierte Snow:

He was glad that I had gone back to writing books: the creative life was the only one for a serious man.

Y continúa Hardy, quien a pesar de su gran talento para las matemáticas, creo que también hubiera hecho una labor destacable en un departamento de recursos humanos:

A man who is always asking ‘Is what I do worth while?’ and ‘Am I the right person to do it?’ will always be ineffective himself and a discouragement to others.

A man who sets out to justify his existence and his activities has to distinguish two different questions. The first is whether the work which he does is worth doing; and the second is why he does it, whatever its value may be. […] Their answers, if they are honest, will usually take one or other of two forms […]

(1) ‘I do what I do because it is the one and only thing that I can do at all well. I am a lawyer, or a stockbroker, or a proffesional cricketer, because I have some real talent for that particular job. […] I agree that it might be better to be a poet or a mathematician, but unfortunately I have no talent for such pursuits.’
I am not suggesting that this is a defence which can be made by most people, since most people can do nothing well at all. […] It is a tiny minority who can do anything really well, and the number of men who can do two things well is negligible. If a man has any genuine talent, he should be ready to make almost any sacrifice in order to cultivate it to the full.

(2) ‘There is nothing that I can do particularly well. I do what I do because it came my way. I really never had a chance of doing anything else.’ And this apology too I accept as conclusive. Is it quite true that most people can do nothing well. If so, it matters very little what career they choose, and there is really nothing more to say about it. It is a conclusive reply, but hardly one likely to be made by a man with any pride; and I may assume that none of us would be content with it.

A man’s first duty, a young man’s at any rate, is to be ambitious. […] the noblest ambition is that of leaving behind one something of permanent value. […] There are many highly respectable motives which may lead men to prosecute research, but three which are much more important than the rest. The first (without which the rest must come to nothing) is intellectual curiosity, desire to know the truth. Then, professional pride, anxiety to be satisfied with one’s performance. Finally, ambition, desire for reputation, and the position, even the power of money, that it brings. It may be fine to feel, when you have done your work, that you have added to the happiness or alleviated the sufferings of others, but that will not be why you did it.

If these are the dominant incentives to research, then assuredly no one has a fairer chance of gratifying them than a mathematician. His subject is the most curious of all — there is none in which truth plays such odd pranks. It has the most elaborate and the most fascinating technique, and gives unrivalled openings for the display of sheer professional skill. Finally, as history proves abundantly, mathematicial achievement, whatever its intrinsic worth, is the most enduring of all.

Luego entra a discutir la utilidad de las matemáticas, e incluso se plantea si las matemáticas pueden considerarse dañinas para la humanidad (Durante la Primera Guerra Mundial, Littlewood dejó sus investigaciones para unirse al cuerpo de balística, doctrina matemática que sirve para matar a la gente. Aunque, bien visto, matar a la gente de un tiro parece menos cruel que matarles a base de golpes con una piedra — o una cucharilla, puestos al caso). Después, sobre la utilidad, pone un par de ejemplos de teoremas chorras de curiosidades de las que a mí me encantan, pero justo para decir que las matemáticas, las de verdad, además de bellas tienen que ser serias. Y a partir de ahí el libro se me hizo un poco cuesta arriba y dejé de tomar notas. Tendré que investigar, en cambio, Mathematical Recreations de Rouse Ball:

(a) 8712 and 9801 are the only four-figure numbers which are integral multiples of their ‘reversals’:

8712 = 4 * 2178
9801 = 9 * 1089

(b) There are just four numbers (after 1) which are the sums of the cubes of their digits, viz.

153 = 13 + 53 + 33
370 = 33 + 73 + 03
371 = 33 + 73 + 13
407 = 43 + 03 + 73

These are odd facts, very suitable for puzzle columns and likely to amuse amateurs, but there is nothing in them which appeals much to a mathematician.

Jo, pues a mí me intriga saber quién averiguó eso, y qué estaba haciendo para encontrarlo…

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