[Eng] G•H•Hardy: A Mathematician’s Apology

12,076 characters2007.07.16

[Eng]G·H·Hardy: A Mathematician’s Apology, translated by Wang Xiyong, Commercial Press, April 2007, 8 yuan

Page5 Preface (C·P· Snow) When A Mathematician’s Apology first appeared, Graham Greene wrote in a review that, like Henry James’s handwriting, this book portrayed no less well what a creative artist is like.

Page46 For a professional mathematician, finding himself writing about mathematics is a dispiriting experience. A mathematician’s role is to do mathematical things, to prove new theorems and add them to mathematics, not to talk about what he or other mathematicians have done. Politicians look down on political commentators, painters despise art critics, and physiologists, physicists, or mathematicians often feel the same way; there is no more profound, or on the whole more justified, contempt than that borne for interpreters. Interpretation, judgment, and appreciation are the work of second-rate minds.////——The work of so-called “science studies” is precisely this sort of work, which scientists so profoundly and reasonably “despise.” I agree with Hardy’s view—interpretation, judgment, and appreciation are the work of second-rate minds. Lacking the ability to become a scientist, I will therefore forever retain my admiration for scientists. Of course, even with such self-mockery, Hardy still wrote this book; in any case, this sort of work is not entirely without meaning or pleasure.

Page58~59 There may be many highly respectable motives that lead people to undertake research, but there are three that are more important than the others. The first—and without it the others scarcely deserve mention—is intellectual curiosity, the desire to know the truth. Then comes pride in one’s profession, the anxiety to be satisfied with one’s performance, the shame felt by any self-respecting craftsman when his work falls short of his ability. Finally there is ambition: the desire to gain fame, status, and even the power or money it brings. When you have finished your work and feel that you have increased the happiness of others or lessened their pain, that may be very gratifying, but it is not why you do the work. So if a mathematician, or a chemist, or even a physiologist, tells me that the driving force of his work is the desire to benefit humanity, I shall not believe him (and even if I did believe him, I should not think much better of him for having such a desire). His dominant motive is what I have already stated. Of course, there is nothing here that should make an honest person ashamed to think this way.////——Like artists, what scientists pursue is entirely “personal”; this is not to say that scientists do not need to take account of society and others’ interests, but such consideration is only ethical and negative in nature—that is, scientists should bear some responsibility for the adverse consequences their research causes and do their best to avoid them, but in any case this consideration is by no means the true motive of scientific research.

Page63 Here I must refute a mistaken idea that is still widely circulated (though perhaps far less widely than twenty years ago), namely Whitehead’s “literati superstition”: that the love of mathematics and aesthetic appreciation are “an obsession confined to a handful of eccentrics in every age.” …………The fact is that there are few subjects more “popular” than mathematics. Most people can appreciate a little mathematics, just as most people can enjoy a lively tune;

Page72 First, in terms of seriousness, the superiority of mathematical theorems is obvious and immense. Chess problems are merely the product of ingenious but very limited combinations of thought, with no fundamental differences among them, and they have no effect on anything outside chess. Even if chess had never been invented, we would still think in much the same way, whereas Euclid’s theorem and the Pythagorean theorem have profoundly influenced thought even outside mathematics.

Page97 So there are two kinds of mathematics. There is the real mathematics of real mathematicians, and there is what I call “ordinary” mathematics, because there is no better word available. Ordinary mathematics can be defended by the arguments of Hobson or other writers of his school, but real mathematics cannot be defended in such a way. If it can be defended at all, then it can only be defended as art. There is not the slightest contradiction or strangeness in this view; it is a view commonly held by mathematicians.////——“If it can be defended at all, then it can only be defended as art. There is not the slightest contradiction or strangeness in this view; it is a view commonly held by mathematicians.”

Page97~98 For the real mathematician there is one comforting conclusion: real mathematics has no use in war. No one has found number theory or relativity to have been used for military purposes, and it seems unlikely that anyone will do so years from now. …………So a real mathematician has a clear conscience, and nothing can diminish the value of his work. Doing mathematical research, as I said when I was at Oxford, is an “innocuous and innocent” profession.////——Not even “years from now”: not long after this book was published in 1940 (Hardy died in 1947), number theory, in the form of “cryptography,” and relativity, in the form of the atomic bomb, profoundly affected modern warfare. What would Hardy have thought?

July 16, 2007

UNIC

2007-07-16 21:48:08 Anonymous 124.117.17.185 [Reply]

“Finally there is ambition: the desire to gain fame, status, and even the power or money it brings.”
———-Artists can be beings who judge themselves according to a faith of pursuing “art.” Or one might say, “God.” This intangible, ever-present testing is somewhat like the second point he mentioned. However, I think that, in fact, just like scientists, for artists too, at times the source of recognition is detached from the masses, which directly makes the pursuit of so-called fame and profit simply become useless, without any reason.

UNIC

2007-07-16 21:53:49 Anonymous 124.117.17.185 [Reply]

“Like artists, what scientists pursue is entirely “personal”; this is not to say that scientists do not need to take account of society and others’ interests, but such consideration is only ethical and negative in nature—that is, scientists should bear some responsibility for the adverse consequences their research causes and do their best to avoid them, but in any case this consideration is by no means the true motive of scientific research.”
____________________I still believe that there are artists and scientists who take the interests of the public or the people as their own duty. It is diverse: some are purely personal, and some are very broad-minded and philanthropic—it depends on what science/art means in their eyes.
Hardy was too absolute, but the innocent are without blame.
But the excerpt above is your own words, right? ~~~~

UNIC

2007-07-16 21:59:50 Anonymous 124.117.17.185 [Reply]

If it can be defended at all, then it can only be defended as art.
I hope this sentence has not the slightest meaning of belittling art.

Gǔ Chù

2007-07-16 22:30:46 http://epr.ycool.com/ [Reply]

Hardy did not belittle art; rather, like many other pure mathematicians, he believed mathematics to be the highest art.
Of course there do exist scientists who take the interests of the public or the people as their own duty; the honorees of China’s Two Bombs, One Satellite of course were all such people, and I have no doubt of their sincerity. Whether one works for the individual or for society mainly depends on different people rather than different disciplines; I have told you this before. But here I am only following Hardy’s line of thought and speaking about scientists as Hardy understood them.

Gǔ Chù

2007-07-16 22:56:19 http://epr.ycool.com/ [Reply]

Sometimes I, too, like Hardy, think that scientists who devote themselves to the public good, just like artists who devote themselves to pleasing the masses, are not “real” scientists or artists. Although I certainly support diverse motivations for research and scholarship (I wrote an article about this specifically before), I must admit that “serving the people” does not really add much to the image of a certain scientist in my mind. Of course, as an ordinary citizen, altruism is certainly admirable and praiseworthy, but for a scientist as a scientist, it is really an irrelevant quality. Hardy also mentioned that if his research results could benefit others, he certainly had no reason not to be glad about that, but this was not the key point of his research activity itself.

UNIC

2007-07-17 00:05:47 Anonymous 222.82.69.241 [reply]

“Just like artists who devote themselves to pleasing the masses….”
Does serving the people simply mean gaining the people’s recognition? Or is it even directly just pleasing the masses?
Serving the people can also mean not being recognized. For example, some writers.

Gu Chu

2007-07-17 09:46:15 http://epr.ycool.com/ [reply]

Then tell me, what does “serving the people” mean for an artist?
What I mean by “devoting oneself to pleasing the masses” is not the same as “gaining the people’s recognition”; the motive of gaining recognition is more like what Hardy called “ambition” or “aspiration.” A truly altruistically driven artist (if such a thing exists) does not necessarily devote himself to gaining the people’s recognition, but rather to bringing what he considers good to the world. Yet here, I think that the motive of dedicating one’s work to the world is in any case no match for the motive of pursuing the work one oneself considers good—if one does not have love and devotion for art to begin with, if one does not have faith in one’s own work and ideals, then with only the motive of giving to others, it is impossible to become a “real” artist. There are many ways to benefit others; why should he choose art? If he himself had not first been deeply attracted by art, how would he have chosen to use art to benefit others? In the final analysis, altruistic motives are always secondary and irrelevant to the bigger picture for an artist, whereas those “personal” motives are what determine an artist as an artist.

UNIC

2007-07-17 17:38:07 Anonymous 220.171.183.101 [reply]

Then
is Tolstoy an artist?
Is Lu Xun an artist?
What is the definition of an artist?

Gu Chu

2007-07-17 19:35:25 http://epr.ycool.com/ [reply]

We once discussed a similar question: if someone creates several widely beloved poems, but does not identify with the life of a poet, does that make him a poet? My view is that he wrote poetry, but he does not count as a true poet; a true poet is a way of life, and does not depend on his works.
Some people may have created epoch-making achievements in the history of science, but that does not mean he must be a true scientist. Some people may live on forever through their writings and works, but they may likewise not be true writers or artists. A true scientist or artist, too, is a way of life; it is a title belonging only to those who take science or art, truth or beauty, as their own lives—and it does not require their works to be all that important or famous.
This is not my definition of an artist (I do not have that authority), but only a somewhat extreme interpretation. Of course I also recognize the usual understanding, such as using artist as a respected title or as the name of a profession. Basically speaking, language always belongs to the public, and the definition of a word ultimately depends on public recognition. What I myself am expressing is not a “judgment” (I have no right to judge who is or is not an artist), but only an attitude or an emotion.

unic

2007-07-17 21:54:47 Anonymous 124.117.17.225 [reply]

Hard to say, let’s keep looking.

Gu Chu

2007-07-20 20:13:13 http://epr.ycool.com/ [reply]

I thought of an analogous way of putting it:
Imagine such a person (this is a very realistic situation): he is a thoroughgoing atheist, and yet he feels that his nation is facing a crisis and urgently needs to be united by some kind of faith, otherwise it will always remain a heap of loose sand. So he chooses to spread a religion by taking practical action himself, teaching people to believe in God, and he does an excellent job at it. As a result, people in their desperate situation become filled with hope and become united…. In terms of behavior, this nationalist is without question a good believer, and may even be a preacher or founder of a religion; yet if we finally came to know his true motives, I think I would still say that he is absolutely not a “real” believer, because the altruistic motive that moved him to devote himself to religion, however noble, is not a religious motive. No matter how successful his proselytizing is, no matter how strictly he follows the doctrine, no matter how much he is recognized by the people, in the final analysis he remains an atheist, not a true believer.
In short, when I emphasize “a real …,” what I am emphasizing is faith.

UNIC

2007-07-21 20:18:29 Anonymous 222.82.73.73 [reply]

“… but is not a religious motive….” I think I understand what you mean: you mean that this still makes use of religion, right? By this so-called “religious motive,” do you mean that it should be that real sense of need for religion that comes only after going beyond reason, right?
Heh, I agree. So that means that when he was treating religion as a tool for restoring the nation, he was actually pouring out a settled value system of his own. And the true religious motive should be only a purely inward sense of searching, a sense of exploration? Rather than the practice of some value system that is actually unrelated to religion, right?
Heh, in that case religion has also become technology, a tool. Actually Christianity and Buddhism seem all right, but Islam in its day was, to a large extent, motivated precisely by considerations of restoring the nation….
What I said above may be wrong, and some of it is still not very clear. I’ve thought very little about this aspect.

Translated from the Chinese original with AI assistance. The original text is authoritative.

Tagsphilosophy book reading science notes mathematics