“Resign yourself to the lifelong sadness that comes from never ­being satisfied,” Zadie Smith counseled in the tenth of her ten rules of writing — a tenet that applies with equally devastating precision to every realm of creative endeavor, be it poetry or mathematics. Bertrand Russell addressed this Faustian bargain of ambition in his 1950 Nobel Prize acceptance speech about the four desires motivating all human behavior: “Man differs from other animals in one very important respect, and that is that he has some desires which are, so to speak, infinite, which can never be fully gratified, and which would keep him restless even in Paradise. The boa constrictor, when he has had an adequate meal, goes to sleep, and does not wake until he needs another meal. Human beings, for the most part, are not like this.”

Ten years earlier, the English mathematician and number theory pioneer G.H. Hardy (February 7, 1877–December 1, 1947) — an admirer of Russell’s — examined the nature of this elemental human restlessness in his altogether fascinating 1940 book-length essay A Mathematician’s Apology (public library).

In considering the value of mathematics as a field of study and “the proper justification of a mathematician’s life,” Hardy offers a broader meditation on how we find our sense of purpose and arrive at our vocation. Addressing “readers who are full, or have in the past been full, of a proper spirit of ambition,” Hardy writes in an era when every woman was colloquially “man”:

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. He must shut his eyes a little and think a little more of his subject and himself than they deserve. This is not too difficult: it is harder not to make his subject and himself ridiculous by shutting his eyes too tightly. […] 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. The first question is often very difficult, and the answer very discouraging, but most people will find the second easy enough even then. Their answers, if they are honest, will usually take one or other of two forms; and the second form is a merely a humbler variation of the first, which is the only answer we need consider seriously.

Most people, Hardy argues, answer the first question by pointing to a natural aptitude that led them to a vocation predicated on that particular aptitude — the lawyer became a lawyer because she naturally excels at eloquent counter-argument, the cricketer a cricketer because he has a natural gift for cricket. In what may sound like an ungenerous sentiment but is indeed statistically accurate, Hardy adds:

I am not suggesting that this is a defence which can be made by most people, since most people can do nothing at all well. But it is impregnable when it can be made without absurdity, as it can by a substantial minority: perhaps five or even ten percent of men can do something rather well. It is a tiny minority who can do something 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.

But while talent exists in varying degrees within each field of endeavor, Hardy notes that the fields themselves occupy a hierarchy of value — different activities offer different degrees of benefit to society. And yet most people, he argues, choose their occupation not on the basis of its absolute value but on the basis of their greatest natural aptitude relative to their other abilities. (Not to do so, after all, renders one the faintly smoking chimney in Van Gogh’s famous lament about unrealized talent: “Someone has a great fire in his soul and nobody ever comes to warm themselves at it, and passers-by see nothing but a little smoke at the top of the chimney.”) Hardy writes:

I would rather be a novelist or a painter than a statesman of similar rank; and there are many roads to fame which most of us would reject as actively pernicious. Yet it is seldom that such differences of value will turn the scale in a man’s choice of a career, which will almost always be dictated by the limitations of his natural abilities. Poetry is more valuable than cricket, but [the champion cricketer Don] Bradman [whose test batting average is considered the greatest achievement of any sportsman] would be a fool if he sacrificed his cricket in order to write second-rate minor poetry (and I suppose that it is unlikely that he could do better). If the cricket were a little less supreme, and the poetry better, then the choice might be more difficult… It is fortunate that such dilemmas are so seldom.

Presaging the ominous twenty-first-century trend of talented mathematicians and physicists swallowed by Silicon Valley for lucrative jobs ranging from the uninspired to the downright pernicious, Hardy adds:

If a man is in any sense a real mathematician, then it is a hundred to one that his mathematics will be far better than anything else he can do, and that he would be silly if he surrendered any decent opportunity of exercising his one talent in order to do undistinguished work in other fields. Such a sacrifice could be justified only by economic necessity or age. […] Every young mathematician of real talent whom I have known has been faithful to mathematics, and not from lack of ambition but from abundance of it; they have all recognized that there, if anywhere, lay the road to a life of any distinction.

Ambition, he argues, has been the motive force behind nearly everything we value as a civilization — every significant breakthrough in art and science, “all substantial contributions to human happiness.” (George Orwell, too, pointed to personal ambition as the first of the four universal motives of great writers.) But while various ambitions can possess us, ranging from the vain and greedy to the most elevated and idealistic, Hardy points to one as the crowning achievement of the purposeful life:

Ambition is a noble passion which may legitimately take many forms… but the noblest ambition is that of leaving behind something of permanent value.

In the remainder of A Mathematician’s Apology, Hardy goes on to explore the particular aspects of mathematics that make it a pursuit of permanent value. Complement this particular portion with Dostoyevsky on the difference between artistic ambition and the ego, David Foster Wallace on the double-edged sword of ambition, and Georgia O’Keeffe on setting priorities for success.