Monday, June 05, 2000

Uncle Petros

On my plane ride back from Belgium, I read Uncle Petros and Goldbach's Conjecture. For those of you not mathematical, Goldbach's Conjecture is that ever even number greater than 2 can be written as the sum of two primes. So, for example, 28=23+5. 100=3+97.

Those of you who know me know that I am a number theorist, so it's hard for me to read this book as anything other than a story about number theory. But I'll try. The narrator's Uncle Petros devotes his life to trying to prove Goldbach's Conjecture. Goldbach's Conjecture is one of the oldest unsolved problems in number theory (since though it has been confirmed for every number tried, it has never been proven true of all numbers). Though it isn't a central question in mathematics, its proof would undoubtedly be a work requiring many interesting advances; in fact, many interesting advances have already resulted from proof attempts.

There I go, making it about the number theory. The point is, Goldbach's Conjecture is a hard problem. Anyone who solved it would likely be known throughout the ages. And that's part of what attracts Uncle Petros -- the chance for "immortality". But the flip side is that anyone who attacks the problem -- no matter how brilliant -- is unlikely to solve it. So Uncle Petros tries, and fails, and is perceived never to solve anything because he can't prove the one thing he is trying to prove. That, says the narrator's father, is Uncle Petro's problem -- his failure to set "attainable goals".

So in a very simple sense, the book is a cautionary tale...set your sights too high, and you're doomed to failure. I have actually seen this happen far too often in mathematics, and it's one reason I'm a little glad to be out of the academic world. "Oh, he only got a partial result." "Oh, his theorems are just generalizations of others' work." "Oh, he has a tenure-track position, but it's not at Princeton." Sometimes mathematicians act as if anything less than transcendant genius is to be derided.

But it's really not that. After all, if nobody ever tries to prove Goldbach's Conjecture, nobody ever will. Clearly Uncle Petros is unbalanced -- having one impossible goal and being tormented by failing to meet it. So maybe what is need is both unattainable goals and accepting an inability to meet them. Reach for the stars, but be happy with the moon.

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