Banquets Of The Black Widowers - By Isaac Asimov Page 0,2

really learned in anything but mathematics and that's all right. Mathematics is what we want out of him. The trouble is that he feels backward; he feels stupid. Damn it, he feels inferior, and when he feels too inferior, he stops working and hides in his room."

Gonzalo said, "So what's the problem? Everyone just has to keep telling him how great he is all the time."

"He's dealing with other mathematicians and they're almost as crazy as he is. One of them, Sandino, hates being second best and every once in a while he gets Pochik into a screaming fit. He's got a sense of humor, this Sandino, and he likes to call out to Pochik, 'Hey, waiter, bring the check.' Pochik can't ever learn to take it."

Drake said, "Read this Sandino the riot act. Tell him you'll dismember him if he tries anything like that again."

"They did," said Trumbull, "or at least as far as they quite dared to. They don't want to lose Sandino either. In any case, the horseplay stopped but something much worse happened. You see there's something called, if I've got it right, 'Goldbach's conjecture'."

Roger Halsted galvanized into a position of sharp interest at once. "Sure," he said. "Very famous."

"You know about it?" said Trumbull.

Halsted stiffened. "I may just teach algebra to junior high school students, but yes, I know about Goldbach's conjecture. Teaching a junior high school student doesn't make me a junior - "

"All right. I apologize. It was stupid of me," said Trumbull. "And since you're a mathematician, you can be temperamental too. Anyway, can you explain Goldbach's conjecture? - Because I'm not sure I can."

"Actually," said Halsted, "it's very simple. Back in 1742, I think, a Russian mathematician, Christian Goldbach, stated that he believed every even number greater than 2 could be written as the sum of two primes, where a prime is any number that can't be divided evenly by any other number but itself and i. For instance, 4 = 2 + 2; 6 = 3 + 3; 8 = 3 + 5; 10 = 3 + 7; 12 = 5 + 7; and so on, as far as you want to go."

Gonzalo said, "So what's the big deal?"

"Goldbach wasn't able to prove it. And in the two hundred and something years since his time, neither has anyone else. The greatest mathematicians haven't been able to show that it's true."

Gonzalo said, "So?"

Halsted said patiently, "Every even number that has ever been checked always works out to be the sum of two primes. They've gone awfully high and mathematicians are convinced the conjecture is true - but no one can prove it."

Gonzalo said, "If they can't find any exceptions, doesn't that prove it?"

"No, because there are always numbers higher than the highest we've checked, and besides we don't know all the prime numbers and can't, and the higher we go, then the harder it is to tell whether a particular number is prime or not. What is needed is a general proof that tells us we don't have to look for exceptions because there just aren't any. It bothers mathematicians that a problem can be stated so simply and seems to work out, too, and yet that it can't be proved."

Trumbull had been nodding his head. "All right, Roger, all right. We get it. But tell me, does it matter? Does it really matter to anyone who isn't a mathematician whether Goldbach's conjecture is true or not; whether there are any exceptions or not?"

"No," said Halsted. "Not to anyone who isn't a mathematician; but to anyone who is and who manages either to prove or disprove Goldbach's conjecture, there is an immediate and permanent niche in the mathematical hall of fame."

Trumbull shrugged. "There you are. What Pochik's really doing is of great importance. I'm not sure whether it's for the Department of Defense, the Department of Energy, NASA, or what, but it's vital. What he's interested in, however, is Goldbach's conjecture, and for that he's been using a computer."

"To try higher numbers?" asked Gonzalo.

Halsted said promptly, "No, that would do no good. These days, though, you can use computers on some pretty recalcitrant problems. It doesn't yield an elegant solution, but it is a solution. If you can reduce a problem to a finite number of possible situations - say, a million - you can program a computer to try every one of them. If every one of them checks out as it's supposed to, then you have your proof. They