Fermat's last theorem is solved, and a generation of tormented German graduate students can now go fishing.

Imagine you have some interest in Biblical archaeology and see advertised a lecture on, say, "Calibrated Radiocarbon Chronology of Royal Judean Storage Jars," or some such. You go to the lecture at the end of which the speaker says, "And, oh, by the way, on Thursday I found the Holy Grail in the basement of a bed-and-breakfast in downtown Jericho. Here it is."

Well, something comparable happened in Cambridge, England, last week. A group of mathematicians attended a conference on -- hold on -- "P-adic Galois Representations, Iwasawa Theory and the Tamagawa Numbers of Motives." They went, as audiences do, expecting entertainment and instruction. What they got was astonishment.

They went to hear Prof. Andrew Wiles deliver three lectures on "Modular Forms, Elliptic Curves and Galois Representations." At the end of the third lecture, Wiles noted that his presentation had just proved Fermat's Last Theorem, the most famous and elusive mathematical puzzle of the last 300 years.

If Wiles' claim holds up -- and its 200 pages of reasoning are so difficult that only a handful of mathematicians are in a position to judge -- he will be hailed for his mathematical genius. He should be equally hailed for his modesty. Dropping his bombshell at the end of a lecture, without a hint of the now usual "cold fusion"-type advance publicity, is in itself an achievement in this age of hype.

In science, modesty and genius do not coexist well together. (In Washington, modesty and cleverness don't.) Einstein is perhaps the most famous exception to the rule. Yet even Watson and Crick, discoverers of the genetic code and not known for their modesty, proved themselves capable of one admirable, indeed immortal, act of understatement. Toward the end of their epic two-page paper revealing the structure of DNA, they noted dryly: "It has not escaped our notice that the specific pairing {i.e., zipper-like structure of DNA} we have postulated immediately suggests a possible copying mechanism for the replication of the genetic material."

For hundreds of years humans had known that hereditary traits are transmitted from parent to child. But they hadn't a clue as to how. Watson and Crick had just provided the clue.

Wiles, however, is due homage not just for his genius and his modesty, but for his courage. Courage is not a quality one normally associates with mathematicians. Yet it should apply to people who work in their attics in secret for seven years without cease on a problem that has eluded the greatest mathematical minds since first proposed in 1637.

I once had a friend at Oxford who drifted into the study of Hegel, that famously impenetrable German philosopher, and was never seen again. There are intellectual black holes, vortexes of endless regression, that mortals ought to stay clear of. Many mathematicians have felt that way about Fermat's Last Theorem.

Its allure lies not just in its longevity but in its simplicity. It can be written on one line: "Xn+Yn=Znis impossible when n 2," meaning that while a square can broken into two smaller squares -- 25 (the square of five) can be broken into 16 (the square of four) plus 9 (the square of three) -- one cannot divide a cube into two smaller cubes, and for that matter, one cannot divide any higher power into two smaller numbers of the same power.

It is a proposition so vexing and mathematically profound that the French Academy of Sciences offered a gold medal and 300 francs for its solution. That was in 1815, the year Napoleon was just settling into his new digs on St. Helena.

It is a proposition so famous that perhaps the one person on Earth most grateful for the Wiles' solution, after the professor's wife and daughters ("Daddy's back!"), is Dr. Martin Kneser of the Gottingen Academy of Sciences. He administers another Fermat prize, the Wolfskehl prize (first offered in 1908, now 7,500 marks). Which means that poor Dr. Kneser must fight his way through the "three meters of correspondence" from every crank on the planet who is sure he has bested Fermat.

How does he handle the mountain of mail? "In recent decades," wrote Kneser's predecessor, "it was handled in the following way: the Secretary of the Akademie divides the arriving manuscripts into (1) complete nonsense, which is sent back immediately, and into (2) material which looks like mathematics." The second category is given to young research assistants forced by poverty and induced by payment to search for the inevitable mistakes.

One would-be Fermat slayer sent half a solution and demanded 1,000 Marks before he would produce the other half. Another also demanded money up front, promising 10 percent of the radio and TV take that would follow his fame and threatening, if denied, to send his solution to Russia.

Consider, then, what Wiles has wrought. A generation of tormented German graduate students can now go fishing. Kneser is free at last. Fermat is vindicated. And the rest of us are treated to a rare, irrefutable demonstration that the hairless ape with the opposable thumb is indeed, now and then, capable of something that deserves the name progress.