8/3/99

1 + 1 = ?

For someone who speaks in terms of M(s)=L(s,o,sym³)L(2s)/L(1+s,o,sym³)L(1+2s), suffering a stroke must have been worrisome, to say the least.
    "Not really," says Steve Gelbart with a gentle smile. "I believed it would come back. But I had to do other things first -- like talk and walk."
    Analytical to the last drop, the theoretical mathematician didn't panic when he lost his reasoning ability. His hard disk, so to speak, had been wiped out.
    Three and a half years later, at the age of 55, the Weizmann Institute professor is back at the blackboard, lecturing on such unfathomably complex subjects as the proof of Fermat's Last Theorem.
    Gelbart then: "you do cannot," he scrawled in giant, childlike letters, 10 days after the stroke. He was trying to write to his wife, "you cannot eat dinner if you stay with me now." 
    Gelbart now: "All of my work concerns making conjectures in number theory more provable. A great step was taken by a man named Wiles, in 1994, when he used his proof of part of these conjectures in order to prove Fermat's Last Theorem. It says Xⁿ+Yⁿ never equals Zⁿ, if X, Y and Z are non-zero integers and ⁿ is bigger than 2. Fermat was right when he said that in 1637, but it was only proved four years ago. It can't be done by a computer because maybe you checked it to 500 billion numbers, but maybe you think if you take 500 billion and one, plus 800 billion and something, it will equal that ⁿ power. No, it doesn't, you'll never get there. See, that's the strange thing, you're proving something infinite never happens. Fermat said he had proof but not enough space in the margins to write it out. It took 350 years. Y'see, it gives you the nonexistence of a solution."
    Gelbart now is making sense -- well, to another mathematician, perhaps.
    He speaks with radiating joy, because of his love for the subject, and because he can speak at all.
    He's still not all the way back, though. His handwriting is poor, and his speech is slow and choppy -- at times, oddly incorrect. During our interview, he termed himself a "praxal mathematician," meaning to say "practical."
    But that's just a minor blip: he's come a long, long way from when he could not read, speak, walk or comprehend complicated conversation. When he relearned English, he found that he'd lost his Hebrew: it came out as English or French. Ironically, though, he could remember some numbers only in Hebrew -- such as his ID and phone numbers.
    It was an arduous recovery, but he knew he was on his way when "my brother asked me about the Reimann-Zeta function. There have been two unsolved problems in math that are very famous: Fermat's Last Theorem, which is now solved, and the behavior of the Reimann-Zeta function.
    "When this began to make sense again, I realized for the first time I was ready to return to work."

GELBART COULD hardly have become anything else in life. His father was a mathematician. His identical twin brother is a chemical physicist in Los Angeles. When he was a year old, little Steve's hair was tousled by none other than Einstein (Gelbart's father was working with him at Princeton). Unfortunately, where he was consecrated by Einstein's touch, he is now bald.
    He was touched, too, by Rachmaninoff, Schumann, Dvorak: following the stroke, he discovered an extraordinary effect of his favorite music. The analytic side of his brain was out to lunch, leaving only the emotional side. "I cried. These guys died long ago, but I felt their music was created just for me. And I cried, I wept."
    The emotional side of his brain still seems stronger: he is anything but dull when he describes his science.
     There is, he explains, no immediate practical use to his work, except for other mathematicians. But 50 years from now it may be crucial for physicists.
    "I study new kinds of automorphic forms which 200 years ago didn't exist. This is taught to PhD people in number theory, people who work in topology.
    "People ask if there's anything new in math anymore. Math doesn't go in toward a final ending. It spreads out. There's more not known than known. When we stand on the shoulders of the last generation of mathematicians, we see a much wider viewpoint than we did before.
    "I think mathematics exists, completely, fully, out there in the universe, and all we're doing is peeling away a little bit and getting at the truth. And that goes on forever.
    "In that sense, God exists. The deeper you get into it, the more you see the interrelationships that make everything connected, in mathematics. And who could think of that?!
    "What am I doing? Hmm. This is the purest form of real invention possible. Mathematicians don't use what was done 500 years ago in, say, technology, but we do use the math. Mathematics transcends all time. It doesn't matter when it was done. Once something is proved, it is the truth. Pure truth is always correct." 
    Step out of his office, go down a flight of stairs, and you'll see what he means. There, encased in glass, is a relic from 1954: Israel's first computer.
    Like Gelbart once upon a time, it is comparatively childlike in its capacity.