The Chudnovsky situation is a national disgrace. Everyone says, “Oh, what a crying shame” & then suggests that they be placed at
The brothers, because they insisted that they were one mathematician divided between two bodies, would have to be hired as a pair. Gregory would refuse to take any job unless David got a job, too, and vice versa. To hire them, a math department would have to create two openings. And Gregory couldn’t teach classes in the normal way, because he was more or less confined to bed. And he might die, leaving the Chudnovsky Mathematician bereft of half its brain.
“The Chudnovskys are people the world is not able to cope with, and they are not making it any easier for the world,” Herbert Robbins said. “Even so, this vast educational system of ours has poured the Chudnovskys out on the sand, to waste. When I go up to that apartment and sit by Gregory’s bed, I think, My God, when I was a mathematics student at Harvard I was in contact with people far less interesting than this. I’m grieving about it.”
“TWO BILLION DIGITS OF PI? Where do they keep them?” Samuel Eilenberg said scornfully. Eilenberg was a distinguished topologist and emeritus professor of mathematics at Columbia University.
“I think they store the digits on a hard drive,” I answered.
Eilenberg snorted. He didn’t care about some spinning piece of metal covered with pi. He was one of the reasons why the Chudnovskys would never get permanent jobs at Columbia; he made it pretty clear that he would see to it that they were denied tenure. “In the academic world, we have to be careful who our colleagues are,” he told me. “David is a nudnik! You can spend all your life computing digits. What for? It’s about as interesting as going to the beach and counting sand. I wouldn’t be caught dead doing that kind of work.”
In his view, there was something unclean about doing mathematics with a machine. Samuel Eilenberg was a member of the famous Bourbaki group. This group, a sort of secret society of mathematicians that was founded in 1935, consisted mostly of French members (though Eilenberg was originally Polish) who published collectively under the fictitious name Nicolas Bourbaki; they were referred to as “the Bourbaki.” In a quite French way, the Bourbaki were purists who insisted on rigor and logic and formalism. Some members of the Bourbaki group looked down on applied mathematics—that is, they seemed to scorn the use of mathematics to solve real-world problems, even in physics. The Bourbaki especially seemed to dislike the use of machinery in pursuit of truth. Samuel Eilenberg appeared to loathe the Chudnovskys’ supercomputer and what they were doing with it. “To calculate the two billionth digit of pi is to me abhorrent,” he said.
“‘Abhorrent’? Yes, most mathematicians would probably agree with that,” said Dale Brownawell, a respected number theorist at Penn State. “Tastes change, though. To see the Chudnovskys carrying on science at such a high level with such meager support is awe-inspiring.”
Richard Askey, a prominent mathematician at the University of Wisconsin at Madison, would occasionally fly to New York to sit at the foot of Gregory Chudnovsky’s bed and talk about mathematics. “David Chudnovsky is a very good mathematician,” Askey said to me. “Gregory is a great mathematician. The brothers’ pi stuff is just a small part of their work. They are really trying to find out what the word ‘random’ means. I’ve heard some people say that the brothers are wasting their time with that machine, but Gregory Chudnovsky is a very intelligent man who has his head screwed on straight, and I wouldn’t begin to question his priorities. Gregory Chudnovsky’s situation is a national problem.”
“IT LOOKS LIKE KVETCHING,” Gregory said from his bed. “It looks cheap, and it is cheap. I don’t think we were somehow wronged. I really can’t teach. So what does one do about it? We barely have time to do the things we want to do. What is life, and where does the money come from?” He shrugged.
At the end of the summer, the brothers halted their probe into pi. They had other things they wanted to do with their supercomputer, and it was time to move on. They had surveyed pi to 2,260,321,336 digits. It was a world record, doubling their previous world record. If the digits were printed in type, they would stretch from New York to Los Angeles.
In Japan, their competitor Yasumasa Kanada reacted gracefully. He told
“You see the advantage of being truly poor,” Gregory said to me. “We had to build our machine, but now we own it.”
M zero had spent most of its time checking the answer to make sure it was correct. “We have done our tests for patterns, and there is nothing,” Gregory said. He was nonchalant about it. “It would be rather stupid if there were a pattern in a few billion digits. There are the usual things. The digit three is repeated nine times in a row, and we didn’t see that before. Unfortunately, we still don’t have enough computer power to see anything in pi.”
And yet…and yet…the brothers felt that they might have noticed something in pi. It hovered out of reach, but seemed a little closer now. It was a slight change in pi that seemed to rise and fall like a tide, as if a distant moon were passing over the sea of digits. It was something random, probably. The brothers felt that they might only have glimpsed the human desire for order. Or was it a wave rippling through pi? Would the wave, if it was there, be the first thread in a tapestry of worlds blossoming in pi? “We need a trillion digits,” David said. Maybe one day they would run the calculation into a trillion digits. Or maybe not. A trillion digits of pi printed in ordinary type would stretch from here to the moon and back, twice. Maybe one day, if they lived and if their machines held together, they would orbit the moon in digits, and would head for Alpha Centauri, seeking pi.
Gregory is lying on his bed in the junkyard, now. He offers to show me the last digits the supercomputer found. He types a command, and suddenly the whole screen fills with pi. It’s the raw Ludolphian number, pouring across the screen like Niagara Falls:
72891 51567 97145 46268 92720 56914 19491 70799 30612 27184
95997 75819 61414 47296 81115 92768 25023 87974 42024 32465
81816 25413 12164 96683 83188 86493 16114 55018 80584 26203
71989 99024 98835 10467 22124 63734 94382 70510 64281 32133
84515 75884 47736 80693 93435 69959 13571 88057 62592 60719
58508 38025 73050 11862 43946 99422 06487 07264 08095 58354
41083 43437 83790 00353 73416 69273 76820 40100 54718 28029
00958 45404 09196 25724 40953 10724 75287 88238 71194 22897
36462 82455 69706 19364 35459 84229 95107 39973 54996 68154
14759 50184 95343 60383 37189 76295 12572 70965 58816 94729
09508 25947 06150 01226 73434 26496 86070 41411 62634 95296
69333 80436 51116 81295 92670 33384 07650 40965 11979 85185
50164 21984 40980 27554 25619 05834 95554 34498 43497 55136
88999 51731 69029 01197 60153 45399 73782 80898 99826 36229
28846 77788 04108 11793 89363 51922 14801 13183 14735 68818
49953 27420 48050 19186 07391 11248 22845 78059 61348 96790
18820 54573 01261 27678 17413 87779 66981 15311 24707 34258
41235 99801 92693 52561 92393 53870 24377 10069 16106 22971
02523 30027 49528 06378 64067 12852 77857 42344 28836 88521
72435 85924 57786 36741 32845 66266 96498 68308 59920 06168
63376 85976 35341 52906 04621 44710 52106 99079 33563 54625
71001 37490 77872 43403 57690 01699 82447 20059 93533 82919
46119 87044 02125 12329 11964 10087 41341 42633 88249 48948
31198 27787 03802 08989 05316 75375 43242 20100 43326 74069
33751 86349 40467 52687 79749 68922 29914 46047 47109 31678
05219 48702 00877 32383 87446 91871 49136 90837 88525 51575
35790 83982 20710 59298 41193 81740 92975 31
