The Widener Library, a huge chunk of a building in the middle of the Harvard Yard, had been named for Harry Elkins Widener. Harry had gone down with the Titanic , possibly having escorted a lady to a lifeboat with a gracious bow. His mother, in giving the money for the building, had said that he liked to read books. Quite likely, she spoke the truth. In any case, the library had a very large number of books. Many of them were not much fun to read, but there were people who read them.
Vic knew that he was entering an area of serious scholarship, and, having climbed the many steps, he yanked open the massive door and charged right through without being challenged. Feeling like a spy, he found the elevator without having to ask any revealing questions, and, following instructions, he went to the top floor.
Widener B was a small wide room with a high ceiling whose windows looked over the interior courtyard. There were a dozen scattered chairs more or less facing the blackboard on one wall, the other walls being covered with shelves of books. In between the books were two persons, Vicki and Ken Martz. Vicki stuck out her tongue at him, but Ken, a jolly middle-aged man, was quite effusive in his greeting. He then remarked, “Yuri and the others will be here shortly.”
Vicki added, “The hexagapod said he can’t come tonight.”
It turned out that the hexagapod was a blind man with a dog, thus having, effectively, six legs. Ken explained, “He has an amazing visual imagination. If there’s some complex figure up on the board, he’ll ask if there’s a line between point x16 and point z13.”
Vicki added, “We share an office over at the computer lab, and I don’t have to worry about putting my feet up on the desk.”
Vicki had a half-time job at the lab, and Ken explained, “She’s a programmer in addition to being a full-time student. And she’s highly paid. Don’t think that you have to pay for her dinner.”
That was news to Vic, but it was nevertheless obvious that Vicki would still keep herself on a strict budget and take advantage of the bargains he could offer at Jordan Marsh.
After a bit, Yuri Litvinov ambled in. Probably in his sixties with an abstracted gait that he might have had even as a young man, he was introduced to Vic by Ken, who described Vic as a ‘promising young mathematician.’ Yuri replied, with an ironic smile, “I was sometimes described in that way an eon or two ago, but I could never discover what was being promised, by whom, or to whom.”
Vicki asked, “Was anyone ever disappointed?”
“Oh, I think many people. But they were too polite to say so.”
Just then, two young men came in, one with a deep southern accent, and the other a tall gaunt man with hollow eyes and sunken cheeks. A little woman, who seemed to be his wife, came running after him. She poked him playfully in the ribs and sat down next to Vicki with an air of rebellion. It seemed more like a club than a class, but Ken finally went to the board.
Vic hadn’t expected it to be anything like high school geometry, and it wasn’t. It turned out that differential geometry was almost a cult, unknown to most mathematicians, but savored by the few. Yuri’s presence was explained by the fact that he was interested in any sort of purely theoretical activity. Ken was proving a theorem, and Vic didn’t understand much. However, at the end, the discussion moved to more general matters.
Vic already knew that the non-Euclidean geometries assumed a different parallel postulate. Instead of having exactly one line parallel to a given line through a point not on the line, they either had more than one, perhaps an infinite number, or none. It was also taken for granted by those present that there were models for each geometry, none being ‘correct.’ For example, if one took a line to be a great circle on a sphere, there would be no lines parallel to that line through a point not on it. In the case of the earth’s equator, any great circle through a point not on it would intersect it (at two places). All well and good. At the moment, it was being suggested that the concepts of intersection and parallelism could be defined, not only for two and three dimensional space, but for space of any number of dimensions. Vic understood that, and even asked a question which was answered informatively.
Afterward, it was off to a well-known cafeteria which stayed open all night and attracted many sorts of people. The lighting was extremely bright, perhaps with the idea of discouraging transactions which more naturally took place in darkness. Vic overheard the other woman, Helen, whisper to Vicki that she hated being so exposed, but the others appeared to be in their element.
They settled at a rectangular table with a white linoleum top in a corner near the front windows. It was mostly away from the street people who sheltered from the cold in the restaurant. Other unfortunates, their coats stuffed with newspapers, could be seen through the windows, moving restlessly around the square. Ken and Yuri, who didn’t eat the food, drank coffee and held the space while the others went through the line. The southerner, John, was next to Vic, and, pointing ahead to Helen and Paul, he said,
“They usually eat naked because they don’t wear clothes when they’re home. I keep wondering if they’ll do the same thing here.”
Helen, overhearing him, said, “Nice people don’t dress at home. But Paul’s more nude than I am. He goes out that way to get the paper every morning, and I’ve noticed that the lady across the street always seems to be sweeping her steps at that time.”
John replied, “If anyone doubts that there are Bohemians living in Cambridge, we take them around to see Helen and Paul.”
Vic, for one, had no doubts.
When they sat down, Paul told a little joke about the president, “Mr. Roosevelt showed that a man can be president as long as he wants to be. Mr. Truman showed that anyone at all can be president. However, General Eisenhower has made these matters academic by showing that we can get along perfectly well without a president.”
Everyone present was a Democrat and Adlai Stevenson supporter, so it went well. After a pause, Yuri said, “People once told similar jokes about the Czar, Nicholas the Second. But it was odd that it eventually seemed necessary to execute him. Rather like destroying something that doesn’t exist.”
Ken replied, “But Yuri, you can destroy a vacuum by putting something in it.”
The discussion took off from there, never entirely serious, but with odd little twists. Vic had never been a party to anything like it, but saw that Vicki was much involved. He kept wondering if this was her idea of elegance, and whether it was, indeed, a kind of elegance.
When the group finally dispersed, he asked, a little tentatively, if he could walk her back to her house. She replied, “I’m really not afraid of being attacked around here, but it would be nice to have company.”
As they set off, she asked, “Were we elegant tonight?”
“It’s a very impressive group, but Ken and Yuri look a lot like most men of their age.”
“Most mathematicians do.”
“Well, I happened to see a picture of Einstein lecturing when he was about thirty five. We’re used to seeing pictures of him as an old man, but he was really quite handsome and glamorous.”
“There are also mathematicians like that. Is it that you want your idols to look a little like movie stars?”
Vic knew he was being teased, but he replied, “Ava Gardner is the most beautiful woman I’ve seen, at least in pictures. But she doesn’t look mathematical. I’ve also read that she pronounces her name ‘Avuh Gadnuh.’ That isn’t good.”
“Okay. So there doesn’t have to be that much star quality. In our group, Helen’s pretty cute.”
“I wasn’t aware of that.”
“That’s because of her frumpy clothes. When we visit and she traipses around in front of you naked, you may change your mind.”
“I’m being pretty silly about this elegance business, aren’t I?”
“Sure. But there’s something there that’s important to you. If you once get it distilled and defined, it might be within reach.”
“I have noticed one thing. Mathematicians talk about elegance all the time.”
“Certainly. An elegant proof is one that’s clear and simple, and yet arrives at a surprising result.”
“So the analogy would be that of a person who’s straight-forward without artifice, but who does surprising things.”
“Yuri is certainly that in the intellectual realm. Would he also have to climb mountains with an ice ax?”
“You’re teasing again.”
“Maybe not so much. Perhaps you’re a person who does have to perform physical feats. However, I don’t think the Eastern European cosmopolitans you’ve read about had hankerings to climb Mt. Everest.”
“No. Probably not.”
“Of course, those people were amusing, and you can’t be amusing without springing some surprises somewhere along the line. Elegance may only require the saying of surprising things, as opposed to doing them.”
At that moment, Vicki looked as if she might actually do some surprising things.
Vic replied, “Of course we are Americans. Even if we tried, we couldn’t be like the old East European intellectuals.”
“Not really. But there isn’t any outright contradiction between being elegant and being a sportsman. You just have to change clothes to go from one to the other.”
That was a joke as well, but it did seem to Vic that there could be hope.
When they reached the Radcliffe quadrangle and the big brick house, Vic wasn’t sure what Vicki might expect. He had seen girls returning from dates getting kissed goodnight, but they hadn’t exactly been on a date. As it turned out, she waved gaily and trotted up the steps. He still had plenty of time to get to Jordan Marsh and Lizzie.