Maggie Eismeier is a freshman at Whitman College. She enjoys math, writing, coffee, and has 16 books above her that aren't for school.

Proof (September 20, 2010. Issue 21.)

A boy and a girl walked through a university campus near Boston. The boy was rangy and angular, a second-class high school football player or else the co-captain of the baseball team. His hair was light brown and probably should have been cut some three weeks earlier. The girl had brown hair in a hefty braid, a determined gait, and a green backpack. Her eyes were blue and stayed closed slightly longer than normal when she blinked.

“What are you thinking of majoring in?” he asked her. They were both second year students in winter coats, a month from declaring their majors.

“Math,” she answered, “or regular engineering.”

“Mechanical engineering?”

She nodded and they took a few more steps, now actually walking side by side. They’d seen each other around, weren’t complete strangers, although neither could remember the other’s name.

“What about you?” she asked.

“Chemistry,” he said. “But I’ve had that decided for about ten years.”

“Why chemistry?”

“Have you heard that saying, the physicist saying, that biology is really chemistry and chemistry is really physics? I like the idea of being in between them, because then I get to understand both ends. A foot in the door of the whole chain. It just kills me, too, how small everything is in chemistry. You’re outwitting your own brain when you learn about anything that small.”

She nodded.

“But physics is really math. So you’re not quite in the middle.”

“I guess,” he said. “But math is just the language. Understanding math is like knowing how to read, you know? Math is practically a sense in science. I don’t know that it’s a link in that chain. I’m Everett, by the way.”

The girl was glad he’d gone first.

“Laurie,” she said. She didn’t have a distinct accent, but when she said her name it was clear to the listener that it was an “a” and a “u”, not an “o”.

“So why math?” Everett asked.

“It’s beautiful,” Laurie told him. She side-stepped a frozen puddle. “I’ve never been good at explaining this. Mathematics is just so graceful and beautiful. There’s no interpretation, no margin of error. Any formula or proof just has what it needs. And whatever that is, it’s always true.”

“And then why Mechanical Engineering?”

“Well, the problem with math is that being perfectly beautiful and precise is just... hard. You’ve got to be a genius, basically, to do anything important. I don’t know if I could live with being an okay mathematician, not really advancing the science. That seems wasteful. But if I were a mechanical engineer, I’d know I was doing something practical. An okay mechanical engineer is a hell of a lot more useful than an okay mathematician.”

Everett shifted his shoulders from side to side.

“Well, yes and no,” he said, jamming his hands deeper in his pockets. “I think a happy mathematician is better than a bored engineer. Wouldn’t you rather get your degree in math, keep looking at what you love?”

“Yes, but it’s not really about what I’d rather. I can’t really put my happiness first, can I?”

Everett said that as far as he knew, she could. He reached into the left-side pocket of his coat, withdrew a pack of gum, and offered Laurie a piece, which she declined. He, too, apparently thought better of it, and put the gum back, this time into the opposite pocket.

“I don’t know, Laurie. What would be wrong with trying to be happy?”

She took a full breath before answering.

“I just, you know, I want to avoid being mediocre. But if I really have to be, if I’m mediocre and useful, that’s at least better than mediocre and pointless. Only a few very special people make real contributions in mathematics. It’s a very special kind of mind you need to be a mathematician.”

“And you’re still considering it.”

A short silence of confirmation.

“Do you have a special kind of mind?”

“You have to be practically a genius to get anything done at all.”

“Are you a genius?”

Laurie paused. Everett started to pause with her, which tripped him up, and by the time he was fully balanced she was back on pace.

“I don’t know. I mean, isn’t everyone here a genius?” She gestured at the buildings, the quad, the other students.

“But really.”

“I don’t know,” Laurie repeated. “There are days that I think so, you know? Sometimes I get myself convinced. But you can convince yourself of anything. What I believe doesn’t mean anything. I need to do something, you know, some serious work, before I could know that. I’d need proof.”

“A mathematician,” said Everett. “But you know, there are things in math that can’t be proven. You must know Gödel’s Incompleteness Theorems. In any formal system, there are true statements that can’t be proven true within the system. Maybe you’re a true statement that can’t be proven.”

“It’s not math, Everett. I’m not.”

“No, no, exactly. This isn’t any formal system. What we have here is no rigorous definition. What is a genius, anyway? I know, Multiple Intelligences Theory, and myelin insulation, and conceptual vs. experimental. There are plenty of types of geniuses. But what do they have in common, really?”

Laurie tucked her chin down and took a few steps with her eyes closed.

“I’d say, as far as genius goes, there’s no definition. There’s no bottom-line agreement, nothing’s hard and fast. So isn’t that kind of as if it doesn’t exist? Genius, I mean.”

“I’m not trying to tell you that I’m a genius. I’m trying to tell you that I think it’s practical to become an engineer. Plenty of people like to draw, they don’t seriously try to become professional artists.”

“Well maybe you are a genius. More importantly, maybe you’ll have a wonderful career and figure out some really fantastic math. And maybe you won’t. But I think you’ll have a hell of a lot more fun doing math than designing rotors or something.”

Laurie was starting to get upset. Her eyes were beginning to sting. She brought her braid to the front.
 “It’s hard to accept, I guess,” she told Everett. “I suppose I’m just kind of obsessed with proof.”

“Bullshit,” said Everett. “But listen. I sit behind you in Real Analysis, and I’ve never once seen you ask for a proof in that class. Sometimes you just take things as they come, which is what you’ve been doing in Real Analysis, and it’s what you should do if you become a mathematician. I mean, it’s the attitude you should have about success and validation. Just take it as it comes. Do it for the beauty; do it just because.”

“Just because isn’t much good to anybody.”

“You being happy is a lot of good to you, and to whoever is with you.”

They were at Laurie’s turn, and she told him so. She waved stiffly to Everett and walked away even more forcefully than usual. Everett continued on, feeling bad for not feeling bad. School went along. For the next weeks they didn’t talk. Laurie asked for a proof once in Real Analysis, mostly for show, and tried to take it in. She copied it down hurriedly and didn’t look at it again. Two days before the end of the semester, one day before major declarations were due, and twenty minutes before her last final exam, she passed Everett in the quad. He handed her a newspaper, smiling.

Goldbach’s Conjecture had been proven. All even numbers greater than two could be expressed as the sum of two primes.

The next day, Laurie went to the registrar’s office and declared a major in Pure Mathematics.