Yannick Grannec - The Goddess of Small Victories

“How can they not believe you, then? Your field is certainty. Everyone knows that two plus two equal four. This is a truth that will always stand!”

“Some truths are temporary conventions. Two and two don’t always equal four.”

“But come on, if I count it out on my fingers …”

“We stopped basing mathematics on felt experience a long time ago. In fact, we make a point of manipulating nonsubjective objects.”

“I don’t understand.”

“I hold you in great respect, Adele, but some subjects are truly beyond you. We’ve talked about this before.”

“Sometimes, you can move a complex idea forward by trying to state it simply.”

“Some ideas can’t be stated simply in ordinary language.”

“That’s exactly it! You imagine yourselves to be gods! You’d do better to take an occasional interest in what’s going on around you! Are you aware of people’s suffering? Do you have the slightest concern about the coming elections? I read the newspaper, Kurt, it’s written in the language of men!”

“You should learn to control your temper, Adele.”

He took my hand, the first time he had ever done so in public, and we walked under the silent arcades to the cross street.

“In certain cases, one can prove a thing and its opposite.”

“That’s nothing new, I specialize in it.”

“In mathematics, this is known as ‘inconsistency.’ In you, Adele, it’s contrariness. I have just proved that there exist mathematical truths that cannot be demonstrated. That is incompleteness.”

“And that’s all?”

Irony never served as a bridge between us; he saw it as a simple error in communication. Sometimes it forced him to reformulate, find an acceptable image. These rare efforts were real proofs of love: a temporary relaxation of the tyranny of perfection.

“Imagine a being with eternal life, a being that spent its immortality taking stock of mathematical truths. Defining what’s true and what’s false. It could never come to the end of its task.”

“God, in short.”

He hesitated a moment before walking forward, the wear of the pavement obscuring the path he’d set for himself.

“Mathematicians are like children who pile truth bricks one on top of another, building a wall to fill the emptiness of space. They ask if all the bricks are solid, if some might not make the whole edifice crumble. I proved that in one part of the wall, certain bricks are inaccessible. As a result, we’ll never be able to verify that the entire wall is solid.”

“You horrible brat, it isn’t nice to spoil other people’s games!”

“My game too, possibly, but at the outset I never thought I would destroy it — just the opposite. 3

“Why don’t you go back to physics, then?”

“Everything in physics is even more uncertain. Especially now. It would take too long to explain it all. Physicists are part of the confusion. They’re looking for a bucket big enough to cover the buckets of the ones who came before. Theories that are even more global.”

“Each of them is trying to piss farther than his playmates.”

“I’m sure my colleagues will fully appreciate your views on scientists, Adele.”

“Bring them on! I’ll teach them about life.”

For several seconds, he considered unleashing me in the cloistered halls of the university by way of retaliation. But the thought didn’t help to relax him.

“They don’t respect me. I know what they’re saying behind my back. Even Wittgenstein, although he distrusts the positivists, takes me for a conjurer, a manipulator of symbols.” 4

“That man hasn’t got all his marbles. He gave his fortune away to some poets and went off to live in a cabin. You’d put your trust in him?”

“Adele!”

“I’m trying to make you laugh, Kurt, but I’m starting to realize that we’re facing an on-to-log-i-cal impossibility.”

“You learned that word in the Nachtfalter’s coat room?”

We reached his street. From a distance I could see a light on in the windows of his apartment: his mother never went to sleep until she heard his footsteps in the hallway. To stay out all night was to sentence her to wakefulness. We joked about it. Sometimes. That night, the lonely one was to be me.

“In a nutshell, you used this logic of yours to prove that there are limits to logic?”

“No, I demonstrated the limits of formalism. The limits of mathematics as we know it.”

“So you didn’t tip all of their precious mathematics into the garbage! You just proved to them that they would never be gods.”

“Leave God out of all this. It’s their faith in the all-powerfulness of mathematical thinking that has been breached. I’ve killed Euclid, struck down Hilbert … I’ve committed sacrilege.”

He got out his travel kit, a sign by which he often brought debates to a close: Don’t come too close, my mother might see you from the window .

“I need to work on my speech. I am meeting Carnap in two days.”

“That bullfrog, he’d like to think he’s bigger than—”

“Adele! Carnap is a good man, he’s helped me enormously.”

“He’s a Red. And he’s going to be in trouble soon enough.”

“You don’t know the first thing about politics.”

“I keep my ear to the ground. And what I’m hearing isn’t so favorable to the intelligentsia, believe me!”

“Adele, I have enough to worry about already. I’m very tired.”

He replaced his keys in his pocket: tonight we would sleep together, and she would be the one to wait.

“You’re finally being reasonable.”

“I only know one way to keep you quiet.”

He had brought his masters’ hopes crashing down — not the hopes they’d placed in him but those they’d entertained about their own omnipotence. His positivist friends wanted to boil down the unsayable , what human language cannot address. In mathematics, limiting research to the discipline’s mechanism was an illusion; Kurt had produced a corrosive result from the very language intended to provide consolidation.

He had never been a blind disciple of the Vienna Circle, even proving to be a wolf in their fold, but his world was a small one and he needed a place for himself in it. He needed the positivists for stimulation, to keep from being carried along by the zeitgeist. This might also have been what he liked about me: my candor. I accepted my intuition as a natural phenomenon. He was attracted by my legs, but he stayed with me for my radiant ignorance. He would say, “The more I think about language, the more astounded I am that people manage to understand each other.” He never spoke in approximations. Surrounded as he was by clever talkers, he preferred keeping silent to being in error. He liked humbleness in the face of truth. This virtue he had to the point of toxicity: unwilling to make a misstep, he would forget to take any step at all.

The bomb was truly a bomb, but its action was delayed. I wasn’t the only one who had trouble understanding it. The very tools he used in his proof were innovations, and even the most gifted mathematicians needed time to absorb their import. At the long-awaited conference, Kurt was overshadowed by the titans of physics — Heisenberg, for instance. The polymath von Neumann spoke in support of him, but a transcript of the conference didn’t even mention Kurt.

Within a few months, however, his discoveries started to gain notice and then became impossible to ignore, witnessed by the fact that any number of adversaries tried to find a flaw in his argument. The radius of the bomb extended across the Atlantic and came back to us in the form of a lecture contract at Princeton University, meaning we would probably be separated. Meanwhile I saw him invaded by a sense of doubt, which was never to leave him again.