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An excerpt from: The Tolman Trick

by Manil Suri

The Wolf River emerges from the Black Forest and winds across the snow-covered land. Its water is so cold it is syrupy, a snowball gets carried several yards before it melts. Chunks of ice floating downstream curve gracefully around bends. Fluid particles move along smoothly, their velocities varying between orderly bounds. But then they encounter an obstacle, and their streamlines begin to break down. The river carries on, even though mathematically, a solution to its flow equations cannot be found.

Which was nonsense, of course, as his mentor Gyorgy would have said: "Nature always provides a solution, it's we mathematicians who are not smart enough to validate her." Tolman scrubbed the steam off the cab window to get a better look at the river. There was a stub of snow projecting from the bank into the water, probably the remnant of an old stone bridge. He was tempted to ask the driver to stop so that he could take a closer look, watch the water hit the corner of the stone and loop around in its complex patterns. Patterns that engineers had recognized, even calculated for decades, but which the mathematical theory had not been able to substantiate. Not, that is, until two years ago, until the publication of his landmark paper on fluid flow around a corner. Tolman marveled at how dramatically the paper had changed his standing in the pecking order. For years, he had clawed and scratched with everyone else in the barnyards of academia for scraps of recognition. Suddenly, he was judged worthy of a seat at the table. Suddenly, he could reach out and nosh from the platters of conference invitations and panel appointments he had only been able to smell before. Attendees at conferences sought him out, instead of walking away when they did not recognize the name on his badge. Overnight, he had become a star, surrounded by a personal solar system of students and junior researchers. Already, some papers had started referring to his argument as "The Tolman Trick" because of the cunning way it bypassed all the difficulties that arose in trying to resolve the corner. (Personally, Tolman would have preferred that his colleagues use the more respectable "Theorem," though he had to admit that "Trick" did sound catchier.) Gyorgy himself, so notorious for his inability to praise the work of his former students, declared himself surprised to hear the result had been proved in his own lifetime. He died a month later.

"It's very beautiful, no? Always soothing to watch water flow." Dixon. On the seat next to him. Tolman made a gesture with his head, halfway between a nod and a no. Soothing was the last word that should come to mind. Streamlines and velocities and Navier-Stokes equations - that's what one should be seeing in water flow. That's what should be flooding the mind of any young person in the field who wanted to do something, become someone, Tolman felt like admonishing Dixon.

They had run into each other on the railway platform at Hausach. Tolman had been pleased to have been recognized by Dixon, from the University of Arbutus, even though they had never met before. He looked at his fellow passenger now, perched on the edge of his seat like an expectant schoolboy, his feet barely reaching the mat, a thick leather satchel clutched in his lap. Tolman felt an avuncular twinge and remembered his own days as a fresh assistant professor, almost twenty-two years ago.

"Did you know that my advisor was Gyorgy?" Tolman told Dixon, shifting his large soft body in his seat. "Back when he was still taking Ph.D. students, before he became such a recluse. He used to throw all sorts of impossible problems at us, without mentioning that mathematicians through the ages had tried and failed to solve them." Tolman chuckled. "I remember when we first heard of the problem of flow past a corner. Bramer was a student of Gyorgy as well, and we both thought it would be an evening's work - we were in our twenties and so naive then. We ended up racing through grad school trying to see who would crack it first. Look how long it took, though, to finally..."

Tolman stopped and ran a hand over his remaining hair to check that it was in place, the way Gyorgy used to do with his own. How to convey to this aspiring young colleague all the effort, all the sacrifice, that good mathematics demanded? The exhausting rivalry that had escalated over the years between Bramer and himself over trying to be the first to prove the result? He searched for some sage advice to bestow on Dixon, but was overcome by the poignancy of his own accomplishment.

"There was something I wanted to ask you about your proof." Dixon undid the strap of his satchel and extracted a sheaf of papers.

"Not a mistake, I hope," Tolman said jovially. He decided he liked this Dixon - the quiet personality, the studiousness he projected as he regarded life from behind his thick black-rimmed glasses. Tolman himself had been equally serious at that age - it had been a way of concealing the terrible shyness he felt. He contemplated asking Dixon if he too was shy - would that be too personal a question?

"Actually," Dixon said, and Tolman looked at him, amazed. He couldn't possibly think there was an error.

"Actually, it's Theorem 2.3. I keep thinking there's something wrong with it."

How absurd. The little runt. Didn't he know the exacting review process that Acta Fluida employed? Didn't he know the result had been endorsed by Gyorgy himself? Tolman felt the skin on the back of his neck begin to itch.

"Perhaps we could go over...?" Dixon stopped, a look of alarm beginning to spread over his face.

Tolman forced his jaw to loosen, his cheek muscles to relax. This was exactly the reaction Dr. Winton had warned against, to prevent the eruption on his neck. It had been a perfectly reasonable request. Why had he become so upset? "Roland, a mathematician," he heard Dr. Winton say. "It's not as if you're trading companies or landing planes. It's not as if playing with numbers can lead to so much strain." He reminded himself that he was now a senior person in the field. Wasn't it his duty to soothe away the doubts of his junior colleagues? What better way to spend the time in the cab than to give a short, calming lecture on his own work?

"Certainly," Tolman said.

By the time they reached Oberwolfach, though, Tolman was ready to pick Dixon up by the scruff of his neck and give him a good shaking. Could the man really be that obtuse? Part of a mathematician's training was to refuse to take any statement at face value, to be skeptical of every line in a proof. But Dixon seemed incapable of accepting anything as true, asking the same questions repeatedly with such mulish persistence that Tolman wished he could hasten him along with a stick. Sensing Tolman.s displeasure, perhaps, Dixon began to freeze up, and, interpreting this as a further digging in of heels, Tolman felt his agitation turn to cold grinning fury.

"I hope you have a wonderful conference," Tolman said through clenched teeth, and Dixon collected his luggage and fled up the Institute steps.

The complete story is available in Issue 1 of the journal SUBTROPICS.