My problem, the Ashford boundary. He clicks the slide. The inner integral expands across the 12-ft screen. This integral, he says, is what we politely call intractable. I have spent 9 years, two textbooks, and the better part of my soul demonstrating why. Today, I'm going to walk you through the latest version of that demonstration. He smiles. And just for fun, because I'm in a generous mood, I'm going to make a small wager.
The room shifts. People sit up. Ashford pulls out a stopwatch from his pocket and holds it up like a prize. If anyone in this hall, he says, can produce a closed-form solution to this integral within 2 minutes, I will resign my chair. I will hand them my office keys. And because I am, above all, a man of my word, he laughs, I I marry them on the spot.
The room laughs. He's enjoying himself. Now, before any of you graduate students get excited, he says, I don't mean you. The Putnam winners can sit down. I mean anyone. The undergrad auditing in the back, the visiting scholar who flew in last night. His eyes drift to the back of the hall. The maintenance staff. He gestures, smiling, toward Whitney who has just rolled her cart into the side aisle. Yes, Ashford says, even the woman with the mop. And I'm a man of my word. Two minutes. Marriage proposal included.
He clicks the stopwatch theatrically. Don't all rush at once. The laughter sharpens. Three people don't laugh. Audrey Whitfield in row three sets her pen down a second time. Henrik in the front row mutters, "Oh, no." under his breath. Eleanor Vance does not move a muscle on the panel. Whitney does not look up. She wipes the marker on her sleeve.
She finishes the row of tiles she was working on. She straightens up. She walks down the side aisle, slowly. The camera operator on the live stream, on instinct, swings to follow her. She stops next to Eleanor Vance at the panel table. She speaks low, just for Eleanor. Professor Vance, may I borrow the floor for the two minutes he's offering?
Eleanor looks at her. A long look. Their eyes lock for almost 3 seconds. Something passes between them that no one else in the room sees. Then Eleanor nods once. By all means, Ms. Brooks. Ms. Brooks. Phones come up across the audience. Someone in the back stands up to record. Ashford turns around at the sound and sees Whitney walking toward the stage. He laughs out loud.
"This is fantastic. By all means. By all means. 2 minutes starting" He clicks the stopwatch with a flourish. "Now." Whitney walks past him. She does not take the marker he holds out. She walks to the tray and picks up a fresh one. She turns to face the board. Behind her, Ashford is grinning at the audience and shaking his head. In front of her, his life's work is glowing on a 12-foot screen.
What was she about to do that nobody in that room could see coming? Whitney does not start solving. She studies the board. For 15 full seconds, she does not move. She just stands there, marker in hand, head slightly tilted, reading the equation top to bottom. Behind her, the auditorium grows quiet. Ashford keeps his smile going, but you can see it start to thin at the edges.
12 seconds. 20 seconds. The stopwatch ticks past 1:40. Then Whitney lifts the marker. She does not write at the bottom of the board. She does not write near the integral itself. She circles a single line near the top. Line three. She turns to the room. "Professor Ashford," she says. Her voice is steady, low, no shake in it.
"On line three, you've assumed your function is continuous at the origin. It isn't. There's a removable discontinuity, but only after you redefine the limit from below." The room goes silent. Not polite silent. The kind of silent where everyone is suddenly listening with their whole body. Henrik Sandberg in the front row slowly looks down at his notes. He looks at the screen. He looks at his notes again. His face goes white.
Eleanor Vance leans forward in her chair. Audrey Whitfield in row three picks her pen back up. Ashford's smile is fixed now. He laughs once, sharply. That is That's a notational convention, Ms. Brooks. It's standard in the field. It's a load-bearing assumption, Professor. If line three is wrong, every line after it inherits the error. Even if, and I'm saying if, that were true, spotting an error is not a solution. The bet was for a closed form, not a critique. He glances at the stopwatch. And the clock is running, by the way.