A lateral step, pulling in a result from topology that had no obvious business being in a combinatorics proof. But it fit. The way a key fits a lock you didn't know existed. Five minutes passed, then ten. The chalk moved faster.
Amanda Cleary, the girl who had closed her notebook, opened it again. She wasn't following the math. She was watching Samantha's hand. The way it never hesitated once it found its rhythm. She would later describe it to a campus journalist as, "Like watching someone write in a language they'd been speaking in their dreams for years."
At the 15-minute mark, Samantha stepped back from problem one. She set the chalk on the tray, looked at what she had written. Six lines of tight interconnected logic that spanned the left third of the board. She checked the final step against the original constraints. Nodded once to herself.
Picked up the chalk, and moved to problem two. This one was harder. She could feel it immediately. The way you feel altitude when you climb. The air thins.
The steps get heavier. Problem two was a generalization question. Could a specific combinatorial identity be extended to higher dimensions while preserving its asymptotic bounds? Whitfield had spent 7 years on this. Talbott at Columbia had co-authored three papers trying to crack adjacent versions of it.
None of them had reached a clean result. Samantha stood still for almost 3 minutes. Her eyes were open, but unfocused. Her left hand hung at her side. Her right hand held the chalk loosely, like a cigarette between thoughts.
The room was so silent that someone in the back row could hear the clock on the wall ticking. Tyler, the lacrosse kid, leaned forward. He wasn't smirking anymore. Then Samantha's hand moved. Not slowly this time, fast.