"From what I'm told, yes. The professor tried to humiliate her. It backfired." Hayes was quiet for 10 seconds, then said, "Send me everything." By the next morning, she had the full photograph, high resolution, taken from three different angles by Amanda Cleary, who had the presence of mind to photograph the board before the janitor could erase it.
Hayes printed them out and spread them across her desk in the visiting faculty office, the way a detective spreads evidence across a table. She started with problem one. The approach was unconventional. That was the first thing she noticed. Standard attempts at this conjecture used Rado's theorem as a starting point and tried to extend it through iterative refinement.
Samantha had bypassed Rado entirely. She had come at the problem through a topological lens, treating the integer partitions as elements of a geometric structure, and proving the result by showing it was a necessary consequence of a connectivity property that nobody had thought to check. It was clean. It was correct. And it was the kind of approach that made Hayes sit back in her chair and say to an empty room, "How did she see that?"
Problem two was more ambitious. The cross-domain mapping from partition sets to simplicial complexes was the kind of move that would get rejected in a grant proposal for being too speculative. But Samantha hadn't written a proposal. She had just done it. And it worked.
The mapping preserved the asymptotic bounds while generalizing the identity to arbitrary dimensions. The proof was tight, self-contained, and Hayes checked three times, complete. She picked up her phone, called Victor Ashworth at Princeton, read him the key steps of problem two over the phone. There was silence. Then came the request: "Read that back to me."
She did. "Eleanor, that's not an incremental result. That's a new method. If this holds, it applies to the entire Burnside class." She called James Whittaker at Cambridge next.
Same reaction. Same long pause. Same request to hear it again. Whittaker added something Ashworth hadn't. "Whoever wrote this has an instinct I haven't seen in 20 years."