Then I stretch before I can stop myself, arms overhead, and the hem lifts another centimetre. The air finds my skin.
So much for no provocation.
‘This is strong work,’ he says to the page. ‘That’s not the textbook approach.’
‘Didn’t use the textbook.’
‘Evidently.’
He’s talking about maths. The rest of him isn’t listening. He hasn’t looked away from the paper since the hip. I could uncross my legs and let my knee drift and watch him lose it.
The moment passes.
I lean forward, elbows on the desk. ‘Can I ask you something about the convergence criteria? In problem three I wasn’t sure if the bound holds for the general case or just the specific.’
He looks up, surprised. I’m being a student—an actual student asking an actual question about actual mathematics.
‘The bound holds generally,’ he says, cautiously. ‘But the proof requires an additional step. Here.’
He turns the page. Adds a note in the margin. The pen moves across the paper. I’ve seen this before. It’s the same thing I do.
We spend forty minutes on mathematics.
I ask questions with known answers and questions without. He explains clearly, patiently, and somewhere around minute twenty, the wall starts to develop hairline cracks, not because I’m pushing but because he’s teaching and teaching is where he lives.
I learn things, in those forty minutes. A neat trick for bounding an integral from below when the upper bound’s stuck. A way of thinking about convergence that is not in the textbook he wrote and taught from, because he has moved on from it since and never updated the text. A one-line aside about a problem in number theory, he says, was the reason he applied to Cambridge, which is more biographical information than he has given me in six weeks, and which he gives me because we are discussing the relevant function. He has forgotten, for three seconds, who he is sitting across from.
He remembers. I watch him remember. He fixes his eyes on the paper, and the next sentence comes back in the teaching voice.
But the forty minutes were mine.
I bend my head over problem four, writing. Peripheral vision is his favourite blind spot. His attention drifts downward. To the chain at my neck, the collar of my t-shirt, my skin. He thinks I can’t see.
He rolls his left sleeve up. The writing side.
One fold. Two.
The freckle near the wrist I haven’t earned the right to know about. I look at the whiteboard.
‘So if the epsilon condition fails,’ I say, ‘the whole proof collapses?’
‘Exactly. Which is why you need a contradiction.’
‘I need a contradiction.’ I finish it before he does. Just the thought arrives, and my mouth follows, and his expression does that thing again. The recognition. Last week’s look, before the wall went up, the same look, now from behind it. Trying to get through.
‘Yes,’ he says. Quiet. ‘Proof by contradiction.’
We sit with that for a second. Two.
Smiling would break it, pushing would shatter it. I let the mathematics do what my body’s been doing for four weeks, and the mathematics is worse because the mathematics is honest, and he can’t dismiss it as a student with a crush and tight jeans.
‘Right.’ He shuffles the pages. Stacks them. The gesture of a session ending, except the session has ten minutes left, and he’s cutting it short, and we both know why.
‘That’s—good progress.’ He exhales. Something larger than a sigh. Like he’s been holding it for weeks, for as long as we’ve been doing this with the books, the cold coffee, the door. ‘These sessions in my office.’
He’s looking at the desk.
‘They’re not working.’
