The night shift and the problem set

There is a kind of student I have taught for fifteen years now and I want to write about him, because nobody writes about him and the people who decide his future do not know he exists.

He finishes a shift at eleven. It might be a kitchen, a warehouse, a supermarket floor, a care home where he lifts a man twice his weight and speaks kindly to him. He walks home or takes a bus, and the bus is warm and he does not sleep on it because if he sleeps he misses the stop. He gets in. The flat is cold. He puts the kettle on and he sits down and he opens the problem set, and it is half past eleven at night, and he has four hours of mathematics in front of him and six hours before the alarm.

He does two of the four. He gets the first one out and the second one nearly out and then the words stop meaning things, and he goes to bed knowing he has not finished, and this is Tuesday, and Wednesday will be the same.

In the morning a young man who did not work last night hands in all four, correct, and goes to breakfast.

What the hours take

People talk about working students as though the cost were time, and it is not really time. Time can be found. You can cut sleep for a term, you can give up the football, you can stop seeing people, and plenty of them do all three.

What it takes is the thing underneath. It takes the loose hour after a lecture when the idea is still warm and you turn it over without meaning to. It takes the argument in a corridor about whether the proof really needs that condition. It takes the reading you do because you are curious rather than because it was set. That is where mathematicians are actually made, in the slack, and the working student has no slack. He has the lecture and he has the sheet and he has the shift, and the three of them lock together like gears with no play in them.

So he learns to be efficient in a way that is not entirely good for him. He learns to find the method that gets the mark. He gets very fast at recognising which question this is. And recognising which question this is will carry him a long way, right up until the day somebody asks him something he does not recognise, which is what an Oxford interview does, and what a trading floor does, and what any real problem does.

What it gives

And yet.

I have taught a great many students who never had to work, and some of them are the finest mathematicians I have met, and I say this without any grievance at all. Money is not a moral failing in either direction.

But there is something the working ones have that I have learned to look for, and it took me years to see it clearly enough to name.

They do not fold.

Put a hard problem in front of a student who has never been genuinely uncomfortable and quite often something goes out of him. Not always. But often. He has been good at this his whole life, and being stuck feels like a verdict, and he goes quiet and waits for you to rescue him. You watch the confidence drain out and you know that in an interview room in December this will happen and there will be nobody there to help.

The one who has been coming home at midnight for three years does not do that. He has been stuck before, in ways that had nothing to do with mathematics, and he has learned that being stuck is a condition you work through rather than a thing that happens to you. You give him a problem beyond him and he sits with it. He tries something stupid and says so. He tries something else. He is not enjoying himself and he does not stop.

That is the thing the interview is looking for. That is precisely the thing. And he has it already, and nobody has told him it counts.

What I do about it

I wish I could say I have solved this. I have not.

What I do is smaller. I tell him what he has, because he does not know. He thinks the boy who handed in four is simply better than him and always will be, and that is not true, and being told it by someone who has taught both is worth more than an hour of teaching.

Then I change what we do with the time. If he has six hours a week and the other has twenty, six hours spent grinding through sheets is six hours wasted, because on that ground he cannot win and does not need to. We spend it on the unfamiliar. One problem he has never seen, worked properly, out loud, with me pushing. Nothing else. He resents it for about a month, because it feels like doing less, and the marks do not move at first.

Then December comes and he is asked something nobody prepared him for, and he is calm, and the boy who handed in four is not.

A note to the person deciding

If you read applications for a living, you have a line in front of you that says the candidate worked twenty hours a week. Most files do not say it. It is one line and it is easy to pass over.

Read it as what it is. That is a person who has already demonstrated, for two or three years, under conditions you did not set and cannot see, that he will keep going when it is unpleasant and unrewarded and nobody is watching.

You will spend the rest of the file looking for evidence of exactly that, dressed up in better clothes.

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