Privately, he had had quite a different idea of what a mathematician’s study might be like; that it might somehow express the terrible things that were thought there. The ordinariness of it all wounded him; he transferred that hurt to mathematics in general, and his respect began to make way for a suspicious resistance.

As the teacher rocked back and forth impatiently in his seat, unsure how to interpret the long silence and the watching eyes, there was already a mood of misunderstanding between them.

‘Now shall we ... will you ... I’m happy to give you any information you might need,’ the teacher began.

Törless set out his reservations and tried to explain their significance for him. But it was as though he was speaking through a thick, dull fog, and the best things he wanted to say stuck in his throat.

The teacher smiled, gave a slight cough, said, ‘If you will excuse me,’ and lit a cigarette, smoking it in quick puffs; the cigarette paper — and Törless took all this in, finding it very common — was greasy and rustled every time it was rolled; the teacher took his pince-nez from his nose, put it back on again, nodded his head ... in the end he wouldn’t let Törless finish.

‘I’m glad, my dear Törless, I’m really very glad,’ he interrupted. ‘Your concerns show that you are serious, they show evidence of independent thought ... of ... hmm ... but it isn’t at all easy to give you the explanation you’re after... you mustn’t misunderstand me.

‘You see, you were talking about the intervention of transcendent, hmm yes ... they’re called transcendent — factors...

‘Now I don’t know how you feel about this; the supersensory, everything that lies beyond the strict laws of reason, is something that follows its own rules. I’m not really equipped to talk about it, it isn’t part of my subject; you can think about it in one way or another, and I would prefer to avoid being controversial ... But where mathematics is concerned, it is quite certain that even here there exists only a natural, purely mathematical context.

‘Now - to be strictly scientific — I would have to set out preconditions that you would barely understand, and we haven’t time for that anyway.

‘You know, I happily concede that for example these numerical values which don’t really exist, ha ha, are no small nut for a young student to crack. You will have to accept that such mathematical concepts are purely mathematical logical necessities. Just think for a moment: at the elementary stage of education, which is where you are at present, it is very difficult to find the correct explanation for many of the things that you will encounter. Fortunately very few students are affected by this, but if someone, as you have done today — and, as I say, I am very pleased — does come and ask, one can only say: my dear friend, you must simply believe; if you can do ten times as much mathematics as you do at the moment, you will understand, but for the time being: believe!

‘That is the only way, my dear Töriess; mathematics is a whole world in itself, and one must have lived in it for a very long time to feel everything that is necessary within it.’

Törless was pleased when the master stopped speaking. Since hearing the door close behind him he had felt that the words were coming from further and further away ... moving towards that other, indifferent side, where all correct yet meaningless explanations lie.

But he was numbed by the torrent of words and by failure, and he didn’t immediately understand that he was now expected to rise to his feet.

Then his teacher, in order to resolve matters once and for all, reached for one final persuasive argument.

On a little desk lay an elegant and expensive volume of Kant. The teacher picked it up and showed it to Törless. ‘You see this book, this is philosophy, it contains the defining aspects of our actions. And if you could feel your way to the bottom of it, you would encounter only such logical necessities, which define everything despite the fact that they themselves cannot be understood without further ado. It’s very much the same with mathematics. And yet we are constantly acting according to those necessities; there you have the proof of how important such things are. But,’ he smiled when he saw that Törless was actually opening the book and flicking through it, ‘forget that for now. I just wanted to give you an example that you would remember in later years; it would be too difficult for you for the time being.’

 

All the rest of that day Törless was in an agitated state.

The fact that he had held Kant in his hand - that quite arbitrary fact, to which he had paid little attention at the time — subsequently affected him very powerfully. He knew the name Kant from hearsay, and for him it had the market value that it generally enjoys among those people who only ever come into remote contact with arts subjects - as the last word in philosophy. And that authority had even been one reason why Törless had hitherto paid so little attention to serious books. Once past the phase of wanting to be a coachman, a gardener or a pastry-maker, very young people tend at first, in their mind’s eye, to stake out the area of their future life’s work wherever their ambition finds the greatest likelihood of achieving excellence. If they say they want to be a doctor, it is sure to mean that at some point they have seen a nicely appointed waiting-room full of people, or a glass case filled with grisly surgical instruments, or something of the kind; if they speak of a diplomatic career, they are thinking of the brilliance and elegance of the international salons: in short, they choose a profession according to the milieu in which they would most like to see themselves, and according to the pose in which they feel they look their best.

Now Törless had only ever heard the name of Kant uttered occasionally and then with a curious expression, as though it was the name of some sinister holy man.