### Weil, Venting

#### Posted by Tom Leinster

From the introduction to André Weil’s *Basic Number Theory*:

It will be pointed out to me that many important facts and valuable results about local fields can be proved in a fully algebraic context, without any use being made of local compacity, and can thus be shown to preserve their validity under far more general conditions. May I be allowed to suggest that I am not unaware of this circumstance, nor of the possibility of similarly extending the scope of even such global results as the theorem of Riemann–Roch? We are dealing here with mathematics, not theology. Some mathematicians may think they can gain full insight into God’s own way of viewing their favorite topic; to me, this has always seemed a fruitless and a frivolous approach. My intentions in this book are more modest. I have tried to show that, from the point of view which I have adopted, one could give a coherent treatment, logically and aesthetically satisfying, of the topics I was dealing with. I shall be amply rewarded if I am found to have been even moderately successful in this attempt.

I was young when I discovered by harsh experience that even mathematicians with crashingly comprehensive establishment credentials can be as defensive and prickly as anyone. I was older when (and I only speak of my personal tastes) I got bored of tales of Grothendieck-era mathematical Paris.

Nonetheless, I find the second half of Weil’s paragraph challenging. Is there a tendency, in category theory, to imagine that there’s such a thing as “God’s own way of viewing” a topic? I don’t think that approach is fruitless. Is it frivolous?

Posted at November 10, 2015 11:41 PM UTC
## Re: Weil, Venting

For what reason or omission I do not know, when I think of Erdős and his imagined Book,

categoricalquestions do not come to mind.