#mathematics

I hope that seeing the excitement of solving this problem will make young mathematicians realize that there are lots and lots of other problems in mathematics which are going to be just as challenging in the future. ↗

— Andrew Wiles

#excitement #future #going #hope #i

I tried to fit it in with some previous broad conceptual understanding of some part of mathematics that would clarify the particular problem I was thinking about. ↗

— Andrew Wiles

#broad #clarify #conceptual #fit #i

It could be that the methods needed to take the next step may simply be beyond present day mathematics. Perhaps the methods I needed to complete the proof would not be invented for a hundred years. ↗

— Andrew Wiles

#complete #could #day #hundred #i

It's fine to work on any problem, so long as it generates interesting mathematics along the way - even if you don't solve it at the end of the day. ↗

— Andrew Wiles

#any #day #end #end of the day #even

We've lost something that's been with us for so long, and something that drew a lot of us into mathematics. But perhaps that's always the way with math problems, and we just have to find new ones to capture our attention. ↗

— Andrew Wiles

#attention #been #capture #drew #find

Well, some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve. ↗

— Andrew Wiles

#hard #hundred #look #mathematics #out

Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness. ↗

— E. T. Bell

#art #creative #feeling #fitness #generality

If indeed, as Hilbert asserted, mathematics is a meaningless game played with meaningless marks on paper, the only mathematical experience to which we can refer is the making of marks on paper. ↗

— E. T. Bell

#experience #game #indeed #making #marks

It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences. ↗

— E. T. Bell

#immortality #itself #marks #mathematics #off

The longer mathematics lives the more abstract - and therefore, possibly also the more practical - it becomes. ↗

— E. T. Bell

#also #becomes #lives #longer #mathematics