Often I have thought about this:-

Is there any real end or a dead stop to maths as a subject? Can there be a time when everything in this beautiful field has been discovered, all possible theorems, axioms, postulates have been found out, and all that is left is their application as we do today.

I know researches have been conducted in the past and are still going on. But is there still anything left to unearth (rather anything "significant") in this 'queen of all sciences'?

I hope it's not a stupid question, because it has triggered my thought process plenty of times.

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    $\begingroup$ Without knowing too much about this axiomatic stuff I guess there is no end as things we already know can always be put into another frame/context and interpreted differently to make things more clear. It is not just about discovering results but also about understanding these in different ways. $\endgroup$
    – noctusraid
    Feb 17, 2017 at 18:16
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    $\begingroup$ You should have a read of Gödel's incompleteness theorems. Quite interesting. en.m.wikipedia.org/wiki/… $\endgroup$
    – Cuhrazatee
    Feb 17, 2017 at 18:17
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    $\begingroup$ Here is a sort of trivial statement: if we (in principle) assume that all math can be formulated over the alphabet of English together with, let's say, a few hundred mathematical symbols, then you could at least limit all possible math to something excessive like $(\text{#symbols})^{1000000\times \text{(human lifetime in seconds)}}$. That's still very big, though. $\endgroup$ Feb 17, 2017 at 18:22
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    $\begingroup$ There is no limit to how many numbers exist, and there is no limit to the properties of numbers. From number theory and googology (fun subjects). $\endgroup$ Feb 17, 2017 at 18:48

1 Answer 1


Not to belabor the cliche that math is art, but this same kind of issue comes up in the arts.

One could easily imagine there are only so many styles of painting. Only so many subjects to draw without essentially coming to repetitions.

Or maybe there are only so many styles of music. All scales have been explored so thoroughly for so many hundreds of years. The choice of instruments which we would ever find appealing is so constrained.

But the arts do just fine. And so will mathematics.


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