How do mathematicians know when to stop?

Mathematical knowledge is like an inverse pyramid, you start at the very bottom with just a very limited number of ideas, and you can build on top of these ideas to discover knew and interesting things. Some blocks expand the pyramid upwards, providing a foundation for new knowledge, and others just fill in gaps that were missing from the lower levels, but whatever is discovered the pyramid just keeps on growing.

Eventually there might be a point where rather than getting wider, the pyramid starts shrinking as it gets higher, this point would be where we have complete mathematical theories of whole branches of mathematics and there are no new questions to be asked. The chance of this actually happening any time in the foreseeable future is pretty negligible though, if it ever happens.

How it doesn't benefits the society?

Can you explain it.

If mathematics is the queen of sciences then psychology is the duchess of york

First the natural numbers were invented for counting. Then, we had to invent addition and subtraction. Multiplication and division soon followed. As if this wasn't enough, mathematicians invented exponentiation for repeated multiplication.

Theoretically, it is possible to keep creating infinitely many theorems and formulas in infinitely many branches of mathematics. So, how do mathematicians know when to stop?

But what's the point of just going on and on if it doesn't benefit society?

But what's the point of just going on and on if it doesn't benefit society?

Why do you think it doesn't benefit society?

I do not think that. I said "What's the point of developing a certain branch of mathematics if it doesn't benefit society?"

Except that learning about maths isn't the same as learning about life. People should learn about stars so that they can appreciate nature.

But any branch of mathematics is just a human invention. Since we could (in theory) invent infinitely many branches of mathematics, how do we decide which branch is more worthy of study than the other? It has to be based on the usefulness.

I do not think that. I said "What's the point of developing a certain branch of mathematics if it doesn't benefit society?"

Allow me to rephrase - what makes you think there can exist a branch of mathematics that cannot benefit society?

Given that we could create a branch of mathematics about anything under the sun, isn't it more likely that it won't benefit society than that it will?

But what's the point of just going on and on if it doesn't benefit society?

Can you explain why this is the case?

Suppose we were living in primitive times and had just invented the decimal system for counting. Inventing the binary system then would not benefit society.

"Number theory of Roman numerals" is another branch of maths that could be invented today but will probably not benefit society.