[thomaskurian89]

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?

[Axion]

when the earth implodes.

Or

when ideas conflict

[raheem94]

(Original post by thomaskurian89)
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?

They don't need to stop.

[Intriguing Alias]

(Original post by raheem94)
They don't need to stop.

^^

[thomaskurian89]

(Original post by raheem94)
They don't need to stop.

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

[olipal]

(Original post by thomaskurian89)
But what's the point of just going on and on if it doesn't benefit society?

You could not have a more appropriate sig.

[tazarooni89]

(Original post by thomaskurian89)
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?

When they have created a single general formula, method or theorem which is applicable to absolutely everything. Or when they have proven that this is impossible, and created formulae, methods and theorems which are as generally applicable as they possibly can be.
So for example, instead of having a formula to solve quadratic equations and a formula to solve cubic equations, derive a formula to solve any polynomial of order n. And then instead of having a method to solve polynomials and a method to solve differential equations, have a single method which will solve both. And carry on like that.

Programme a computer with the final resulting formulae, and there will no longer be any need for mathematicians to do anything.

[Arekkusu]

We didn't "invent" it, if anything maths invented us, maths is the abstraction of the same logic of our universe that makes physics happen.

[raheem94]

(Original post by thomaskurian89)
But what's the point of just going on and on if it doesn't benefit society?

How it doesn't benefits the society?

Can you explain it.

[cuckoo99]

(Original post by thomaskurian89)
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?

Maths is the purest science. Science is about discovery. Maths is about discovering ways to solve problems. aslong as there are problems there will be an opportunity to attempt to reason with those problems and find an answer. example: we created simple addition so we could accumalate the amount of objects seen with our eyes, But how could we count objects that were perceived as half of that object? we couldn't because we hadent invented fractions... This is just my opinioun anyways and my opinioun is that perhaps 1 day if humans dont die out, we will reach a place of true understanding of the universe. there would be no need for science and life as we know it would become boring

[Jodin]

(Original post by thomaskurian89)
But what's the point of just going on and on if it doesn't benefit society?

! It's fun! So it benefits me at least which seems enough reason to do it. It makes a great number of people happy (mathematicians at least), how many people would you like it to benefit? And obviously, one rather doesn't know if something is going to 'benefit society' until they research it.

[kingkongjaffa]

I would suppose that mathematics is created at greatest pace when there is a direct scientific need for it, Once everything there is to know about the universe has been discovered then perhaps things would stop but even then people would find novel ways of using mathematics so I doubt even then progress would stop completely. Also things like prime numbers and other mathematical enigma will be researched for a very long time yet,

So in answer to your question, how do they know when to stop, perhaps when there's nothing left for them to do.
But there's a lot to be done so they won't stop for a long time yet

[JongKey]

(Original post by thomaskurian89)
But what's the point of just going on and on if it doesn't benefit society?

Stop. Just stop.

[thomaskurian89]

(Original post by raheem94)
How it doesn't benefits the society?

Can you explain it.

It is not necessary that all branches of maths benefit society directly or indirectly.

[Sternumator]

(Original post by thomaskurian89)
But what's the point of just going on and on if it doesn't benefit society?

They do benefit society. Mathematicians don't just define new things for no reason, they are useful for describing and understand something.

[mimx]

(Original post by thomaskurian89)
But what's the point of just going on and on if it doesn't benefit society?

The thing about discoveries that enhance 'society' is that a lot of the time you can't really tell what will be particularly useful in advance and think we should go find that out because it will help us do x. So we do mathematics for mathematics' sake and maybe we get some beneficial stuff from it.

If not then we enjoyed doing it anyway.

[Venomilys]

you're looking at it from a naive point of view. We didn't invent numbers, numbers were already there, it just took us time to understand it.

The invention of new, breath-taking mathematics that allows us to travel at the speed of light will probably never exist. Why? because, as humans, we can't fathom the complexity that is science. So you could argue there is a 'peak'.

[thomaskurian89]

(Original post by Ilyas)
The invention of new, breath-taking mathematics that allows us to travel at the speed of light will probably never exist.

That's because it's not possible to travel at the speed of light. (Special relativity)

[raheem94]

(Original post by thomaskurian89)
It is not necessary that all branches of maths benefit society directly or indirectly.

Read this article: http://www.dpmms.cam.ac.uk/~wtg10/importance.pdf

[Rubgish]

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.