This is pure maths. Some areas have surprising applications, so if you found a fast way of factorizing large numbers into primes, for instance, has major security implications. But other areas - it's just of interest as maths. For instance the four colour theorem. We now know that every map can be coloured with four colours, with no two colours touching each other.
Martin Gardner as an April Fool's joke put forward this as a supposed "counterexample" of the four colour theorem
But as you can see it can be coloured with four colours, no two areas of the same colour touching.
So proving the theorem had absolutely no practical relevance. Nobody had discovered a map that needed more than four colours, and wasn't any practical problem that needed a counter example requiring five colours.
Still, mathematicians are not content with purely empirical results like that, because sometimes you get huge monstrous counter examples. We needed a proof to know if it is true or not.
Same with twin primes. No practical relevance as far as I know. Just pure maths.
Like a great work of art. Or a piece of music. Or a sculpture. Or a beautiful garden. We do many things which have no direct practical value, and many people devote their entire lives to activities that have no practical value - and certainly no survival value. Pure maths is like that.
Still - though the theorem wouldn't have any practical consequences, as far as I know, it is possible that the proof would. It might involve some new ideas.
Most likely- just - that it is of wider value in other areas of pure maths.
And occasionally you get surprising connections, e.g. between the Jones polynomial of knot theory and Chern–Simons theory, a topological quantum field theory.
But by and large, pure maths isn't of any particular practical use. It's just interesting in its own right.
With the twin primes conjecture, recent development is a continual reducing of the smallest gap between primes (in the limit).
It's now known that you can find infinitely many "prime pairs" with a gap between the primes of at most 246.
Bounded gaps between primes
Martin Gardner as an April Fool's joke put forward this as a supposed "counterexample" of the four colour theorem
But as you can see it can be coloured with four colours, no two areas of the same colour touching.
So proving the theorem had absolutely no practical relevance. Nobody had discovered a map that needed more than four colours, and wasn't any practical problem that needed a counter example requiring five colours.
Still, mathematicians are not content with purely empirical results like that, because sometimes you get huge monstrous counter examples. We needed a proof to know if it is true or not.
Same with twin primes. No practical relevance as far as I know. Just pure maths.
Like a great work of art. Or a piece of music. Or a sculpture. Or a beautiful garden. We do many things which have no direct practical value, and many people devote their entire lives to activities that have no practical value - and certainly no survival value. Pure maths is like that.
Still - though the theorem wouldn't have any practical consequences, as far as I know, it is possible that the proof would. It might involve some new ideas.
Most likely- just - that it is of wider value in other areas of pure maths.
And occasionally you get surprising connections, e.g. between the Jones polynomial of knot theory and Chern–Simons theory, a topological quantum field theory.
But by and large, pure maths isn't of any particular practical use. It's just interesting in its own right.
With the twin primes conjecture, recent development is a continual reducing of the smallest gap between primes (in the limit).
It's now known that you can find infinitely many "prime pairs" with a gap between the primes of at most 246.
Bounded gaps between primes
About the Author
Robert Walker
Writer of articles on Mars and Space issues - Software Developer of Tune Smithy, Bounce Metronome etc.Studied at Wolfson College, Oxford
Lives in Isle of Mull
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