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Could someone please point out the benefits and implications of this? Does this bring us closer to some very important solution or does it have some real world

Could someone please point out the benefits and implications of this? Does this bring us closer to some very important solution or does it have some real world applications? Edit: I suppose this is a related article talking about the same problem from December 2017. What changed since then? https://www.quantamagazine.org/secret-link-uncovered-between-pure-math-and-physics-20171201/ https://www.quantamagazine.org/secret-link-uncovered-between...

rocqua 9y ago
The benefits are that mathematicians think it is interesting, and this allows us to answer mathematical questions we could not answer before. There might be practical applications I do not know of, but that's not the point of fundamental mathematical research. For a thorough defense of mathematics, consider 'A mathematicians apology' by G.H. Hardy or [1], a modern response to that. To summarize [1], the argument is that the main product of mathematics is an environment that creates mathematicians. Those mathematicians can the use their problem solving skills in practical applications. [1] https://ldtopology.wordpress.com/2017/03/18/a-new-mathematicians-apology/ https://ldtopology.wordpress.com/2017/03/18/a-new-mathematic...
- deleted 9y ago
  [deleted]
- saagarjha 9y ago
  That’s a defense of math in general; do you know what the benefits of this particular proof are? I’m not looking for practical applications; rather, could it help solve other problems in the field? Is it an important result in its own right?
  - rocqua 9y ago
    This shows that an oft talked about new technique in Diophantine equations actually works. The excitement is more due to proof-of-concept than the immediate logical implications.
sesqu 9y ago
This article is about (mathematical) application. They applied Kim's algorithm to find all rational solutions to a particularly hairy equation.
- colomon 9y ago
  If I read the article correctly, they already had all the solutions. They used the new approach to prove that there were no other solutions.
  - pcvpcvpcv 9y ago
    They didn't know they had all the solutions until they now proved there're no more solutions.
behindmyscreen 9y ago
Kim's solution appears to be a better method to use for discovering the roots of a Diophantine equation that has finite roots. This could have impacts on computational encryption....it could also just make mathematics in this area easier to work through.

rocqua 9y ago

The benefits are that mathematicians think it is interesting, and this allows us to answer mathematical questions we could not answer before. There might be practical applications I do not know of, but that's not the point of fundamental mathematical research. For a thorough defense of mathematics, consider 'A mathematicians apology' by G.H. Hardy or [1], a modern response to that. To summarize [1], the argument is that the main product of mathematics is an environment that creates mathematicians. Those mathematicians can the use their problem solving skills in practical applications. [1] https://ldtopology.wordpress.com/2017/03/18/a-new-mathematicians-apology/ https://ldtopology.wordpress.com/2017/03/18/a-new-mathematic...

deleted 9y ago
[deleted]
saagarjha 9y ago
That’s a defense of math in general; do you know what the benefits of this particular proof are? I’m not looking for practical applications; rather, could it help solve other problems in the field? Is it an important result in its own right?
- rocqua 9y ago
  This shows that an oft talked about new technique in Diophantine equations actually works. The excitement is more due to proof-of-concept than the immediate logical implications.

sesqu 9y ago

This article is about (mathematical) application. They applied Kim's algorithm to find all rational solutions to a particularly hairy equation.

colomon 9y ago
If I read the article correctly, they already had all the solutions. They used the new approach to prove that there were no other solutions.
- pcvpcvpcv 9y ago
  They didn't know they had all the solutions until they now proved there're no more solutions.

behindmyscreen 9y ago

Kim's solution appears to be a better method to use for discovering the roots of a Diophantine equation that has finite roots. This could have impacts on computational encryption....it could also just make mathematics in this area easier to work through.