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> This is a huge deal, if true. What's the potential benefit to humanity that could come about if this is true, without any other dependencies, over the next 3
by throwaway0255 8y ago
> This is a huge deal, if true.
What's the potential benefit to humanity that could come about if this is true, without any other dependencies, over the next 30 years?
- Cyph0n 8y agoThat's just not how pure mathematics works. For instance, imagine asking that same question about Euler's totient function 50 years before RSA was developed. I am sure that there are countless other examples where a seemingly useless theorem aided in a practical problem decades or centuries later.
- throwaway0255 8y agoNow I and other non-mathematicians can look into Euler's totient function and RSA, and learn more. Thanks for answering. So is there really never a proof in pure mathematics with more obvious or immediate near-term applications? Are there any historical examples of that? A major breakthrough in mathematics that once understood, it was immediately obvious that it was going to make X work better, and then it did?
- adrianN 8y agoMathematics with immediate payoff is usually called physics or computer science. For example the simplex method for linear programming made a lot of things more efficient.
- pure-awesome 8y agoThe maths that has an immediate near-term application usually falls, almost by definition, under applied mathematics (or possibly a related field, such as physics, engineering, computer science etc.). Pure mathematics essentially concerns itself with the mathematics of mathematics. It's basically the process of trying to either prove certain "empirically discovered" mathematical facts, or understand deeply what those facts mean in a more general way. Understanding this type of mathematics in this deep way allows further mathematics to bud off of that specific
- adrianN 8y agoA deeper understanding of pure mathematics? That's like asking what benefits Michelangelo's works had for humanity.
- pure-awesome 8y agoI mean... not quite... Unless you're talking about improvements in artistic techniques, the art itself doesn't really lead to something more practical, whereas pure mathematics actually does often lead to applications in other fields.
- adrianN 8y agoModern mathematics is so incredibly abstract that I'd be very surprised if more than a minuscule fraction of all published theorems ever had practical applications. If you count that you should also count improvements in for example chemistry (pigments) or the theory of human perception that were initiated by art.