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1. You're confusing theoretical math vs. applied math. Google doesn't benefit from algebraic topology. 2. Startups would exist -- just not as many. The cost wo

by cpks 12y ago

1. You're confusing theoretical math vs. applied math. Google doesn't benefit from algebraic topology. 2. Startups would exist -- just not as many. The cost would be slightly higher; they'd have to pay employees either fair salaries, or give fair levels of equity. The current situation -- long hours, low salary, crooked options -- would not persist.

eurleif 12y ago
>You're confusing theoretical math vs. applied math. Google doesn't benefit from algebraic topology. Not yet, maybe. But it does benefit from number theory, which was considered to have no practical applications until people realized we could do encryption with it.
- cpks 12y ago
  Two ways to look at it: 1. Return on investment. Every hour spent on applied math generates a lot more applications (not to mention elegant mathematics) than the same spent on theoretical math. Theoretical math has about as much value as knitting and crochet. Does someone occasionally come up with something of value? Sure. Does it have more value than any other hobby? Not really. 2. With encryption in particular, Diffie-Hellmen is simple enough that public key would have been created regardless of research in theoretical math. Furthermore, most of the people developing such (including Diffie, Hellmen, Merkle, Rivest, Shamir, Adleman, etc.) have applied backgrounds. Indeed, most are computer scientists, rather than mathematicians. The same goes for cryptographic protocols, doubly so. Symmetric encryption, in contrast, does build a little bit on theoretical math, but it's also just an arms race. More knowledge about number theory helps both cryptography and cryptanalysis about equally. There's no reason to believe that more number theory makes us in any way more secure. Cryptography itself would exist without number theory (indeed, history is a bit fuzzy as to whether something like the scytale or number theory came first, and regardless, there is no reason to believe one fed the other).

by cpks 12y ago

eurleif 12y ago

>You're confusing theoretical math vs. applied math. Google doesn't benefit from algebraic topology. Not yet, maybe. But it does benefit from number theory, which was considered to have no practical applications until people realized we could do encryption with it.

cpks 12y ago
Two ways to look at it: 1. Return on investment. Every hour spent on applied math generates a lot more applications (not to mention elegant mathematics) than the same spent on theoretical math. Theoretical math has about as much value as knitting and crochet. Does someone occasionally come up with something of value? Sure. Does it have more value than any other hobby? Not really. 2. With encryption in particular, Diffie-Hellmen is simple enough that public key would have been created regardless of research in theoretical math. Furthermore, most of the people developing such (including Diffie, Hellmen, Merkle, Rivest, Shamir, Adleman, etc.) have applied backgrounds. Indeed, most are computer scientists, rather than mathematicians. The same goes for cryptographic protocols, doubly so. Symmetric encryption, in contrast, does build a little bit on theoretical math, but it's also just an arms race. More knowledge about number theory helps both cryptography and cryptanalysis about equally. There's no reason to believe that more number theory makes us in any way more secure. Cryptography itself would exist without number theory (indeed, history is a bit fuzzy as to whether something like the scytale or number theory came first, and regardless, there is no reason to believe one fed the other).