131–140 of 439 posts
Is there a real world outcome to this result?
I think it's fair to say that this could lead to certain new things becoming known about the distribution of primes. This could have implications for cryptographic algorithms that depend on prime numbers being hard to find.
That depend on large semiprimes being hard to factor.
Math used to be a young person game, but it now requires so much knowledge just to get to the frontiers of human knowledge, not to speak of making a dent into uncharted territory, that results are being obtained later and later in life. When mathematicians have had time to accrue sufficient knowledge while still being sharp enough to make the intellectual leap. The sad part is that as the trend continues we may reach…
Another angle here, I remember seeing a study where some children were just... taught algebra. Like given high school algebra classes in 3rd grade, and kids were able to absorb all that abstract reasoning "just fine" (according to the study).
Of course there's only so much abstraction that can be done, but I think we shouldn't assume we are at the end of history on much of anything (except for parsing algorithms)
Earlier quoted context omitted.
RSA depends on large prime factors being hard to recover from their product.
If it were just that, it would be trivial to break. It's the fact you generate the key after a modulus operation that makes it difficult to recover.
Factoring that large integer directly yields the user's private key.
Two additional notes: 1. Zhang posted an attempt at solving this problem in 2007 that he later more or less admitted was flawed: https://mathoverflow.net/questions/131221/yitang-zhangs-2007... . But speaking with mathematicians who are intimately familiar with Zhang's previous work, there seems to be good reason to be optimistic nevertheless. First, the idea behind Zhang's proof is similar to the zero-repulsion ideas…
Earlier quoted context omitted.
Someone needs to make a movie about his life, or at least a documentary.
Sadly, they would probably make it a schmaltzy Oscar-grab of a movie, like they did with Ramanujan's story.
There was a scientist who did his best stuff while he was working as a patent clerk.
Patent clerk (at least back then) is a more skilled job than it sounds, as it's someone that actually reviews the patents rather than just a general office dogsbody, so you have to understand the technology and to some extent the science in those patents. It's not totally unrelated to being a scientist and definitely a less surprising early career job than delivery driver.
If someone tells you they were a “clerk” for a Supreme Court judge don’t be surprised when later in life they have an impressive legal career
Earlier quoted context omitted.
I think it's fair to say that this could lead to certain new things becoming known about the distribution of primes. This could have implications for cryptographic algorithms that depend on prime numbers being hard to find.
Careful, prime numbers are not hard to find. Like, try openssl prime -generate -bits 2048 Congratulations, you just found a prime that is big enough for every cryptographic protocol that uses prime numbers (not counting unusual and non-deployed post-quantum proposals). Some number theory research may impact the security of cryptosystems, but not all results do.
Earlier quoted context omitted.
It's the moral equivalent of making major headway against P!=NP; or, proving that there are no global hidden variables in QM; or, that there's a clear path ("just engineering") to room-temperature semiconductors.
>room-temperature semiconductors I suppose superconductors. Semiconductors are well in the room temperature regions :)
Math used to be a young person game, but it now requires so much knowledge just to get to the frontiers of human knowledge, not to speak of making a dent into uncharted territory, that results are being obtained later and later in life. When mathematicians have had time to accrue sufficient knowledge while still being sharp enough to make the intellectual leap. The sad part is that as the trend continues we may reach…
The abstractions need to be understood, but potentially only to a level of n-1. Isn't this one of the core principles of proofs?