19 ms·

Mathematicians clear hurdle in quest to decode primes

251 points by akeck 5y ago

zwkrt 5y ago
I love how every quote by the mathematician clearly states that this does not bring us appreciably closer to the Riemann hypothesis, or that it is very unlikely, while the bulk of the article seems to imply otherwise.
- gavagai691 5y ago
  While I had a couple of gripes with the article, I don't get the sense that the article exaggerates the significance of this work. The (Generalized) Riemann Hypothesis implies the (Generalized) Lindelof Hypothesis. The latter is a particularly important consequence of GRH. Not only is it worthwhile, if you are interested in GRH, to verify its predictions (if you proved one of the predictions false, then you would disprove GRH, and if you proved it true, this would in some sense provide "theoretical support" for GRH), but Lindelof is useful in is own right. In particular, it can sometimes serve as a substitute for GRH, and results that can substitute for GRH (such as Bombieri-Vinogradov, zero-density estimates, and subconvexity estimates) are very valuable. Contexts where subconvexity estimates can serve in place of GRH include Quantum Unique Ergodicity, and representations of integers by ternary quadratic forms. For this reason, this paper is a much bigger deal (in the analytic number theory world / in my opinion) than the paper a couple years back that made big headlines about Jensen polynomials (and Nelson's paper is surely one of the biggest results in the last couple of years in analytic number theory). While the latter was more of a "curiosity" / cute paper on an obscure way of thinking about RH, Nelson's paper is big progress on a well-studied weaker form of GRH with significant utility for applications. (I mean, of course, applications in mathematics.)
  - gavagai691 5y ago
    (To expand on this a bit: the reason that GRH is so important is because of its ubiquitous applications in mathematics. Maybe you can think of these applications as different food items, whose recipes call for GRH. The problem is that GRH is a very hard ingredient to come by! (That is, if you want your result to be "unconditional," in the sense of not assuming anything unproven.) In some of these cases, however, (such as the two mentioned in the comment above), substituting the Generalized Lindelof Hypothesis in place of GRH (remarkably) would give you a result just as good! (Think "I can't believe it's not GRH!") Unfortunately, Lindelof is also presently out of reach in almost all contexts. Subconvexity estimates are partial progress towards Lindelof. If you substitute them in place of GRH in your recipes, you'll get something better than if you used the cheapest ingredient (the convexity bound), but not something quite as good as if you had used Lindelof or GRH. Some of the most important results in analytic number theory are "I can't believe it's not GRH!" in their respective contexts. Here is one such example: For applications in sieve theory (e.g., the 2013 breakthrough work on bounded gaps in primes), the Bombieri-Vinogradov theorem is a substitute for GRH that is just as good as GRH.)
- charlieyu1 5y ago
  Scientific journalism. Buzzwords, speculations that don’t sound plausible to the scientific community, etc
  - Ericson2314 5y ago
    I don't think that's fair. Much scientific journalism, by focusing on exciting unexpected results, leaves one with an impression that there is too much dogma and perhaps other errors. Math is very hard, but has the luxury of correctness being better defined and easier to verify than about any other field. There simply isn't as much room for conspiracy thinking. And accordingly, the articles in Quanta Magazine are both great to read and don't have a side effect of causing any outsider smugness. That isn't to say math doesn't have controversies. The utility of proof assistance and degree to which people should study and use unifying frameworks like Category Theory are examples of ongoing controversies. But it's very fortunate that to be immune to issues like widespread replication crises. Math is really really different than Science.
    - SantalBlush 5y ago
      I'm not aware of category theory being controversial. A much better example would be Mochizuki's IUT controversy.
      - Ericson2314 5y ago
        It's not controversial in terms of correctness, but it is still a bit controversial in terms of whether it's worth the effort? See all those "but does this help me get results for existing problems?" type questions. There have always been mathematicians that prefer to first establish more structure vs those that just want to get down to business. Category theory especially in the past really pushed the envelope on the "more structure" side of things, inflaming those old tensions.
- pelasaco 5y ago
  probably different than the author from the article, the Mathematician wasn't interested in generating clicks.
- deleted 5y ago
  [deleted]
btmiller 5y ago
What impact would this have on elliptic curve cryptography?
- deleted 5y ago
  [deleted]
- echelon 5y ago
  I am not a mathematician or cryptographer, but here's my understanding (please, please correct me if I'm wrong) Modern cryptography relies on the hardness of integer factorization. Things you want to hide are intractable to calculate on even the most powerful machines due to the underlying math not being workable in polynomial time (or similar low degree time). Age of the universe hard to brute force with our machines and known algorithms. It has to do with the complex structure of the problem in our intuitive dimension. We haven't thought of any possible way to speed it up classically, and it's not apparent if there are such techniques. The Riemann Hypothesis conjectures that there is a way to know the distribution of primes in a higher dimensional imaginary math. That the unintuitive and difficult system that gives us primes in real number space is somehow contained in a larger imaginary space, with some kind of regular structure, and that they are immediately accessible and calculable once you know the trick. If the hypothesis is true, it's quite possible that NP hard problems are the same. That in some unintuitive higher dimension math we can solve the hardest problems in polynomial time. NP-hard problems are also proven to be equivalent complexity, and if you figure out one then the rest are also solvable. If we figure out the trick behind it all (if such a thing exists), we might break everything. Or maybe we'll prove that there is no such free lunch. I'm one of the ones hoping for computing to be easy. It would unlock so many possibilities. Fast math, in silico experiments, protein folding, etc. It unfortunately would also break all of the underpinnings of our industry, though. SSL, privacy, crypto, infosec, everything about the Internet... Most people are betting that primes are hard, and it certainly does look that way.
  - jayski 5y ago
    i have no idea why this great comment got down voted.
orena 5y ago
It might be that the Riemann Hypothesis will be the first of Math's "Hard Problems" that will be solved by AI before humans...
- fulvioterzapi 5y ago
  It might. However, since there's no record of AI solving big, open conjectures such as the Riemann Hypothesis, I find this quite unlikely.
  - orena 5y ago
    Well, you don't know how many years humans will need in order to solve it ;-).
mikewarot 5y ago
I suspect somewhere in the Riemann-Zeta function is a reciprocal that only cancels out all the imaginary terms once and only once, thus any number with more than one factor wouldn't cancel out. I haven't the math skills to find that reciprocal.
gavagai691 5y ago
Two inaccuracies in the article. For purposes of simplicity, the author writes "But the Lindelöf hypothesis says that as the inputs get larger, the size of the output is actually always bounded at 1% as many digits as the input." But this is a case where simplification goes too far. What Lindelof says is that the size of the output is always bounded by ε% as many digits as the input, for ANY (arbitrarily miniscule) ε > 0. Second, the subtitle "Paul Nelson has solved the subconvexity problem..." is strange. The subconvexity problem, for a given L-function, is to lower the percentage described above from 25% to "any positive number"; in other words, to bridge the gap between the convexity bound (which is "trivial") and Lindelof (a consequence of GRH). The only way that the statement "Paul Nelson has solved THE subconvexity problem..." could maybe be accurate is if Nelson proved the Lindelof hypothesis for "all" L-functions. Which is far from the case. (What makes subconvexity so interesting, as Nelson says in the article, is that it is a problem where you can make partial progress towards a particularly important consequence of GRH. And Nelson's result is exactly that: partial progress.) More accurate would be "Paul Nelson has made significant progress on the general subconvexity problem."
- kevinventullo 5y ago
  I’m confused by your second paragraph. The article describes the subconvexity problem for a given L-function as lowering the bound from 25% to x% for some x < 25. That is, 25% is the “convexity bound” and the existence of such an x is a “subconvexity bound.” My understanding is that Nelson has indeed done this for every L-function, although the exact x varies with the L-function. How is that not solving the subconvexity problem?
  - gavagai691 5y ago
    A subconvex bound is any bound that beats the convexity bound of 25%. If you would define "the subconvexity problem" as beating the 25% bound AT ALL (or in other words providing any subconvex bound), then the statement in the subtitle would be closer to accurate. But this is not (I think) how most people would speak, and I wouldn't say this. I would say the subconvexity problem is the problem of bridging the gap between 25% (convexity) and 0% (Lindelof). Subconvexity bounds for various L-functions (zeta, Dirichlet L-functions, and higher rank L-functions) are a very active area of research, and so it seems strange to me to say "the subconvexity problem is solved." "My understanding is that Nelson has indeed done this for every L-function." One minor note. Nelson's work applies if the L-function is automorphic. By the Langlands philosophy, this should be true for any reasonable L-function, but this is far from known, even in, e.g., the simple case of the L-function corresponding to the tensor product of two automorphic L-functions. Edit: I am wrong about the statement "this is not (I think) how most people would speak." It looks like beating the convexity bound at all is often described as "solving the subconvexity problem," e.g. in the introduction here https://link.springer.com/article/10.1007/s002220200223 https://link.springer.com/article/10.1007/s002220200223. This description is a bit strange to me, but if it is standard then it is unfair for me to call it an "inaccuracy," persay; thanks for pointing this out.
Victerius 5y ago
Young enough for a Fields? There is a ceremony later this year, but it's probably too soon. So he could be awarded a Fields in 2026 if he's not yet 40. He received his PhD in 2011. Also, according to MathGenealogy, his grand-grand-grand-grand-grand-grand-grand-grand thesis advisor was none other than Poisson himself. Poisson's advisers were Lagrange and Laplace. Lagrange's was Euler. Euler's was Bernoulli. Bernoulli's was another Bernoulli. You can go back to the late 15th century to find mathematicians with "unknown" advisors.
- JadeNB 5y ago
  > There is a ceremony later this year, but it's probably too soon. Maybe this is what you meant by "it's probably too soon", but almost certainly the decisions about who gets it have already been made.
- gavagai691 5y ago
  My bets are on another analytic number theorist for the Fields this cycle, namely James Maynard.
easytiger 5y ago
I remember as a teen when my parents got me a pc (they could Ill afford) as an upgrade from the, by then 10 years old, hand-me-down ZX Spectrum. I was in awe at how many primes I could find on my cyrix 333Mhz on my own noddy code Left it running all day when at school. Never found any thing of value but I learned how to Beowulf cluster and learned a lot about arbitrary integer implementation Simpler times
- ackbar03 5y ago
  Is finding primes of all things really the first thing you did with a computer as a teen? You could have invented Facebook or Napster
  - wiz21c 5y ago
    The first thing I'd do today is a spam filter :-)
  - kybernetyk 5y ago
    I invented Napster but then Justin Timberlake stole my idea.
  - easytiger 5y ago
    I know. I'm fairly sure i did develop them but just deleted as i thought nobody would want that
    - axiosgunnar 5y ago
      In fact, nobody does want Facebook, so you were right
      - easytiger 5y ago
        I actually built in the 90s a site that was kinda like reddit but just for BBC news articles (they only started comments a few years ago) and a comedy/satire news site ala the onion. in retrospect teenage me should prob have told other people about my websites
deleted 5y ago
[deleted]
saimiam 5y ago
This fascination with primes is has, of late, seemed to be a little misplaced to me. Primes emerge as a property of the number system that you have. The number system itself is an an approximation of the natural world where actions like addition, subtraction, multiplication and division exist. The natural world in question is, as far as we know today, what we humans observe. Now, imagine a second world which was excellent at approximations to the extent that their entire Standard model depended on differentiation and integrations. Would they care as much about primes and try to fit everything into “beautiful” math? I don’t know the answer to this but I’ve found this thought experiment useful to put our maths in its place.
- kzrdude 5y ago
  I don't think we have even managed to imagine a world where the natural numbers wouldn't be a useful building block. That means the natural numbers are a fundamental logical building block of any formal system like mathematics, doesn't matter what the laws of physics are.
- deleted 5y ago
  [deleted]
- misja111 5y ago
  I don't see how you could model the world without addition or subtraction. Even if you started out with differentiation, wouldn't addition and subtraction be implicitly defined by it? And once you have those, you have multiplication and division as well, and primes.
optimalsolver 5y ago
Is there a reason we're obsessed with primes beyond aesthetics? Why does this set of numbers garner all the headlines as opposed to some other arbitrary integer sequence like the Recamán numbers [0] ? If tomorrow someone discovered a closed-form equation for the nth prime, how would mathematics/the world change? [0] https://en.wikipedia.org/wiki/Recamán%27s_sequence https://en.wikipedia.org/wiki/Recamán%27s_sequence
- iNic 5y ago
  Yes. Just within mathematics prime numbers have a tendency to show up in many fields not obviously related to number theory. As an example: in the study of symmetries (group theory [0]) important to number theory, geometry and even many parts of physics prime numbers help us decompose a complicated symmetry into simpler ones (using Sylow theorems [1]. Prime numbers are also used for cryptography due to their computational properties. Also I think we have shown using a variant of Galois theory that there can not be a closed from solution for the nth prime. But there are more headlines about the primes relative to its prevalence in research. I would guess that this is because - they can easily be explained to people - have been studied for thousands of years - open problems still persist In other parts of research you might need at least an undergraduate degree just to understand the definitions, which makes headlines less sexy. [0] https://en.wikipedia.org/wiki/Finite_group https://en.wikipedia.org/wiki/Finite_group [1] https://en.wikipedia.org/wiki/Sylow_theorems https://en.wikipedia.org/wiki/Sylow_theorems
  - slx26 5y ago
    I think it's about the fact that they are a mystery at the heart of maths. You can start describing maths from the unit, the addition and the negative sign. If you start combining those, you get the natural numbers, the integers, ... but even before the natural numbers come the prime numbers. Primes are the most fundamental set of numbers in mathematics, from which you can generate the natural numbers. But as you say, even after so many years they are still relevant, useful and mysterious. They are on a wildly different category from other sets and numerical series. They are the most central element of maths that we still don't understand. And central means that so many other parts of maths derive from it, and therefore we end up coming across prime numbers everywhere. We use them to analyze so many other parts of maths, but yet they remain elusive to analysis themselves. It's a fundamental, recurrent mystery that's also an extremely useful tool... one of the most beautiful things we know.
hwers 5y ago
Starting to think quantamagazine writes headlines this vague as a conscious clickbait strategy by now because these pull the biggest audience.
- deleted 5y ago
  [deleted]
cybertronic 5y ago
Paul Nelson aka czm of quake 3 pro scene! https://www.youtube.com/watch?v=PcbpIntnG8c https://www.youtube.com/watch?v=PcbpIntnG8c
- fourseventy 5y ago
  Holy crap! I had no idea. I was a big follower of the quake 3 and ut2k4 scene back in the day.
- gavagai691 5y ago
  I don't believe it... it's really him https://www.youtube.com/watch?v=ZHpG135ge7Y https://www.youtube.com/watch?v=ZHpG135ge7Y !

251 points by akeck 5y ago

I love how every quote by the mathematician clearly states that this does not bring us appreciably closer to the Riemann hypothesis, or that it is very unlikely, while the bulk of the article seems to imply otherwise.

gavagai691 5y ago
While I had a couple of gripes with the article, I don't get the sense that the article exaggerates the significance of this work. The (Generalized) Riemann Hypothesis implies the (Generalized) Lindelof Hypothesis. The latter is a particularly important consequence of GRH. Not only is it worthwhile, if you are interested in GRH, to verify its predictions (if you proved one of the predictions false, then you would disprove GRH, and if you proved it true, this would in some sense provide "theoretical support" for GRH), but Lindelof is useful in is own right. In particular, it can sometimes serve as a substitute for GRH, and results that can substitute for GRH (such as Bombieri-Vinogradov, zero-density estimates, and subconvexity estimates) are very valuable. Contexts where subconvexity estimates can serve in place of GRH include Quantum Unique Ergodicity, and representations of integers by ternary quadratic forms. For this reason, this paper is a much bigger deal (in the analytic number theory world / in my opinion) than the paper a couple years back that made big headlines about Jensen polynomials (and Nelson's paper is surely one of the biggest results in the last couple of years in analytic number theory). While the latter was more of a "curiosity" / cute paper on an obscure way of thinking about RH, Nelson's paper is big progress on a well-studied weaker form of GRH with significant utility for applications. (I mean, of course, applications in mathematics.)
- gavagai691 5y ago
  (To expand on this a bit: the reason that GRH is so important is because of its ubiquitous applications in mathematics. Maybe you can think of these applications as different food items, whose recipes call for GRH. The problem is that GRH is a very hard ingredient to come by! (That is, if you want your result to be "unconditional," in the sense of not assuming anything unproven.) In some of these cases, however, (such as the two mentioned in the comment above), substituting the Generalized Lindelof Hypothesis in place of GRH (remarkably) would give you a result just as good! (Think "I can't believe it's not GRH!") Unfortunately, Lindelof is also presently out of reach in almost all contexts. Subconvexity estimates are partial progress towards Lindelof. If you substitute them in place of GRH in your recipes, you'll get something better than if you used the cheapest ingredient (the convexity bound), but not something quite as good as if you had used Lindelof or GRH. Some of the most important results in analytic number theory are "I can't believe it's not GRH!" in their respective contexts. Here is one such example: For applications in sieve theory (e.g., the 2013 breakthrough work on bounded gaps in primes), the Bombieri-Vinogradov theorem is a substitute for GRH that is just as good as GRH.)
charlieyu1 5y ago
Scientific journalism. Buzzwords, speculations that don’t sound plausible to the scientific community, etc
- Ericson2314 5y ago
  I don't think that's fair. Much scientific journalism, by focusing on exciting unexpected results, leaves one with an impression that there is too much dogma and perhaps other errors. Math is very hard, but has the luxury of correctness being better defined and easier to verify than about any other field. There simply isn't as much room for conspiracy thinking. And accordingly, the articles in Quanta Magazine are both great to read and don't have a side effect of causing any outsider smugness. That isn't to say math doesn't have controversies. The utility of proof assistance and degree to which people should study and use unifying frameworks like Category Theory are examples of ongoing controversies. But it's very fortunate that to be immune to issues like widespread replication crises. Math is really really different than Science.
  - SantalBlush 5y ago
    I'm not aware of category theory being controversial. A much better example would be Mochizuki's IUT controversy.
    - Ericson2314 5y ago
      It's not controversial in terms of correctness, but it is still a bit controversial in terms of whether it's worth the effort? See all those "but does this help me get results for existing problems?" type questions. There have always been mathematicians that prefer to first establish more structure vs those that just want to get down to business. Category theory especially in the past really pushed the envelope on the "more structure" side of things, inflaming those old tensions.
pelasaco 5y ago
probably different than the author from the article, the Mathematician wasn't interested in generating clicks.
deleted 5y ago
[deleted]

btmiller 5y ago

What impact would this have on elliptic curve cryptography?

deleted 5y ago
[deleted]
echelon 5y ago
I am not a mathematician or cryptographer, but here's my understanding (please, please correct me if I'm wrong) Modern cryptography relies on the hardness of integer factorization. Things you want to hide are intractable to calculate on even the most powerful machines due to the underlying math not being workable in polynomial time (or similar low degree time). Age of the universe hard to brute force with our machines and known algorithms. It has to do with the complex structure of the problem in our intuitive dimension. We haven't thought of any possible way to speed it up classically, and it's not apparent if there are such techniques. The Riemann Hypothesis conjectures that there is a way to know the distribution of primes in a higher dimensional imaginary math. That the unintuitive and difficult system that gives us primes in real number space is somehow contained in a larger imaginary space, with some kind of regular structure, and that they are immediately accessible and calculable once you know the trick. If the hypothesis is true, it's quite possible that NP hard problems are the same. That in some unintuitive higher dimension math we can solve the hardest problems in polynomial time. NP-hard problems are also proven to be equivalent complexity, and if you figure out one then the rest are also solvable. If we figure out the trick behind it all (if such a thing exists), we might break everything. Or maybe we'll prove that there is no such free lunch. I'm one of the ones hoping for computing to be easy. It would unlock so many possibilities. Fast math, in silico experiments, protein folding, etc. It unfortunately would also break all of the underpinnings of our industry, though. SSL, privacy, crypto, infosec, everything about the Internet... Most people are betting that primes are hard, and it certainly does look that way.
- jayski 5y ago
  i have no idea why this great comment got down voted.

orena 5y ago

It might be that the Riemann Hypothesis will be the first of Math's "Hard Problems" that will be solved by AI before humans...

fulvioterzapi 5y ago
It might. However, since there's no record of AI solving big, open conjectures such as the Riemann Hypothesis, I find this quite unlikely.
- orena 5y ago
  Well, you don't know how many years humans will need in order to solve it ;-).

mikewarot 5y ago

I suspect somewhere in the Riemann-Zeta function is a reciprocal that only cancels out all the imaginary terms once and only once, thus any number with more than one factor wouldn't cancel out. I haven't the math skills to find that reciprocal.

gavagai691 5y ago

Two inaccuracies in the article. For purposes of simplicity, the author writes "But the Lindelöf hypothesis says that as the inputs get larger, the size of the output is actually always bounded at 1% as many digits as the input." But this is a case where simplification goes too far. What Lindelof says is that the size of the output is always bounded by ε% as many digits as the input, for ANY (arbitrarily miniscule) ε > 0. Second, the subtitle "Paul Nelson has solved the subconvexity problem..." is strange. The subconvexity problem, for a given L-function, is to lower the percentage described above from 25% to "any positive number"; in other words, to bridge the gap between the convexity bound (which is "trivial") and Lindelof (a consequence of GRH). The only way that the statement "Paul Nelson has solved THE subconvexity problem..." could maybe be accurate is if Nelson proved the Lindelof hypothesis for "all" L-functions. Which is far from the case. (What makes subconvexity so interesting, as Nelson says in the article, is that it is a problem where you can make partial progress towards a particularly important consequence of GRH. And Nelson's result is exactly that: partial progress.) More accurate would be "Paul Nelson has made significant progress on the general subconvexity problem."

kevinventullo 5y ago
I’m confused by your second paragraph. The article describes the subconvexity problem for a given L-function as lowering the bound from 25% to x% for some x < 25. That is, 25% is the “convexity bound” and the existence of such an x is a “subconvexity bound.” My understanding is that Nelson has indeed done this for every L-function, although the exact x varies with the L-function. How is that not solving the subconvexity problem?
- gavagai691 5y ago
  A subconvex bound is any bound that beats the convexity bound of 25%. If you would define "the subconvexity problem" as beating the 25% bound AT ALL (or in other words providing any subconvex bound), then the statement in the subtitle would be closer to accurate. But this is not (I think) how most people would speak, and I wouldn't say this. I would say the subconvexity problem is the problem of bridging the gap between 25% (convexity) and 0% (Lindelof). Subconvexity bounds for various L-functions (zeta, Dirichlet L-functions, and higher rank L-functions) are a very active area of research, and so it seems strange to me to say "the subconvexity problem is solved." "My understanding is that Nelson has indeed done this for every L-function." One minor note. Nelson's work applies if the L-function is automorphic. By the Langlands philosophy, this should be true for any reasonable L-function, but this is far from known, even in, e.g., the simple case of the L-function corresponding to the tensor product of two automorphic L-functions. Edit: I am wrong about the statement "this is not (I think) how most people would speak." It looks like beating the convexity bound at all is often described as "solving the subconvexity problem," e.g. in the introduction here https://link.springer.com/article/10.1007/s002220200223 https://link.springer.com/article/10.1007/s002220200223. This description is a bit strange to me, but if it is standard then it is unfair for me to call it an "inaccuracy," persay; thanks for pointing this out.

Victerius 5y ago

Young enough for a Fields? There is a ceremony later this year, but it's probably too soon. So he could be awarded a Fields in 2026 if he's not yet 40. He received his PhD in 2011. Also, according to MathGenealogy, his grand-grand-grand-grand-grand-grand-grand-grand thesis advisor was none other than Poisson himself. Poisson's advisers were Lagrange and Laplace. Lagrange's was Euler. Euler's was Bernoulli. Bernoulli's was another Bernoulli. You can go back to the late 15th century to find mathematicians with "unknown" advisors.

JadeNB 5y ago
> There is a ceremony later this year, but it's probably too soon. Maybe this is what you meant by "it's probably too soon", but almost certainly the decisions about who gets it have already been made.
gavagai691 5y ago
My bets are on another analytic number theorist for the Fields this cycle, namely James Maynard.

easytiger 5y ago

I remember as a teen when my parents got me a pc (they could Ill afford) as an upgrade from the, by then 10 years old, hand-me-down ZX Spectrum. I was in awe at how many primes I could find on my cyrix 333Mhz on my own noddy code Left it running all day when at school. Never found any thing of value but I learned how to Beowulf cluster and learned a lot about arbitrary integer implementation Simpler times

ackbar03 5y ago
Is finding primes of all things really the first thing you did with a computer as a teen? You could have invented Facebook or Napster
- wiz21c 5y ago
  The first thing I'd do today is a spam filter :-)
- kybernetyk 5y ago
  I invented Napster but then Justin Timberlake stole my idea.
- easytiger 5y ago
  I know. I'm fairly sure i did develop them but just deleted as i thought nobody would want that
  - axiosgunnar 5y ago
    In fact, nobody does want Facebook, so you were right
    - easytiger 5y ago
      I actually built in the 90s a site that was kinda like reddit but just for BBC news articles (they only started comments a few years ago) and a comedy/satire news site ala the onion. in retrospect teenage me should prob have told other people about my websites

deleted 5y ago

[deleted]

saimiam 5y ago

This fascination with primes is has, of late, seemed to be a little misplaced to me. Primes emerge as a property of the number system that you have. The number system itself is an an approximation of the natural world where actions like addition, subtraction, multiplication and division exist. The natural world in question is, as far as we know today, what we humans observe. Now, imagine a second world which was excellent at approximations to the extent that their entire Standard model depended on differentiation and integrations. Would they care as much about primes and try to fit everything into “beautiful” math? I don’t know the answer to this but I’ve found this thought experiment useful to put our maths in its place.

kzrdude 5y ago
I don't think we have even managed to imagine a world where the natural numbers wouldn't be a useful building block. That means the natural numbers are a fundamental logical building block of any formal system like mathematics, doesn't matter what the laws of physics are.
deleted 5y ago
[deleted]
misja111 5y ago
I don't see how you could model the world without addition or subtraction. Even if you started out with differentiation, wouldn't addition and subtraction be implicitly defined by it? And once you have those, you have multiplication and division as well, and primes.

optimalsolver 5y ago

Is there a reason we're obsessed with primes beyond aesthetics? Why does this set of numbers garner all the headlines as opposed to some other arbitrary integer sequence like the Recamán numbers [0] ? If tomorrow someone discovered a closed-form equation for the nth prime, how would mathematics/the world change? [0] https://en.wikipedia.org/wiki/Recamán%27s_sequence https://en.wikipedia.org/wiki/Recamán%27s_sequence

iNic 5y ago
Yes. Just within mathematics prime numbers have a tendency to show up in many fields not obviously related to number theory. As an example: in the study of symmetries (group theory [0]) important to number theory, geometry and even many parts of physics prime numbers help us decompose a complicated symmetry into simpler ones (using Sylow theorems [1]. Prime numbers are also used for cryptography due to their computational properties. Also I think we have shown using a variant of Galois theory that there can not be a closed from solution for the nth prime. But there are more headlines about the primes relative to its prevalence in research. I would guess that this is because - they can easily be explained to people - have been studied for thousands of years - open problems still persist In other parts of research you might need at least an undergraduate degree just to understand the definitions, which makes headlines less sexy. [0] https://en.wikipedia.org/wiki/Finite_group https://en.wikipedia.org/wiki/Finite_group [1] https://en.wikipedia.org/wiki/Sylow_theorems https://en.wikipedia.org/wiki/Sylow_theorems
- slx26 5y ago
  I think it's about the fact that they are a mystery at the heart of maths. You can start describing maths from the unit, the addition and the negative sign. If you start combining those, you get the natural numbers, the integers, ... but even before the natural numbers come the prime numbers. Primes are the most fundamental set of numbers in mathematics, from which you can generate the natural numbers. But as you say, even after so many years they are still relevant, useful and mysterious. They are on a wildly different category from other sets and numerical series. They are the most central element of maths that we still don't understand. And central means that so many other parts of maths derive from it, and therefore we end up coming across prime numbers everywhere. We use them to analyze so many other parts of maths, but yet they remain elusive to analysis themselves. It's a fundamental, recurrent mystery that's also an extremely useful tool... one of the most beautiful things we know.

hwers 5y ago

Starting to think quantamagazine writes headlines this vague as a conscious clickbait strategy by now because these pull the biggest audience.

deleted 5y ago
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cybertronic 5y ago

Paul Nelson aka czm of quake 3 pro scene! https://www.youtube.com/watch?v=PcbpIntnG8c https://www.youtube.com/watch?v=PcbpIntnG8c

fourseventy 5y ago
Holy crap! I had no idea. I was a big follower of the quake 3 and ut2k4 scene back in the day.
gavagai691 5y ago
I don't believe it... it's really him https://www.youtube.com/watch?v=ZHpG135ge7Y https://www.youtube.com/watch?v=ZHpG135ge7Y !