Top Mathematician Says He's Solved a 160-Year-Old Maths Problem Worth $1 Million - Page 1
Forum section: electronics / general

author: BrianHG
author_rank: Super Contributor
timestamp: September 26, 2018, 10:36:03 am
content: Quotehttps://www.sciencealert.com/top-mathematician-sir-michael-atiyah-solved-a-160-year-old-1-million-maths-problem-riemann-hypothesishttps://youtu.be/jXugkzFW5qYhttps://www.claymath.org/millennium-problems/riemann-hypothesis

author: CJay
author_rank: Super Contributor
timestamp: September 26, 2018, 12:02:30 pm
content: If my understanding of the hypothesis is correct then it's going to have a somewhat adverse effect on the security of a lot of encryption products

author: Marco
author_rank: Super Contributor
timestamp: September 26, 2018, 01:11:47 pm
content: How many pages is the proof?

author: m98
author_rank: Frequent Contributor
timestamp: September 26, 2018, 01:30:47 pm
content: I call black magic.

author: Mattjd
author_rank: Regular Contributor
timestamp: September 26, 2018, 07:44:28 pm
content: Quote from: Marco on September 26, 2018, 01:11:47 pm1 pageQuote from: m98 on September 26, 2018, 01:30:47 pmassuming his proof by contradiction is correct. then it depends, as he said, if you believe proof by contradiction is valid or not.Proof by contradiction is very powerful, but of course it has its problems.

author: Mattjd
author_rank: Regular Contributor
timestamp: September 26, 2018, 07:58:00 pm
content: https://math.stackexchange.com/questions/2930742/what-is-the-todds-function-in-atiyahs-paper

author: taydin
author_rank: Frequent Contributor
timestamp: September 26, 2018, 08:11:43 pm
content: Quote from: CJay on September 26, 2018, 12:02:30 pmCould be. But when it comes to cryptology, the math is very complex, and the best people involved in that field are mostly working for the government/intelligence agencies. So when that expert says "RSA is an open standard that is peer reviewed", if that "peer" is any good, he's probably also working for the government/intelligence agencies.Us mere mortals can never really know if a particular encryption algorithm is absolutely secure, unless our math advances to the level of those "peers". And without knowing, we have to assume that all encryption algorithms invented by the "peers" have a back door that can be used by the government/intelligence agencies.

author: mtdoc
author_rank: Super Contributor
timestamp: September 26, 2018, 08:18:18 pm
content: Quote from: taydin on September 26, 2018, 08:11:43 pmI agree. Though if governments had universal access to all encryption, then they would not need to be pursuingthis.

author: taydin
author_rank: Frequent Contributor
timestamp: September 26, 2018, 08:43:47 pm
content: Quote from: mtdoc on September 26, 2018, 08:18:18 pmYes, we can never be sure. All we can do is thought experiments ...It is possible that a private company implements a new and powerful encryption algorithm independent of the government. In this case the government would want to use the force of law to render that algorithm ineffective for itself.All the whining of the government about encryption preventing governments from catching bad guys could also be a smoke screenThe governments want people to think that their communication is private, which will yield better intel. I always remember the special browser setting, a checkbox that says "don't track me"How many people check that box and think they are untracked now?

author: CJay
author_rank: Super Contributor
timestamp: September 26, 2018, 09:16:19 pm
content: Quote from: taydin on September 26, 2018, 08:11:43 pmYou'd certainly hope they are.The way us Brits are supposed to have invented the programmable computer and asymmetric public key encryption but kept it secret for decades and can't help but wonder if that hypothesis has been cracked a long time ago but been kept under wraps because it's 'useful'.

author: Mattjd
author_rank: Regular Contributor
timestamp: September 26, 2018, 09:45:43 pm
content: At the end of the day, even if the proof is valid. It doesnt change much atm. Cryptologists and the like already operate under the assumption that the RH is true. Additionally, the first million primes or so have been computed, following the Riemann zeta function, RH would just give more.Clever people would have to take the results and try to find ways that to helps exploit current algorithms and what not.

author: Cerebus
author_rank: Super Contributor
timestamp: September 26, 2018, 10:10:27 pm
content: Quote from: CJay on September 26, 2018, 12:02:30 pmNot really, one application of the Riemann hypothesisif provedis a way to calculate thenumberof primes less than a given number, something that at the moment is more a matter of guesswork. It is no help with the innate difficulty of prime factorization of composite numbers, which is the crux of many public key encryption algorithms. It won't break any prime based encryption schemes, but may demonstrate that they are either harder or easier to break than currently believed by putting an upper bound on the difficulty of the prime factorization involved in cracking a particular encryption scheme.

author: TerraHertz
author_rank: Super Contributor
timestamp: September 27, 2018, 10:55:47 am
content: Dear oh dear. Fascinating, but I find his speech cadence nearly impossible to follow, and that tiny 'slides' box is completely unreadable.Hopefully there'll be a more accessible explanation sometime.

author: Cerebus
author_rank: Super Contributor
timestamp: September 27, 2018, 12:01:41 pm
content: Quote from: TerraHertz on September 27, 2018, 10:55:47 amGood luck with that - given that the Riemann hypothesis itself, expressed in its simplest form, is already inaccessible to probably 99% of the population, an accessible explanation of the proof of it is going to be quite a way off.A mathematician I know was saying that there are probably 10 or 20 people in the world qualified to validate Atiyah's proof (people who knowboththeir way around the R.H.andthe types of mathematics used by Atiyah in his proof).

author: BrianHG
author_rank: Super Contributor
timestamp: September 27, 2018, 03:25:56 pm
content: Quote from: TerraHertz on September 27, 2018, 10:55:47 amIt significantly helps if you both turn on closed captioning and play the video at 1.5x speed. Not perfect, but, at least you can make it through his un-evenly timed with accent speech.To see full screen size slides, use this video link:https://hitsmediaweb.h-its.org/Mediasite/Play/35600dda1dec419cb4e99f706197a3951dAnd click on "swap video elements" to shrink the speaker and enlarge the slides in the presentation.These is a bi-directional index seek on this player to each slide.

author: Marco
author_rank: Super Contributor
timestamp: September 28, 2018, 03:34:41 pm
content: Quote from: Mattjd on September 26, 2018, 07:44:28 pmIf math is subtly inconsistent then we have really big problems to begin with.Since the proof is so short it seems an ideal case for using a proof assistant to me, why rely on a consensus of experts when hard logic suffices?

author: Cerebus
author_rank: Super Contributor
timestamp: September 28, 2018, 04:08:15 pm
content: Quote from: Marco on September 28, 2018, 03:34:41 pmSomethingBertrand Russellfigured out a long time ago, which led to the reformulation of mathematics on axiomatic lines.

author: Vtile
author_rank: Super Contributor
timestamp: September 28, 2018, 07:57:44 pm
content: Math is nothing except subtly inconsistent outside our four basic functions +,-,* & /Doesn't make any less useful though

author: dmills
author_rank: Super Contributor
timestamp: September 28, 2018, 08:37:12 pm
content: Quote from: Cerebus on September 28, 2018, 04:08:15 pmAnd then along came Godel and broke that (In a very similar way)!Regards, Dan.

author: Marco
author_rank: Super Contributor
timestamp: September 28, 2018, 10:00:45 pm
content: Incompleteness is less of a problem than inconsistent.

author: Mattjd
author_rank: Regular Contributor
timestamp: September 29, 2018, 10:42:06 pm
content: Quote from: Vtile on September 28, 2018, 07:57:44 pmthey're operators not functions

author: Mattjd
author_rank: Regular Contributor
timestamp: September 29, 2018, 10:49:01 pm
content: consistency in math btw is NEVER being able to prove both X and NOT(X) simultaneously

author: Tepe
author_rank: Frequent Contributor
timestamp: October 01, 2018, 12:36:37 pm
content: Quote from: Mattjd on September 29, 2018, 10:42:06 pmThat's basically a question of syntax

author: T3sl4co1l
author_rank: Super Contributor
timestamp: October 01, 2018, 04:05:43 pm
content: Quote from: Mattjd on September 29, 2018, 10:49:01 pmCorrect. Which is consequently why Godel proved the eponymous Incompleteness Theorem: either a math system is too simple, i.e. incomplete (and probably not very useful overall); or it's inconsistent (i.e., it is possible to prove true "P AND NOT P").The argument is often told as a statement in prepositional calculus. The statement is constructed as an interpreter of prepositional calculus, operating on some given number. It just so happens, the number is constructed to code for an inconsistent statement. (A statement in PC can only be built stepwise from the rules of the system; but any finite number can be constructed with finite steps, arbitrarily without the code equivalent being subject to rules.*) It's the logical equivalent of (and predecessor to) the Halting Problem.*In modern terms, a sort-of equivalent is coding in any syntactically checked high-level language, versus loading a (relatively large) number that itself just so happens to be machine code. The code compiled from the language must follow the structure of that language (of course, practical computing languages are not made nearly so limited as mathematical systems are, so it is still possible to express the Halting Problem in, say, a few dozen statements...), whereas the number is completely arbitrary and unstructured (until something happens to read that number as some coded system, and it turns out to have interesting effects).Tim

author: Cerebus
author_rank: Super Contributor
timestamp: October 01, 2018, 04:58:13 pm
content: Quote from: Tepe on October 01, 2018, 12:36:37 pmMathematically the relationship is actually {x|xis an operator } ⊂ {y|yis a function }, that is, all operators are functions, not all functions are operators. However,operatoris used loosely and is very loosely defined (except in the most rigorous textbooks) and in general mathematicians will useoperatorwhen the function it represents is being applied to aring,fieldorvector spaceand/or rules ofassociativityandcommutativityare brought into play in respect offunctional composition. Basically, if you ask two mathematicians for a dichotomous formal definition ofoperatorandfunctionyou will get two different formal answers, but they'd probably agree that an operator is like pornography, they know one when they see one.

author: Marco
author_rank: Super Contributor
timestamp: October 01, 2018, 05:20:02 pm
content: Quote from: T3sl4co1l on October 01, 2018, 04:05:43 pmThen it would be termed the Inconsistency Theorem and suicide rates among mathematicians would be far higher than they are.