10 ms·

AI maths whiz creates tough new problems for humans to solve

145 points by tzury 6y ago

tuyguntn 6y ago
no examples of formula's generated by AI and if they are correct or proven incorrect? Without examples this seems an advertisement to non-existing product. Anyone can create AI then with simple function pick_N_random(=, +, -, *, /, pi, e, alpha, tetta, 1,2,3,4,5,6,...)
- imhoguy 6y ago
  AI? Much overused buzzword these days. Don't we have metaheuristics (genetic algorithms etc.) which already do exactly what the article states as novel?
  - batterylow 6y ago
    Meta-heuristics aren’t the current buzzword, likewise evolutionary algorithms won’t be front paging anytime soon... unless it’s neuroevolution disguised as a novel contribution in 2021. Sprinkle on some blockchain and you’re onto a winner!
- buryat 6y ago
  the link to the project is in the article
jzer0cool 6y ago
TLDR; AI machine called: Ramanujan Machine. Attempts at finding formula. Tries to determine whether the following constants are "irrational" or "rational" number. Constants mentioned: Catalan’s constant, Apery’s constant Unrelated: I never heard of the above 2 constants before. Although, I have met someone who speaks Catalan and from Catalonia.
- tecleandor 6y ago
  That names comes from the Belgian mathematician Eugène Charles Catalan.
warent 6y ago
THIS is mind-bendingly awesome. What are the implications of this for technological advancement? Will we be getting to a point where machines are inventing new things that revolutionize life as we know it? I'm thinking about the difference in technology from now vs. 1920s. Could we be moving toward another advancement leap of such a proportion? Just consider for a moment how far we've come. In the past, all our machines were purely mechanical---steam engines, water cranks, etc. Now we're creating machines that discover math. Amazing!
- colordrops 6y ago
  It does seem like an amazing project, but I'm struggling to see how this has any significant implications for technological advancement.
- FrozenVoid 6y ago
  Its just a continued fraction generator that looks for fractions equal to constants. Not an AI, more like search function with optimization.
- bawolff 6y ago
  The singularity is not yet upon us, and we have had machines generating math since the 70s with the proof of the 4 colour theorem.
- layoutIfNeeded 6y ago
  Yaay! I fucking love science™ too!
  - dang 6y ago
    "Don't be snarky." https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html
- trenchgun 6y ago
  It is intellectual scam.
heinrichf 6y ago
The praise from popular press and the promotion by the authors should be put into context of what mathematicians think of it. Two blog posts by a professor at U. Chicago, qualifying it of intellectual fraud: https://www.galoisrepresentations.com/2019/07/17/the-ramanujan-machine-is-an-intellectual-fraud https://www.galoisrepresentations.com/2019/07/17/the-ramanuj... https://www.galoisrepresentations.com/2019/07/07/en-passant-v/ https://www.galoisrepresentations.com/2019/07/07/en-passant-...
- Daniel51 6y ago
  Irrelevant.
  - Daniel51 6y ago
    The Nature paper presents several new conjectures related to the Catalan constant, pi^2, and zeta(3) (Apéry's constant): http://www.ramanujanmachine.com/wp-content/uploads/2020/06/catalan.pdf http://www.ramanujanmachine.com/wp-content/uploads/2020/06/c... http://www.ramanujanmachine.com/wp-content/uploads/2020/06/pi_square.pdf http://www.ramanujanmachine.com/wp-content/uploads/2020/06/p... http://www.ramanujanmachine.com/wp-content/uploads/2020/06/zeta3.pdf http://www.ramanujanmachine.com/wp-content/uploads/2020/06/z... The main criticism of the blog is "that the program has not yet generated anything new", but the post does not refer to these results. So it seems that this blog post is currently irrelevant and out-dated compared to the Nature publication.
- QuesnayJr 6y ago
  This is shocking stuff. I encourage everyone to read these two links.
- dealforager 6y ago
  Man, this is an example of how difficult it is to know what is BS or not if you're not an expert on the subject. On one hand, this article was published in Nature, which I thought was trustworthy. On the other, there's this comment on a social media platform that links to a blog that also seems legit. No wonder misinformation spreads so fast. Even after reading both, I don't know what to make of it. The reaction and comments here just confuse me more.
sradman 6y ago
The Nature article is about [1]: > The Ramanujan Machine is a computer algorithm, named after the Indian mathematician Srinivas Ramanujan, which generates conjectures similar to what proposed by Ramanujan. The #Criticism section states: > Prof. Frank Calegari criticized the Ramanujan Machine claiming that the program has not yet generated anything new and dubbed it as "absurd" and an "intellectual fraud". [1] https://en.wikipedia.org/wiki/Ramanujan_Machine https://en.wikipedia.org/wiki/Ramanujan_Machine
- David147 6y ago
  Funny that no other name other than Frank Calegari's appear in the Wikipedia page
- heinrichf 6y ago
  This page appears as if it was written by the authors or the PR department of the university...
magnio 6y ago
The GitHub repo contains more details on how the algorithm works: https://github.com/AnonGit90210/RamanujanMachine https://github.com/AnonGit90210/RamanujanMachine > We have continued fractions which are generated by polynomials. What does that mean? object of the type: a(0)+b(1)/(a(1)+b(2)/...)) where a,b are polynomials with integer coefficients. This is the RHS. On the LHS we have a function of some constant, either rational or ULCD. A ULCD function is of the type f(const)=(u/const + const/l + c)/d while a rational function is the ratio of two polynomials. We seek for a match between some LHS function on a constant to a continued fraction. To do this, we enumerate over the coefficients of a,b and those of the rational func on the LHS/the ulcd parameters. They're all integers. We actually don't compare between the LHS to a continued fraction, but to a continued fraction after we applied some function to it, e.g. contfrac^2, sqrt(contfrac), 1/contfrac etc. In order to enhance the algorithm's complexity, we first enumerate over the parameters of the RHS, saving the results to a hashtable, then enumerate over the LHS and look for a match in the table. This is a TMTO (time-memory tradeoff), it's called MITM (meet in the middle), you can look it up if it's not clear. We first find matches, then filter redundant results (discussed later on), filter only continued fractions that converge fastly, find how fast they are converging, and how many iterations we should calculate to get the desired precision. We calculate them to that precision, and filter again. This doesn't seems that complicated, but at the same time probably gives no mathematical insights as to how to derive those formulaes. I can see how this would look pointless to some people.
deleted 6y ago
[deleted]
David147 6y ago
The two blog posts by Frank Calegari are from July 2019 and irrelevant to the paper in Nature (from February 2021). The paper went through peer review by mathematicians and experts in the field.
- alisonkisk 6y ago
  What was changed in the new paper? Hard to say "irrelevant" when the blog post directly influenced a rewrite of the paper.
  - scihive 6y ago
    There are several new conjectures related to the Catalan constant, pi^2, and zeta(3) (Apéry's constant): http://www.ramanujanmachine.com/wp-content/uploads/2020/06/catalan.pdf http://www.ramanujanmachine.com/wp-content/uploads/2020/06/c... http://www.ramanujanmachine.com/wp-content/uploads/2020/06/pi_square.pdf http://www.ramanujanmachine.com/wp-content/uploads/2020/06/p... http://www.ramanujanmachine.com/wp-content/uploads/2020/06/zeta3.pdf http://www.ramanujanmachine.com/wp-content/uploads/2020/06/z... From looking at Calegari's blog post, he didn't comment on any them so far...
    - deleted 6y ago
      [deleted]
CyberRabbi 6y ago
> “Until I can detect a well-developed ‘sense of mathematical taste’ in AI, I expect its role to be that of an important auxiliary tool, not that of independent discoverer.” AI, no, but ML, yes. ML can only make estimates, e.g. compute functions, it doesn’t have judgement. That requires a human decision maker. It goes back to what I learned in primary school about computers: “a computer can only do what you tell it to do.”
David411 6y ago
The paper offers new and improved convergence rates for the Catalan constant, presenting new results in a short period of time. Calegari talking nonsense..
bluepoint 6y ago
To be fair creating mathematical problems that are hard or impossible to solve is not really very hard.
Thorrez 6y ago
So this is essentially AI-guided fuzzing for math equations?

145 points by tzury 6y ago

no examples of formula's generated by AI and if they are correct or proven incorrect? Without examples this seems an advertisement to non-existing product. Anyone can create AI then with simple function pick_N_random(=, +, -, *, /, pi, e, alpha, tetta, 1,2,3,4,5,6,...)

imhoguy 6y ago
AI? Much overused buzzword these days. Don't we have metaheuristics (genetic algorithms etc.) which already do exactly what the article states as novel?
- batterylow 6y ago
  Meta-heuristics aren’t the current buzzword, likewise evolutionary algorithms won’t be front paging anytime soon... unless it’s neuroevolution disguised as a novel contribution in 2021. Sprinkle on some blockchain and you’re onto a winner!
buryat 6y ago
the link to the project is in the article

jzer0cool 6y ago

TLDR; AI machine called: Ramanujan Machine. Attempts at finding formula. Tries to determine whether the following constants are "irrational" or "rational" number. Constants mentioned: Catalan’s constant, Apery’s constant Unrelated: I never heard of the above 2 constants before. Although, I have met someone who speaks Catalan and from Catalonia.

tecleandor 6y ago
That names comes from the Belgian mathematician Eugène Charles Catalan.

warent 6y ago

THIS is mind-bendingly awesome. What are the implications of this for technological advancement? Will we be getting to a point where machines are inventing new things that revolutionize life as we know it? I'm thinking about the difference in technology from now vs. 1920s. Could we be moving toward another advancement leap of such a proportion? Just consider for a moment how far we've come. In the past, all our machines were purely mechanical---steam engines, water cranks, etc. Now we're creating machines that discover math. Amazing!

colordrops 6y ago
It does seem like an amazing project, but I'm struggling to see how this has any significant implications for technological advancement.
FrozenVoid 6y ago
Its just a continued fraction generator that looks for fractions equal to constants. Not an AI, more like search function with optimization.
bawolff 6y ago
The singularity is not yet upon us, and we have had machines generating math since the 70s with the proof of the 4 colour theorem.
layoutIfNeeded 6y ago
Yaay! I fucking love science™ too!
- dang 6y ago
  "Don't be snarky." https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html
trenchgun 6y ago
It is intellectual scam.

heinrichf 6y ago

The praise from popular press and the promotion by the authors should be put into context of what mathematicians think of it. Two blog posts by a professor at U. Chicago, qualifying it of intellectual fraud: https://www.galoisrepresentations.com/2019/07/17/the-ramanujan-machine-is-an-intellectual-fraud https://www.galoisrepresentations.com/2019/07/17/the-ramanuj... https://www.galoisrepresentations.com/2019/07/07/en-passant-v/ https://www.galoisrepresentations.com/2019/07/07/en-passant-...

Daniel51 6y ago
Irrelevant.
- Daniel51 6y ago
  The Nature paper presents several new conjectures related to the Catalan constant, pi^2, and zeta(3) (Apéry's constant): http://www.ramanujanmachine.com/wp-content/uploads/2020/06/catalan.pdf http://www.ramanujanmachine.com/wp-content/uploads/2020/06/c... http://www.ramanujanmachine.com/wp-content/uploads/2020/06/pi_square.pdf http://www.ramanujanmachine.com/wp-content/uploads/2020/06/p... http://www.ramanujanmachine.com/wp-content/uploads/2020/06/zeta3.pdf http://www.ramanujanmachine.com/wp-content/uploads/2020/06/z... The main criticism of the blog is "that the program has not yet generated anything new", but the post does not refer to these results. So it seems that this blog post is currently irrelevant and out-dated compared to the Nature publication.
QuesnayJr 6y ago
This is shocking stuff. I encourage everyone to read these two links.
dealforager 6y ago
Man, this is an example of how difficult it is to know what is BS or not if you're not an expert on the subject. On one hand, this article was published in Nature, which I thought was trustworthy. On the other, there's this comment on a social media platform that links to a blog that also seems legit. No wonder misinformation spreads so fast. Even after reading both, I don't know what to make of it. The reaction and comments here just confuse me more.

sradman 6y ago

The Nature article is about [1]: > The Ramanujan Machine is a computer algorithm, named after the Indian mathematician Srinivas Ramanujan, which generates conjectures similar to what proposed by Ramanujan. The #Criticism section states: > Prof. Frank Calegari criticized the Ramanujan Machine claiming that the program has not yet generated anything new and dubbed it as "absurd" and an "intellectual fraud". [1] https://en.wikipedia.org/wiki/Ramanujan_Machine https://en.wikipedia.org/wiki/Ramanujan_Machine

David147 6y ago
Funny that no other name other than Frank Calegari's appear in the Wikipedia page
heinrichf 6y ago
This page appears as if it was written by the authors or the PR department of the university...

magnio 6y ago

The GitHub repo contains more details on how the algorithm works: https://github.com/AnonGit90210/RamanujanMachine https://github.com/AnonGit90210/RamanujanMachine > We have continued fractions which are generated by polynomials. What does that mean? object of the type: a(0)+b(1)/(a(1)+b(2)/...)) where a,b are polynomials with integer coefficients. This is the RHS. On the LHS we have a function of some constant, either rational or ULCD. A ULCD function is of the type f(const)=(u/const + const/l + c)/d while a rational function is the ratio of two polynomials. We seek for a match between some LHS function on a constant to a continued fraction. To do this, we enumerate over the coefficients of a,b and those of the rational func on the LHS/the ulcd parameters. They're all integers. We actually don't compare between the LHS to a continued fraction, but to a continued fraction after we applied some function to it, e.g. contfrac^2, sqrt(contfrac), 1/contfrac etc. In order to enhance the algorithm's complexity, we first enumerate over the parameters of the RHS, saving the results to a hashtable, then enumerate over the LHS and look for a match in the table. This is a TMTO (time-memory tradeoff), it's called MITM (meet in the middle), you can look it up if it's not clear. We first find matches, then filter redundant results (discussed later on), filter only continued fractions that converge fastly, find how fast they are converging, and how many iterations we should calculate to get the desired precision. We calculate them to that precision, and filter again. This doesn't seems that complicated, but at the same time probably gives no mathematical insights as to how to derive those formulaes. I can see how this would look pointless to some people.

deleted 6y ago

[deleted]

David147 6y ago

The two blog posts by Frank Calegari are from July 2019 and irrelevant to the paper in Nature (from February 2021). The paper went through peer review by mathematicians and experts in the field.

alisonkisk 6y ago
What was changed in the new paper? Hard to say "irrelevant" when the blog post directly influenced a rewrite of the paper.
- scihive 6y ago
  There are several new conjectures related to the Catalan constant, pi^2, and zeta(3) (Apéry's constant): http://www.ramanujanmachine.com/wp-content/uploads/2020/06/catalan.pdf http://www.ramanujanmachine.com/wp-content/uploads/2020/06/c... http://www.ramanujanmachine.com/wp-content/uploads/2020/06/pi_square.pdf http://www.ramanujanmachine.com/wp-content/uploads/2020/06/p... http://www.ramanujanmachine.com/wp-content/uploads/2020/06/zeta3.pdf http://www.ramanujanmachine.com/wp-content/uploads/2020/06/z... From looking at Calegari's blog post, he didn't comment on any them so far...
  - deleted 6y ago
    [deleted]

CyberRabbi 6y ago

> “Until I can detect a well-developed ‘sense of mathematical taste’ in AI, I expect its role to be that of an important auxiliary tool, not that of independent discoverer.” AI, no, but ML, yes. ML can only make estimates, e.g. compute functions, it doesn’t have judgement. That requires a human decision maker. It goes back to what I learned in primary school about computers: “a computer can only do what you tell it to do.”

David411 6y ago

The paper offers new and improved convergence rates for the Catalan constant, presenting new results in a short period of time. Calegari talking nonsense..

bluepoint 6y ago

To be fair creating mathematical problems that are hard or impossible to solve is not really very hard.

Thorrez 6y ago

So this is essentially AI-guided fuzzing for math equations?