AI is discovering patterns in pure mathematics that have never been seen before • Hacker News Board

Re: AI is discovering patterns in pure mathematics that have never been seen before

#21

Post by alphanumeric0 » Sat, Dec 11, 2021, 5:59 PM UTC

number6 wrote: post #15

mdp2021 wrote: post #11

Earlier quoted context omitted.

What do you imply.

That math is invented not discovered

Mathematical notation is invented but what about the patterns it describes? Did someone invent the notion of exponential growth or decay? Or did we discover this mathematical pattern in many different areas of study?

Also, from Wikipedia: "Most of mathematical activity consists of discovering and proving (by pure reasoning) properties of abstract objects. These objects are either abstractions from nature (such as natural numbers or "a line"), or (in modern mathematics) abstract entities that are defined by their basic properties, called axioms." - https://en.wikipedia.org/wiki/Mathematics

Re: AI is discovering patterns in pure mathematics that have never been seen before

#22

Post by RosanaAnaDana » Sat, Dec 11, 2021, 6:03 PM UTC

6gvONxR4sf7o wrote: post #16

cschmid wrote: post #9

I don't normally complain about this, but that result has been at least four times on the front page in the last two weeks: https://news.ycombinator.com/item?id=29514642 https://news.ycombinator.com/item?id=29424749 https://news.ycombinator.com/item?id=29405380 https://news.ycombinator.com/item?id=29208141 Finding mathematical patterns and relations by fitting expressive functions has actually been a common technique…

Not only has it been on the front page a bunch; each time it’s posted, it’s further and further through the game of telephone from science to pop journalism, and less and less accurate.

It might be interesting to map the quality of the hn conversations to the distance from the source in either time or internet distance.

Re: AI is discovering patterns in pure mathematics that have never been seen before

#23

Post by turnersr » Sat, Dec 11, 2021, 6:03 PM UTC

tbrake wrote: post #8

meiji163 wrote: post #4

I'm a fan of deepmind and all, but this story has been way overblown based on what I saw in the actual code. There's nothing particularly new about mathematicians using computers to investigate and make conjectures, even if you add ML into it.

> but this story has been way overblown based on what I saw in the actual code. Could you expand on this? What code did you see, where, and doing what? Were you part of this team? > There's nothing particularly new about mathematicians using computers to investigate and make conjectures, even if you add ML into it. I think you're being needlessly reductive here. The article itself explicitly states that "using comput…

Here's the code https://github.com/deepmind/mathematics_conjectures/blob/mai...

Re: AI is discovering patterns in pure mathematics that have never been seen before

#24

Post by bryan0 » Sat, Dec 11, 2021, 6:16 PM UTC

cschmid wrote: post #9

I don't normally complain about this, but that result has been at least four times on the front page in the last two weeks: https://news.ycombinator.com/item?id=29514642 https://news.ycombinator.com/item?id=29424749 https://news.ycombinator.com/item?id=29405380 https://news.ycombinator.com/item?id=29208141 Finding mathematical patterns and relations by fitting expressive functions has actually been a common technique…

Just to add some more detail to this. The first link [0] you referenced is one I submitted a while ago. It did not gain much attention and I was not really surprised since the same underlying research was being reported by different sources in variously vague ways.

Anyway, I received an email from HN yesterday saying they wanted to put it on the “second-chance pool” and I could do so by clicking a link to repost it. I never received an email from HN before and I was curious what would happen, so I clicked to repost, and of course it then shot to the top of the front page.

0: https://news.ycombinator.com/item?id=29514642

Re: AI is discovering patterns in pure mathematics that have never been seen before

#25

Post by thoraway66 » Sat, Dec 11, 2021, 6:20 PM UTC

pure_simplicity wrote: post #14

for_i_in_range wrote: post #10

Alternate title: AI (a man-made concept) is discovering patterns in another man-made concept.

I would disagree with the idea that maths is man-made. It is discovered. If it were man made, then we should have power to change it as we wish. But you could still say: A mathematical structure is analysing mathematics.

You mean physical structures. Math is just glyphs we use to cart around awareness of the motions of this reality.

I know it’s romantic to escape into the neverending-ness of reality, but we exist in a pretty well established perimeter of physical constraints, and we have yet to find even a theory that would let us break them.

A few academic tricks here and there is hardly concrete proof we can.

I think we’re looking the wrong way. What if we’re each a metaverse forced to live literally?

Give me designer drugs that bootstrap such a detailed hallucination, I think it happened. Way less wasteful than these toys like VR we just throwaway.

Don’t make the math literal, make the cognitive simulation so detailed it feels like it’s literal.

Maybe aliens didn’t die off. They just took resource consumption seriously.

Re: AI is discovering patterns in pure mathematics that have never been seen before

#26

Post by irrational » Sat, Dec 11, 2021, 6:20 PM UTC

m3kw9 wrote: post #19

cschmid wrote: post #9

I don't normally complain about this, but that result has been at least four times on the front page in the last two weeks: https://news.ycombinator.com/item?id=29514642 https://news.ycombinator.com/item?id=29424749 https://news.ycombinator.com/item?id=29405380 https://news.ycombinator.com/item?id=29208141 Finding mathematical patterns and relations by fitting expressive functions has actually been a common technique…

I haven’t seen it yet so it’s alright for me.

This is the dirty secret of reposts. It is only people who spend their lives on HN and see (and somehow remember) every single previous post that care about reposts.

Re: AI is discovering patterns in pure mathematics that have never been seen before

#27

Post by Someone » Sat, Dec 11, 2021, 6:22 PM UTC

derefr wrote: post #2

That’s actually pretty cool (and not the hyperbole that articles about use of AI in science usually are.) Current-gen Deep Leaning systems are really good at “riffing on” text inputs. So feed them a bunch of known math conjectures , and new conjectures should fall out. Not that this is a new thing — mathematicians have been using various procedural generation methods to formulate conjectures since Prolog was invented…

I think the challenge is to only/mostly generate interesting conjectures. For example “All natural numbers are larger than minus ten” or “no prime is divisible by 10,000” are valid theorems, but not interesting, and could have zillions of equally uninteresting variations.

There often are zillions of ways to phrase a theorem that aren’t too obvious, initially. For example, https://en.wikipedia.org/wiki/Tic-tac-toe#Variations gives a few games that are isomorphic to tic-tac-toe.

I fear a theorem generator would come up with lots of such theorem variants, with most of them being uninteresting to mathematicians (such isomorphies typically are considered interesting if they join two fields hitherto considered disjunct or if it takes mathematicians long to figure out that they are essentially, synonymous)

Re: AI is discovering patterns in pure mathematics that have never been seen before

#28

Post by garbagetime » Sat, Dec 11, 2021, 6:33 PM UTC

alphanumeric0 wrote: post #21

number6 wrote: post #15

Earlier quoted context omitted.

That math is invented not discovered

Mathematical notation is invented but what about the patterns it describes? Did someone invent the notion of exponential growth or decay? Or did we discover this mathematical pattern in many different areas of study? Also, from Wikipedia: "Most of mathematical activity consists of discovering and proving (by pure reasoning) properties of abstract objects. These objects are either abstractions from nature (such as nat…

I agree that some mathematical concepts, such as exponential growth, are expressed in nature. But does the fact that a thing is expressed in nature imply that it cannot be invented? And what of mathematical concepts not expressed in nature?

On a different point, I'd argue that all conceptual inventions are discoveries. So, showing that a mathematical concept was discovered would not be enough to prove it was not invented.

Re: AI is discovering patterns in pure mathematics that have never been seen before

#29

Post by ianliu » Sat, Dec 11, 2021, 6:40 PM UTC

cschmid wrote: post #9

I don't normally complain about this, but that result has been at least four times on the front page in the last two weeks: https://news.ycombinator.com/item?id=29514642 https://news.ycombinator.com/item?id=29424749 https://news.ycombinator.com/item?id=29405380 https://news.ycombinator.com/item?id=29208141 Finding mathematical patterns and relations by fitting expressive functions has actually been a common technique…

The review paper is really interesting: "Machine-Learning Mathematical Structures"

Re: AI is discovering patterns in pure mathematics that have never been seen before

#30

Post by swayvil » Sat, Dec 11, 2021, 6:49 PM UTC

Consider Greg Egan : Diaspora. It's a sci fi novel

In it there's something called "The Science Mines".

In the Science Mines a researcher (An AI person) explores paths of logic and conjecture, tunneling into the raw earth of "all possibilities". Discovering patterns, theorems.

We have invented The Science Mines.