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

#41

Post by gjm11 » Sat, Dec 11, 2021, 11:10 PM UTC

JadeNB wrote: post #7

> "While mathematicians have used machine learning to assist in the analysis of complex data sets, this is the first time we have used computers to help us formulate conjectures or suggest possible lines of attack for unproven ideas in mathematics." This is not true. Doron Zeilberger has long used Shalosh Ekhad to formulate conjectures: https://www.wired.com/2013/03/computers-and-math .

Pedantic note: Shalosh B. Ekhad. The middle initial is important, because the name derives from the fact that the original Shalosh B. Ekhad was an AT&T 3B1 computer. ("Shalosh" is the HEbrew name for the number 3, and "ekhad" is the Hebrew name for the number 1.)

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

#42

Post by DenisM » Sun, Dec 12, 2021, 7:20 AM UTC

cgriswald wrote: post #32

Someone wrote: post #27

Earlier quoted context omitted.

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#Var…

> ... and could have zillions of equally uninteresting variations. Which themselves could generate uninteresting theorems: Theorem: The set of such uninteresting variations of "All natural numbers are larger than minus ten" is countably infinite. Proof: Let the uninteresting variations of "All natural numbers are larger than minus ten" be represented as "All natural numbers are larger than minus n" where n is a natur…

The set of all theorems, or even all statements, is countably infinite. The symbolic representation of a statement is only a string of characters and can be converted to a very large integer.

Even our notion of uncountable sets is itself countable, in that we use language to reason about them. It actually pretty sad - we’re are two-dimensional creatures in the three-dimensional world.

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

#43

Post by JadeNB » Sun, Dec 12, 2021, 4:16 PM UTC

gjm11 wrote: post #41

JadeNB wrote: post #7

> "While mathematicians have used machine learning to assist in the analysis of complex data sets, this is the first time we have used computers to help us formulate conjectures or suggest possible lines of attack for unproven ideas in mathematics." This is not true. Doron Zeilberger has long used Shalosh Ekhad to formulate conjectures: https://www.wired.com/2013/03/computers-and-math .

Pedantic note: Shalosh B. Ekhad. The middle initial is important, because the name derives from the fact that the original Shalosh B. Ekhad was an AT&T 3B1 computer. ("Shalosh" is the HEbrew name for the number 3, and "ekhad" is the Hebrew name for the number 1.)

Thank you! I did not realise that.