Machine generates mathematics we've never seen before

[Alan Grayson]

https://www.sciencealert.com/scientists-invented-a-machine-that-generates-mathematics-we-ve-never-seen-before

[Bruno Marchal]

On 10 Feb 2021, at 04:26, Alan Grayson <agrays...@gmail.com> wrote:

https://www.sciencealert.com/scientists-invented-a-machine-that-generates-mathematics-we-ve-never-seen-before

Interesting. It illustrates that machine can learn to ask “interesting” questions, and amusingly, let the hard work of answering them to human mathematicians.

Some day, a machine will come with a new cardinal, closer to the Kunen bound, bigger than the Laver cardinal  (at the edge of the set theoretical universe). But even such a machine can only justify an infinitesimal portion of the arithmetical reality, or even of the PI_1 arithmetical reality, because if such machine is inconsistent, even Q (RA) will know it. Q has no idea what a large cardinal is, but it has a precise idea of what is a machine which believes in ZFC + a cardinal of Laver exists. Emulating is not interpreting. Anyone can emulate Einstein brain, but that does not mean anyone can understand what Einstein says. Q believe that PA can prove Q’s consistency, but that does not help Q, really.

I remind Q is just first order predicate calculus + the axioms:

0 ≠ s(x)
s(x) = s(y) -> x = y
x = 0 v Ey(x = s(y))    
x+0 = x
x+s(y) = s(x+y)
x*0=0
x*s(y)=(x*y)+x

Bruno

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