If math is more than proof, we need to better celebrate the rest of it

Posted by num42 3 hours ago

If math is more than proof, we need to better celebrate the rest of it(terrytao.wordpress.com)

64 points | 30 commentspage 2

E-Reverance 2 hours ago|

Jacob Tsimerman claims [1] we might have superhuman expositors by April, so then what?

[1] https://youtu.be/H7_d_sgui6o?t=4436 (timestamped url)

steinwinde 29 minutes ago||

Thanks for pointing me to this video - it's been interesting to follow the discussion! (I personally don't see that math has lost its purpose at all in the past months. I mean, where would we be, if we were thrown at these AI based mathematical proofs and had no mathematicians and specialists?! Much of this discussion is about a disciplin readjusting its way of work and tasks.)

omnicognate 1 hour ago|||

The people building AI claim it will surpass human intelligence in all respects and prerhaps kill us all. Should we just cease all human activity on the basis of what AI might do in future?

Personally, I doubt AI can surpass a good human explainer because explanation requires empathy, which benefits from being an instance of the kind of entity you are explaining the thing to. That gives you a way of exploring and evaluating the space of possible explanations that isn't available to an LLM.

ViscountPenguin 2 hours ago||

It's all good until we have superhuman appreciators :)

trhway 2 hours ago||

It starts to sound like medieval science - "understanding" instead of proofs. And like a medieval army loosing a battle in the open field tries to retreat back into the fortress, people, facing the prospects of machine doing intelligent tasks better than humans, start to retreat into areas like intuition which supposedly aren't reachable by the machine. Some go even further starting to talk about religion. It is very Hegelian that the crown jewel achievement of our civilization starts to drive people away from the foundational principles of that civilization.

card_zero 2 hours ago|

Basing science on proof (or anyway believing that you can) is Logical Positivism, a mindset that opposes the method of falsifiability. But of course mathematics is all about proof, and for that reason I was wary of it for a very long time.

trhway 1 hour ago||

>Basing science on proof (or anyway believing that you can) is Logical Positivism, a mindset that opposes the method of falsifiability

not really. You can consider positive proof as an experiment confirming your theory and the negative proof and counter examples as an experiment falsifying your theory.

card_zero 1 hour ago||

Yes, really. "Positive proof" opposes the concept of falsification. You can only have it within a system formal logic, and science can contain those, but isn't one.

trhway 30 minutes ago||

>"Positive proof" opposes the concept of falsification.

no. Positive proofs have nothing to do with falsification. They just tell you that there is no point in spending effort on searching for negative proofs and counter examples. They don't prevent nor prohibit you from spending that effort. They just advise you that that effort will be wasted.

It is like nobody prevents from experiments to turn lead into gold. Of from searching for a right angled triangle violating Pythagoras.

aborsy 1 hour ago|

Mr. Tao is an excellent politician. Lots of awards and texts, yet no major problem solved.

It seems now that NS is solved he is mobilizing the community to convince taxpayers continue to pay even though AI may do a better job in his work.

Also, his opinion of AI has continually changed in the past years, after the capabilities were demonstrated.

vatsachak 1 hour ago||

Gr8 b8 m8