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What does the end of mathematics look like?

awanderingmind.blog

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Re: What does the end of mathematics look like?

#11

Post by BSDobelix »

N2yhWNXQN3k9 wrote: post #7

This article is written in an unnecessarily extravagant style, IMO. Also, I appreciate anonymity, but, to my point > I live by myself in a remote mountain cave beyond the ken of civilised persons, and can only be contacted during a full moon, using certain arcane rites that are too horrible to speak of. Okay.

>>I live by myself in a remote mountain cave

= I live in California, and the nearest Starbucks is more than 20 miles away.

>>can only be contacted during a full moon

= As a night person, I am awake when the streetlight outside my house turns on.

>>certain arcane rites that are too horrible to speak of

= In order to contact me, you must install Microsoft Teams.

Overall, it's not that bad, except for the MS team thing. ;)

Re: What does the end of mathematics look like?

#12

Post by nottorp »

N2yhWNXQN3k9 wrote: post #7

This article is written in an unnecessarily extravagant style, IMO. Also, I appreciate anonymity, but, to my point > I live by myself in a remote mountain cave beyond the ken of civilised persons, and can only be contacted during a full moon, using certain arcane rites that are too horrible to speak of. Okay.

As always, HN has no sense of humour...

Re: What does the end of mathematics look like?

#13

Post by milesrout »

nottorp wrote: post #12
N2yhWNXQN3k9 wrote: post #7

This article is written in an unnecessarily extravagant style, IMO. Also, I appreciate anonymity, but, to my point > I live by myself in a remote mountain cave beyond the ken of civilised persons, and can only be contacted during a full moon, using certain arcane rites that are too horrible to speak of. Okay.

As always, HN has no sense of humour...

Writing like a wanker isn't funny.

Re: What does the end of mathematics look like?

#14

Post by bubblyworld »

BSDobelix wrote: post #11
N2yhWNXQN3k9 wrote: post #7

This article is written in an unnecessarily extravagant style, IMO. Also, I appreciate anonymity, but, to my point > I live by myself in a remote mountain cave beyond the ken of civilised persons, and can only be contacted during a full moon, using certain arcane rites that are too horrible to speak of. Okay.

>>I live by myself in a remote mountain cave = I live in California, and the nearest Starbucks is more than 20 miles away. >>can only be contacted during a full moon = As a night person, I am awake when the streetlight outside my house turns on. >>certain arcane rites that are too horrible to speak of = In order to contact me, you must install Microsoft Teams. Overall, it's not that bad, except for the MS team thing.…

The man is south african, we are geologically blessed and have a lot of pleasant remote mountain caves =)

Re: What does the end of mathematics look like?

#17

Post by n4r9 »

A_D_E_P_T wrote: post #2

We'll know that the time draws nearer when an AI confirms or refutes Mochizuki's proof of the abc conjecture. As of right now, I don't think they're capable of doing that. And, as they can't even check a very (very!) complex proof, they won't be able to conjure any inhumanly complex proofs de novo . Also: > To expand: what if the practice of mathematics becomes completely determined by the diktats of a vast capitalis…

Why would an AI confirmation or rejection be more convincing than the proof itself?

Re: What does the end of mathematics look like?

#18

Post by gilleain »

N2yhWNXQN3k9 wrote: post #7

This article is written in an unnecessarily extravagant style, IMO. Also, I appreciate anonymity, but, to my point > I live by myself in a remote mountain cave beyond the ken of civilised persons, and can only be contacted during a full moon, using certain arcane rites that are too horrible to speak of. Okay.

Perhaps the writer is a fan of Grothendieck who did almost exactly this - lived in a remote village in the Pyrenees

https://en.wikipedia.org/wiki/Alexander_Grothendieck#Retirem...

"Local villagers helped sustain him with a more varied diet after he tried to live on a staple of dandelion soup." - like most people would.

Re: What does the end of mathematics look like?

#19

Post by BSDobelix »

bubblyworld wrote: post #14
BSDobelix wrote: post #11

Earlier quoted context omitted.

>>I live by myself in a remote mountain cave = I live in California, and the nearest Starbucks is more than 20 miles away. >>can only be contacted during a full moon = As a night person, I am awake when the streetlight outside my house turns on. >>certain arcane rites that are too horrible to speak of = In order to contact me, you must install Microsoft Teams. Overall, it's not that bad, except for the MS team thing.…

The man is south african, we are geologically blessed and have a lot of pleasant remote mountain caves =)

Okay, I will revert everything. The cave, the moon, and the rituals are all real. It's impressive how much reality is based on location :-)

Re: What does the end of mathematics look like?

#20

Post by esperent »

n4r9 wrote: post #17
A_D_E_P_T wrote: post #2

We'll know that the time draws nearer when an AI confirms or refutes Mochizuki's proof of the abc conjecture. As of right now, I don't think they're capable of doing that. And, as they can't even check a very (very!) complex proof, they won't be able to conjure any inhumanly complex proofs de novo . Also: > To expand: what if the practice of mathematics becomes completely determined by the diktats of a vast capitalis…

Why would an AI confirmation or rejection be more convincing than the proof itself?

Rejection: an incredibly complex proof can fall for (comparatively) simple reasons. If the AI scans the entire proof and says yep, there's the flaw, page 126 theorem X contradicts then a human can verify this without having to understand the whole proof.

This could lead to the proof being rejected entirely, or fixed and strengthened.

Confirmation: if the AI understands it well enough that we're even considering asking it to confirm the proof, then you can do all kinds of things. You can ask it to simplify the entire proof to make it easier for humans to verify. You can ask it questions about parts of the proof you don't understand. You can ask it if there's any interesting corollaries or applications in other fields. Maybe you can even ask it to rewrite the whole thing in LEAN (although, like the author, I know nothing about LEAN and have no idea if this would be useful).

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