You expect an arxiv only paper to be cited? Do you even know fuck all about scientific research? Do you think someone can slap "Foundations of" in an arxiv title and we are mandated to cite it?

Yes, I'd expect a 2 year old preprint from a rising research in this utlra-niche field to likely be discussed when someone is claiming to have a sweeping solution on exactly the same research question

Maybe not necessarily so, but while looking through the paper's bibliography I get the sense that these were AI-gathered references because there seems to be gaps in the current literature on this topic

You bemoan the cherry picked example and counter with an unfalsifiable claim. Certainly we have remembered much more math than Calculus, and much of it has been of practical use.

How can we hope to quantity the expenditure on math we've collectively forgotten? It's unknowable by definition. The only reasonable thing to do is to determine the value added after the expense paid. Even in a world where calculus is the only thing that we took away from the math of 1700s my guess is that this is still an economically beneficial calculation.

The claim is falsifiable; the bulk of 18th century math is "forgotten" in the sense that few, if any, people still use or apply or even know about it.

It's not "forgotten" in the technical sense that one _can_ still go dig into the dusty archives of any number of old university libraries, and review learned journals, diaries, commonplace books, personal correspondence, and so on from the 1700s that describe the mathematical work of the day in detail.

You can then systematically review that work, and test whether the claim that "nearly all mathematical output of the 18th century has been generally forgotten and never found any use."

I hypothesize that this experiment will show that nearly all of the mathematical output of the time long ago fell into oblivion. This is a falsifiable claim.

Your claim is still rubissh, as you neglected to interact with the rest of my comment: economic utility does not necessitate all mathematical output directly contributes.

You redefine "forgot" to make it falsiable, but also neglect that you need to refute that some "forgotten" work didn't contribute to new work down the line.

Whataboutism. Two evils are still evil.

Probably yes. Only a handful of mathematicians work on this particular problem, and ALL of them do not exclusively work on this problem, while having administrative and teaching duties.

The real issue is we'll never know. The rich are willing to risk it all on charismatic CEO psychopaths but not on humans.

No you see people that use AI generally don't bother to consider this unimportant detail. Or they ask the AI to "double check" its work.

Nah, I tried to post a long reply yesterday, but YC was glitching, so I just gave up.

You forgot to include empirical evidence of your claim, since I'd like to double check it.

It's a great comedy that we move the buck from "I don't trust the human proof" to "I don't trust the Lean proof" despite the level of trust dramatically increasing. Moving to HOL-light might be another modest increase in trust, but to pretend the implementation of HOL-light has never had bugs and it's kernel could never have a bug is hubris.

We have a significant case split here:

A human mathematician writes a Lean proof:

- Unlikely that the mathematician would cheat with Lean bugs or even know how to find one. Trust increases.

An AI writes a Lean proof:

- AIs have been "ambitious" in their goals in the past and do know how to find Lean bugs and exploit them. Trust decreases.

Hearing someone say "the future of proofs is Lean" is a bit like hearing someone say "the future of programming is Rust." Sorry to disappoint, or happy to inform, there are hundreds of programming languages actively being used, and Rust is not even the most used language. To think that proof assistants, fancy programming languages, would be any different is suspiciously motivated.

I hear you but point me to one novel formalization right now that is not Lean. It’s really becoming a refacto standard. Which is lovely but terrible for pedegogy

??? Look at any conference that publishes mechanized results? You'll see plenty of Isabelle, ACL2, Rocq, Agda. You exist in the pop science bubble. If Lean has done anything it's advertised itself well. It did a good job of that as far back as the Liquid Tensor Experiment, and it's pissed many people off in the community with it's marketing antics.

So you'd rather give money to the company that stole the copyrighted material of experts and academics instead of giving them money? Sure some textbooks are corporate greed schemes themselves, but many others are just the work of a group of professors

they literally said that they think Mamdani is doing the right thing and that they understand they're hindering their education by using AI the way they are, did you even read the comment before making your response?

Missing information is different from paying the person who steals information instead of paying the person that produces it. Did you bother to think critically before you replied, or is an AI doing all your thinking as well?

You mean that technology that resulted in a massive bubble, wasn't marketed as replacing all labor and giving the rich personal slaves? You mean the technology that enables human communication and creativity instead of promoting human isolation and stealing human creativity?

Horseshit. ~30% of US citizens are happy with this state of affairs. ~30% are completely disengaged, believe ridiculous things like "both sides are the same" or feel like politics doesn't effect them. ~30% voted for Harris, Biden, and Clinton before that.