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>Dr. Tao

Professor Tao.


Has Lean proved the Four Colour Theorem? I thought only Rocq had.

It’s an aggregated list, not a list of formalisations in Lean - the checkbox is “things formalised in any prover”.

AI is hopeless at using existing code, it likes to append only.

With the size of the proof object, a potential buffer overflow comes to mind.

It doesn't seem execution was a problem. From Kevin Buzzard's blog:

I’ve compiled the code base and run comparator on it — it checks out. It is a gigantic proof (over 13.4 million lines of code) and takes nearly 20 times as long to compile as Lean’s mathematics library (on a machine with 96 cores!). Lean can be sluggish when jumping from file to file on a repo of this size (even on a machine with 500G of ram, which Anthropic also gave me access to), but Anthropic also supplied me with some html documents which are easier in practice to explore (clone the repo and open with a web browser).

500G of RAM is not actually that huge tbh (I was looking to buy a used 1TB server blade for some personal stuff a while ago but it was too much hassle) so I don't guess there was too much potential for buffer overflows.


Buffer overflows are trivial to check for at runtime (~proof-checking-time) and Lean does this. Just like Java does it.

I’d wager a million gazillion bucks that this is not the case.


So would you also say no chance of a stack overflow or any type of surreptitious storage overflow anywhere in the runtime do you think?

I would say it’s very unlikely to be the case here at least.

Of course some bugs in Lean may exist (I don’t have deep insight into Lean’s implementation and there have been bugs before), but I find it unlikely to be systematical or in a format that could affect the proof.

As I understand it, Lean is implemented in Lean and emits/compiles to C. In that C code, I’d be very surprised if any buffer overflows or stack overflows exist.

Such overflows are not difficult or expensive to detect, so if any were there, it should cause a crash instead of an incorrect result.

It’s not as in handwritten C where you can forget or omit a bounds check.

I’d say it is even less likely than seeing an overflow in the Core of Java cause an incorrect result (i.e. corruption instead of a crash) - because Lean uses the De Bruijn principle of reducing to a very small Core, that is easier to keep correct (others in this thread have expanded on this I better than I can I think).

Out of pure curiosity: Do you believe otherwise or have a reason to think I am mistaken?


No I don't have any reason to believe you are mistaken other than general suspicion.

Stack overflows are also trivial to check for, if one wants to. It's just comparing two pointers, plus checking for arithmetic overflow (in case the pointers run past the maximum value of the pointer type).

I'd feel so much more excited if this was done in Metamath. Tiny checker kernel, no complicated dependent types, way less to go wrong.

Not mm0?

13 million lines of code, a lot of which is new to Mathlib. So it hasn't built on what is already there but synthesised a bunch of new stuff.

LLM generated Lean code in the past has been known to exploit bugs in the Lean kernel, it would be foolish to rule this out happening again.


US centric viewpoints. The UK is running out of space for landfills. Burning it is best for all.

And reuse better.

Ridiculous bag analogy they use - I think we all have a bunch of plastic bags as it's easy to forget to take one out - much better if I remembered a cotton one.


Repo will be inactive and obsolete within 12 months.


Probably better for the environment too.


The carbon footprint of producing an EV is higher than an ICE. Nobody disputes that.

But the lower carbon footprint of operating the an EV makes the EV have a lower footprint over the life of the vehicle. This is true even if your electricity comes purely from coal, as a coal power plant gets an economy of scale that an ICE doesn't achieve. If your power comes from a renewable source, then the trade-off happens even sooner.


the problem is where these lithiums are sourced from and that raises the costs of human rights


Questioning the lithium source is valid, but also a red herring when we're talking about environmental impact.

But yes, battery minerals can involve human rights abuses. But ICE vehicles are also built from steel, aluminum, copper, rubber, electronics, and metals that can involve forced labor, unsafe mining, land displacement, pollution, or exploitative labor. The ethical issue is supply chain due diligence across the whole auto industry, not just lithium.

Funny how some people (Mostly anti-EV folks) only discover supply chain ethics only when the car has a battery.


what car company is using forced labor as you are claiming that is pretty serious, almost all except China, are built in countries with strong labor unions.

what I really hate is that EVs have given people a false sense of superiority that seemingly stems from their curious unwillingness to look at the ugly environmental and human rights abuses around the lithium sourcing.


> what car company is using forced labor as you are claiming that is pretty serious, almost all except China, are built in countries with strong labor unions.

You're conflating final car assembly with the sourcing of the raw materials.

GM's report [0] says "We have reason to believe that certain of the 3TG in our products may have originated in a Covered Country [1] and may not have all come from recycled or scrap sources."

Honda admits [2] "Among all the smelters and refiners disclosed to us by our suppliers, we determined that some of them processed minerals sourced in the DRC or its adjoining countries."

I read reports from other car manufacturers and they're all full of the same weasel words. Ford says "We do not knowingly procure materials that contribute to child and forced labor, bribery and corruption, conflict, or environmental concerns" [3] while admitting "Through our 2023 data collection and due diligence efforts described below, Ford has reason to believe some 3TG contained in our products may come from Covered Countries."

[0] https://investor.gm.com/static-files/5e0ea429-ded3-40ca-b3a1...

[1] SEC defines "Covered Country" as "the Democratic Republic of the Congo or an adjoining country"

[2] https://global.honda/en/investors/news/news20250522/main/0/l...

[3] https://www.sec.gov/Archives/edgar/data/37996/00000379962400...


It's been over a week. I answered your question and you seem to have ignored it.


> the ugly environmental and human rights abuses around the lithium sourcing.

Be specific, please, and for completeness compare to the impacts of fossil fuel extraction and production for ICE vehicles.

Lithium supply chains: Environmental impacts and trade-offs analysis - https://www.sciencedirect.com/science/article/pii/S235248472...

  Most world lithium production is attributed to spodumene mining in Australia, Brazil, Zimbabwe, and Canada, and to brine operations in Chile, China, and Argentina


you've refused to answer a simple question twice so for the third time : what car company is using forced labor as you are claiming?


Can you please link to these prior two occasions you've asked me this question?

I have no recollection of ever having addressed you or being addressed by you before this interaction. (EDIT: we have had zero intersection in HN comments for at least 16 days.)

I suspect you've confused a user name.

Still, to address your question, for the very first time, there are reports of car companies in China, Japan and elsewhere being linked to third party forced labour practices - Toyota, for one example, made a comprehensive statement in 2021 to explain how they were acting to mitigate (ie minimise, reduce, limit) their existing exposure to Forced Labor of Migrant Workers and the Modern Slavery Acts. That 13 page statement is essentially a confession that Yes, they did rely on parts in the supply chain with a forced labour element and Yes, we will minimise this but it will likely be hard to entirely eliminate this.

If you like I can link to this statement, should you be unable to unable to find it yourself.

Would you now be kind enough to expand on your statement about the lithium supply chain and sensibly compare it to the environmental damages of the fossil fuel industry?


No


> Greg Smith from ISIS as well as collaborators

Didn't know ISIS gave a hoot about gluten free.


It is unfortunate that at some point in midst of numerous renaming itself after a brief stint in mass media around 2014 the programming on both side was so successful that the latin string of "isis" to this day is basically reduced in many westerners minds as a pavlovian reflex to this meaning, ironic because most arabs in egypt and elsewhere lack the association

so kudos to the article/institute, leaving as it is

great band btw

> The name ISIS is not an acronym: it refers to the Ancient Egyptian goddess and the local name for the River Thames. The name was selected for the official opening of the facility in 1985, prior to this it was known as the SNS, or Spallation Neutron Source. The name was considered appropriate as Isis was a goddess who could restore life to the dead, and ISIS made use of equipment previously constructed for the Nimrod and Nina accelerators.[0]

[0]https://en.wikipedia.org/wiki/ISIS_neutron_source


I work there, and when we give tours and people raise the issue, I like to point out that we had the name first and so we're not changing it. Though we did once get an official reminder that, to avoid ambiguity, we had to always say 'ISIS Neutron Source' in full on immigration and customs paperwork, especially in anything that also uses the word 'nuclear'.


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