Il me semble que Metamath (auquel a participé Mario Carneiro, très impliqué dans Lean également), est plus proche de ZFC
en.wikipedia.org/wiki/Metamath
en.wikipedia.org/wiki/Metamath
Metamath - Wikipedia
en.wikipedia.org
September 19, 2026 at 6:47 PM
Il me semble que Metamath (auquel a participé Mario Carneiro, très impliqué dans Lean également), est plus proche de ZFC
en.wikipedia.org/wiki/Metamath
en.wikipedia.org/wiki/Metamath
@dougmerritt @ColinTheMathmo I don't think "The real numbers that are left over after rational and irrational are excluded is an empty set" means constructively what one might think from classical intuition.
Mostly I want to point to the issue https://github.com/metamath/set.mm/issues/4299
One […]
Mostly I want to point to the issue https://github.com/metamath/set.mm/issues/4299
One […]
Original post on sfba.social
sfba.social
September 18, 2026 at 10:18 PM
@dougmerritt @ColinTheMathmo I don't think "The real numbers that are left over after rational and irrational are excluded is an empty set" means constructively what one might think from classical intuition.
Mostly I want to point to the issue https://github.com/metamath/set.mm/issues/4299
One […]
Mostly I want to point to the issue https://github.com/metamath/set.mm/issues/4299
One […]
@dougmerritt @ColinTheMathmo Ooh nice. The part from timestamps 2:42 to 14:15 was nice to listen to, since I just finished a formalization of Bertrand's postulate from IZF axioms in metamath which uses the prime counting function π, the Chebyshev theta function, etc. Seeing them in this talk was […]
Original post on sfba.social
sfba.social
September 18, 2026 at 7:46 PM
@dougmerritt @ColinTheMathmo Ooh nice. The part from timestamps 2:42 to 14:15 was nice to listen to, since I just finished a formalization of Bertrand's postulate from IZF axioms in metamath which uses the prime counting function π, the Chebyshev theta function, etc. Seeing them in this talk was […]
@freekwiedijk.bsky.social Do you have any strong feelings regarding the best way to learn a proof assistant: use the pre-existing library & formalize something, or start from scratch?
For logical frameworks, you almost always "start from scratch" (well, not Isabelle, I guess). For Metamath, though?
For logical frameworks, you almost always "start from scratch" (well, not Isabelle, I guess). For Metamath, though?
September 17, 2026 at 1:15 PM
@freekwiedijk.bsky.social Do you have any strong feelings regarding the best way to learn a proof assistant: use the pre-existing library & formalize something, or start from scratch?
For logical frameworks, you almost always "start from scratch" (well, not Isabelle, I guess). For Metamath, though?
For logical frameworks, you almost always "start from scratch" (well, not Isabelle, I guess). For Metamath, though?
Maybe the best way to learn Metamath is to formalize Bourbaki's bizarre foundations in Metamath 🤔
September 15, 2026 at 11:38 PM
Maybe the best way to learn Metamath is to formalize Bourbaki's bizarre foundations in Metamath 🤔
This is an important thread not just because of the analysis of the use of LLMs in math research, but also because it reveals how a world-class mathematician thinks about math.
#mathematics #math #MetaMath #ArtificialIntelligence #AI
Source: buff.ly/BaAeSJV
#mathematics #math #MetaMath #ArtificialIntelligence #AI
Source: buff.ly/BaAeSJV
September 14, 2026 at 5:03 PM
This is an important thread not just because of the analysis of the use of LLMs in math research, but also because it reveals how a world-class mathematician thinks about math.
#mathematics #math #MetaMath #ArtificialIntelligence #AI
Source: buff.ly/BaAeSJV
#mathematics #math #MetaMath #ArtificialIntelligence #AI
Source: buff.ly/BaAeSJV
What's a good tutorial (or introduction) to the Metamath proof assistant?
September 10, 2026 at 1:01 AM
What's a good tutorial (or introduction) to the Metamath proof assistant?
Jeremy Lindsay, Cezary Kaliszyk, Christine Rizkallah: Optimising Metamath Proofs for Human Working Memory https://arxiv.org/abs/2609.07097 https://arxiv.org/pdf/2609.07097 https://arxiv.org/html/2609.07097
September 9, 2026 at 6:42 AM
Jeremy Lindsay, Cezary Kaliszyk, Christine Rizkallah: Optimising Metamath Proofs for Human Working Memory https://arxiv.org/abs/2609.07097 https://arxiv.org/pdf/2609.07097 https://arxiv.org/html/2609.07097
OK, here's a thing I'd like AI companies to pour money into: reducing the size of the smallest-known Turing machine whose provability of halting is independent of ZFC: current record seems to be 549 states https://github.com/andrew-j-wade/metamath-turing-machines
But surely we can grind out […]
But surely we can grind out […]
Original post on mathstodon.xyz
mathstodon.xyz
September 5, 2026 at 2:10 AM
OK, here's a thing I'd like AI companies to pour money into: reducing the size of the smallest-known Turing machine whose provability of halting is independent of ZFC: current record seems to be 549 states https://github.com/andrew-j-wade/metamath-turing-machines
But surely we can grind out […]
But surely we can grind out […]
And its alternatives, like Lee and Rudnicki's first-class "alternative aggregates" (which Mario Carneiro independently reinvented for Metamath), and Lean's "tuples + coercions".
Doubtless there are others. As I said, I feel like it's an understudied aspect of proof assistants.
Doubtless there are others. As I said, I feel like it's an understudied aspect of proof assistants.
August 31, 2026 at 1:34 PM
And its alternatives, like Lee and Rudnicki's first-class "alternative aggregates" (which Mario Carneiro independently reinvented for Metamath), and Lean's "tuples + coercions".
Doubtless there are others. As I said, I feel like it's an understudied aspect of proof assistants.
Doubtless there are others. As I said, I feel like it's an understudied aspect of proof assistants.
A recent discussion explores whether the mathematical community should support alternatives to Lean, such as Metamath, to improve soundness and set-theoretic foundations. While Lean dominates, AI advancements may now make developing a rival library feasible.
Are We Stuck with Lean? (115)
news.ycombinator.com
July 30, 2026 at 7:49 PM
A recent discussion explores whether the mathematical community should support alternatives to Lean, such as Metamath, to improve soundness and set-theoretic foundations. While Lean dominates, AI advancements may now make developing a rival library feasible.
@andrejbauer Heh, some years ago I wrote "Fortunately, metamath helps with one of the biggest hurdles: noticing when one is even using the law of the excluded middle or the axiom of choice." Not surprised that was also true of your audience.
July 15, 2026 at 2:02 PM
@andrejbauer Heh, some years ago I wrote "Fortunately, metamath helps with one of the biggest hurdles: noticing when one is even using the law of the excluded middle or the axiom of choice." Not surprised that was also true of your audience.
通过RPG游戏学习数学证明:Dungeon Proof Crawler与Metamath Zero的创新探索
https://qian.cx/posts/CA8A5FF8-C18E-4918-83B0-670A031F38CB
https://qian.cx/posts/CA8A5FF8-C18E-4918-83B0-670A031F38CB
July 8, 2026 at 5:15 PM
通过RPG游戏学习数学证明:Dungeon Proof Crawler与Metamath Zero的创新探索
https://qian.cx/posts/CA8A5FF8-C18E-4918-83B0-670A031F38CB
https://qian.cx/posts/CA8A5FF8-C18E-4918-83B0-670A031F38CB
Как игра в RPG помогает изучать математические доказательства: обзор Dungeon Proof Crawler и Metamath Zero
https://kripta.biz/posts/84C2AEC8-99D3-4963-8C4F-E1A68B9D98AD
https://kripta.biz/posts/84C2AEC8-99D3-4963-8C4F-E1A68B9D98AD
July 8, 2026 at 5:12 PM
Как игра в RPG помогает изучать математические доказательства: обзор Dungeon Proof Crawler и Metamath Zero
https://kripta.biz/posts/84C2AEC8-99D3-4963-8C4F-E1A68B9D98AD
https://kripta.biz/posts/84C2AEC8-99D3-4963-8C4F-E1A68B9D98AD
This is nominally an ad for the Harvard Mathematics Department, but it is really an ad for mathematics, and a very good one.
#mathematics #math #MetaMath
Source:https://buff.ly/nY4JJxk
#mathematics #math #MetaMath
Source:https://buff.ly/nY4JJxk
May 28, 2026 at 5:01 PM
This is nominally an ad for the Harvard Mathematics Department, but it is really an ad for mathematics, and a very good one.
#mathematics #math #MetaMath
Source:https://buff.ly/nY4JJxk
#mathematics #math #MetaMath
Source:https://buff.ly/nY4JJxk
Significantly boosts math reasoning on Ascend NPUs, MetaMath-Mistral-7B even outperforms larger models on GSM8K. But it's still based on Mistral 7B v0.1, lacking newer refinements. Tough to see this 7B truly beating Llama 3 8B in production, NPU efficiency aside.
Solve for Success: Meet MetaMath-Mistral-7B, the Ascend-Optimised Reasoning Specialist
aichina.news
May 25, 2026 at 12:25 PM
Significantly boosts math reasoning on Ascend NPUs, MetaMath-Mistral-7B even outperforms larger models on GSM8K. But it's still based on Mistral 7B v0.1, lacking newer refinements. Tough to see this 7B truly beating Llama 3 8B in production, NPU efficiency aside.
April 28, 2026 at 5:01 PM
@jdw Oh nice that's the piece we were missing to finish our proof of https://us.metamath.org/mpeuni/nrt2irr.html . As soon as we translate your proof from Agda to Metamath we should be set.
nrt2irr - Metamath Proof Explorer
us.metamath.org
April 21, 2026 at 9:19 PM
@jdw Oh nice that's the piece we were missing to finish our proof of https://us.metamath.org/mpeuni/nrt2irr.html . As soon as we translate your proof from Agda to Metamath we should be set.
PS. I had to look up Klowden, her bio is the second link.
#mathematics #math #MetaMath #ArtificialIntelligence #AI
Source:https://bit.ly/3PvJBGd
Klowden:https://buff.ly/2qcXz7k
#mathematics #math #MetaMath #ArtificialIntelligence #AI
Source:https://bit.ly/3PvJBGd
Klowden:https://buff.ly/2qcXz7k
April 6, 2026 at 5:01 PM
PS. I had to look up Klowden, her bio is the second link.
#mathematics #math #MetaMath #ArtificialIntelligence #AI
Source:https://bit.ly/3PvJBGd
Klowden:https://buff.ly/2qcXz7k
#mathematics #math #MetaMath #ArtificialIntelligence #AI
Source:https://bit.ly/3PvJBGd
Klowden:https://buff.ly/2qcXz7k
Not to quibble, but this is Andrew Wiles on being persistent.
#mathematics #math #MetaMath #quote
Source:https://buff.ly/Q9OZSyf
#mathematics #math #MetaMath #quote
Source:https://buff.ly/Q9OZSyf
March 19, 2026 at 1:02 PM
Not to quibble, but this is Andrew Wiles on being persistent.
#mathematics #math #MetaMath #quote
Source:https://buff.ly/Q9OZSyf
#mathematics #math #MetaMath #quote
Source:https://buff.ly/Q9OZSyf
I came to an agreement with my metamath prof that I could use other letters than psi and xi as metavariables because mentally pronouncing xi and psi (as a Classics major) while doing exercises for him was driving me insane.
March 7, 2026 at 2:40 PM
I came to an agreement with my metamath prof that I could use other letters than psi and xi as metavariables because mentally pronouncing xi and psi (as a Classics major) while doing exercises for him was driving me insane.