u/hou32houKeli (keli-language.gitbook.io)in r/ProgrammingLanguages • Recommends
Microsoft Lean Theorem Prover
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#lean#theoremprover#formalmathematics
The Future of Mathematics?
Microsoft Research
359K subscribers • 11 videos on Hallway
- Recommended by 11 people: 9 on Hacker News, 1 on Lobsters and 1 in engineering communities.
- A classic. People kept recommending it from 2019 to 2025.
- Presented by Kevin Buzzard, Professor of Pure Mathematics at Imperial College London
- Linked in the descriptionSlides on microsoft.com
- An opinion. It argues one side of a question engineers disagree on.
Intermediate. Assumes working knowledge.
116K views7 years ago11 recommendations
Computer scienceProgramming languagesFormal methods and verificationComputation and complexityMath for programmers
Kevin Buzzard explains why the Lean theorem prover will shape the future of mathematics and describes his experiences digitizing university curricula.
As a professor of pure mathematics, my job involves teaching, research, and outreach. Two years ago I got interested in formal methods, and I learned how to use the Lean theorem prover developed at MSR. Since then I have become absolutely convinced that tools like Lean will play a role in the future of mathematics. With the help of a team of enthusiastic undergraduates at my university, we have begun to digitize our curriculum using Lean, and things are moving very fast. I will talk about our achievements, as well as the issues and challenges that we have faced. Reaching the staff has proved harder because these tools are not currently mature enough to be a useful tool for high-level mathematical research. I believe that this situation will inevitably change. Mathematician Tom Hales, famous for proving the Kepler conjecture, has a project called Formal Abstracts which will ultimately offer several new tools to research mathematicians. Hales has chosen to use Lean as the back end for his project. I will finish by discussing his vision, my thoughts on the construction of the tools I am convinced we can make, and finally I will speculate on the future of mathematics. No advanced mathematical knowledge will be assumed. Talk slides: microsoft.com/en-us/research/uploads/prod/2019/09/The-Future… Learn more about this and other talks at Microsoft Research: microsoft.com/en-us/research/video/the-future-of-mathematics…Why it's here
11 people recommend thisWhat people say. Engineers and mathematicians recommend this talk for its engaging argument on why formal theorem provers are crucial for the future of mathematics.
raphon Lobsters • Recommends
The Future of Mathematics?
This is a talk by Prof Kevin Buzzard given at Microsoft Research recently. In it, he proposes a program for formalizing the undergraduate mathematics curriculum in Lean. I personally found it fascinating, partly because this goal resonates strongly with me, but also because of the cultural and sociological observations. The overlap between "real mathematicians" and the the theorem proving space is incredibly tiny, so Prof Buzzard has been able to make a significant impact, working with undergrad…
stephenSinniahon Hacker News • Recommends
On “Learning How to Prove: From the Coq Proof Assistant to Textbook Style”
I was watching a video by Kevin Buzzard, he talks about using Lean Theorem Prover, seems pretty interesting link to this video
infogulchon Hacker News • Recommends
On “Alloy is a language for describing structures and a tool for exploring them”
Last week Microsoft Research posted an interesting talk by Kevin Buzzard 1 from Imperial College London about how he wants to formalize all mathematics with theorem provers. He's currently using LEAN 2. Half of the talk is a discussion of the challenges he's faced convincing other mathematicians that this is valuable, and the other half is about his success using LEAN as a tool to teach undergraduates about formal proofs in general. I think Alloy was mentioned at the end, but not really compared to LEAN. 1: link to this video 2: link
Nzenon Hacker News • Recommends
On “A Code Glitch May Have Caused Errors in More Than a Hundred Published Studies”
…hts cultural misunderstanding and apathy on both sides of the domain divide. He also references the idea that the people who might make the appropriate tools may not have stayed in academia. So, he's structured his courses around using LEAN with the indirect consequence that power users (undergrads) may choose to become open source committers. 0 link to this video One hour of presentation and then 15 min of q/a. My favorite is around 1:04:00 when someone asks a second time why he disprefers coq, and Buzzard complains that it can't represent some advanced quotient type that he'd have to work around. I'm reminded of 1 1 link Dangling by a trivial feature…
carapaceon Hacker News • Recommends
On “Building the Mathematical Library of the Future”
Oh man that was fun! Totally nerd-sniped my day though. Got me to go back and re-watch Kevin Buzzard's talk at MS Research in re: Lean, "The Future of Mathematics?" link to this video link
andrewncon Hacker News • Recommends
On “Z3 Tutorial”
That was a delightful tutorial, I recently watched a talk about the Future of Mathematics0 with respect to theorem proving and formalization. I enjoy this area a lot and love to see it getting more attention. 0 - link to this video
oolonthegreaton Hacker News • Recommends
On “Some stuff I found interesting about number theory research”
wanted to drop a link to buzzard's very interesting talk link to this video starting at 13:00 he talks about that frailness. also loved the bit about "elders" at 40:37
liupson Hacker News • Recommends
On “The year in math and computer science”
> pure math (topology and countability) and computer science have almost no overlap in the short term. This is an unexpected opinion. What do you mean by this? I would argue the opposite. Look at Formal Verification0. Here's a great video about a popular formal verfication proof assitant: link to this video A quote from the mathematician in the video expressing enthusiasm for using computers for mathematics: "All I want to do... I don't want to do mathematics on pen and paper anymore, because I don't trust it, and I don't trust other people that use it; which is everyone." (in case people only read this quote, instead of watching the lecture, the tone is tongue-in-cheek) Formal Verification would see…
pason Hacker News • Recommends
On “Lean4 helped Terence Tao discover a small bug in his recent paper”
Kevin Buzzard (a professional mathematician) has a few good talks about Lean link to this video from 2019 at MS Research link (2022 at ICM international math congress)
ookdatnogon Hacker News • Recommends
On “Project to formalise a proof of Fermat’s Last Theorem in the Lean theorem prover”
I watched this video years ago and found it interesting. It's a talk by Kevin Buzzard, a pure mathematician who got really interested in theorem proving software, and he explains his motivation. link to this video
contravarianton Hacker News • Mentions
On “F# RISC-V Instruction Set Formal Specification”
The main reason code isn't considered a formal specification is that it's not intended to be either formal or a specification. That doesn't mean you cannot write a formal specification in code. If anything code allows for a higher level of formality than all but the most formal mathematics. Which is why some mathematicians are advocating that mathematical proofs should be specified as code 1. You shouldn't confuse the existence of these languages to mean that any code not capable of expressing mathematical proofs is not formal. It might be limited, but not informal. 1: link to this video
drdecaon Hacker News • Mentions
On “Can Computers Prove Theorems?”
…f the theorem is expressed in the way that you want it to be. I’m on my phone right now, and the phone youtube app doesn’t give me a permalink, but I’ll try and edit this comment soon on laptop to include link to the comment section. Edit : here are links to what Mario Carneiro said in the thread click the read all replies to read the full thread) link to this video link to this video…
JulianWasTakenon Hacker News • Mentions
On “Ask HN: What are you using new programming languages for?”
Lean 1 2 3 To try and revitalize my math life a bit... There are some things I quite miss, and learning Lean was my idea to force myself to get back in the swing of things. 1: link 2: link 3: link to this video
stablenodeon Hacker News • Mentions
On “Graphical Linear Algebra”
"Are you the high priest and decider of the usefulness of mathematics? To be honest, it almost sounds like some category theorist was super mean to you..." Interesting and totally not ad hominem response... I believe Kevin Buzzard (an actual mathematician) had a few words about this last year: link to this video
ookdatnogon Hacker News • Mentions
On “Ask HN: How to learn mathematical proofs from scratch?”
At Imperial College London there's an intro to proofs course taught with interactive exercises supported by a proof assistant, Lean. The exercises (and the proof assistant) are freely available online at link . Disclaimer: I didn't fully work through this game, I never studied at ICL and I can't vouch for its effectiveness, I simply heard about it and thought it was interesting and relevant to your question. (Here's also a talk by the professor about his rationale for using Lean: link to this video ).