100 theorems in Lean

https://leanprover-community.github.io/100.html

#HackerNews #100theorems #Lean #TheoremProver #Mathematics #Proofs

@benleis Here is a visual proof of Ptolemy's theorem I just draw.

#geometry #maths #proofs

🥳#call4reading #NewPublicationQIC

✍️Unconditional #Proofs of #Quantumness Between Small-Space #Machines #by A. C. Cem Say and M. Utkan Gezer

🔗https://doi.org/10.2478/qic-2025-0002

Dimension 126 Contains Twisted Shapes, Mathematicians Prove

https://www.quantamagazine.org/dimension-126-contains-strangely-twisted-shapes-mathematicians-prove-20250505/

#HackerNews #Dimension126 #TwistedShapes #Mathematics #Proofs #Geometry

Source : Quanta Magazine / Jordana Cepelewicz

https://www.quantamagazine.org/mathematical-beauty-truth-and-proof-in-the-age-of-ai-20250430/
#mathematics #maths #math #proofs

Join our discussion on #proofs and #proofAssistants in our latest episode of it’s not just numbers! And don’t forget to look at the links in the show notes if you want to try them out

You can find the episode on https://creators.spotify.com/pod/show/not-just-numbers/episodes/S2E06---Proofs-and-proof-assistants-with-Sander-Dahmen-and-Jim-Portegies-e31knov or your favourite podcast platform

#mathematics #education

I'm still fumbling about in the dark with Lean, but my goal for my first big project is to implement system F sub omega and prove its type safety. I'm going to try some simpler lambda calculi first, probably, because I fear that which I do not understand.

Question: Does anyone have tips/examples/guides as to how to start to practically describe a type theory? I started out trying to define evaluation and de Bruijn indices etc and got lost in the weeds. Is there a way to operate fully at a higher level, and only really talk about the types? And if I'm only interested in proving the theory, and not with efficient execution, is there a better way for me to represent scopes/contexts?

#lean #programminglanguagetheory #PLT #proofs #TAPL #Lean4

#Reading #proofs. #AcWriMo #day2 #AcWriMo2024

@loopspace @tao For me, the most natural approach would be in the context of formal logic. Start with the set of all proofs for a given statement (in a specified formal system, with some axioms given, for example) and then introduce some transformations that transform a proof into an equivalent one. Changing the order of the proof steps is a possible transformation, and the morst trivial one. Then these transformations define an equivalence relation, and voilà!, you have a concept for proof equivalence.

The challenges here are of course (1) to find a definition that is meaningful in the real life of mathematicians, and (2) to prove interesting things with these concepts. One would try to define invariants, for example.

I have done nothing concrete in this direction and do not know whether anyone else has, but maybe there is something.

#Logic #Proofs #ProofTheory

A while a go I started working on a modal semantics for defining errors in distributed computing via types. The results have now appeared in a chapter for a volume dedicated to one my PhD mentors and teacher Göran Sundholm. The actual formalism is a bit far away from the tons of things I learned from him, but it touches on the issues of correctness and errors in proofs part of his philosophical research.

#proofs #computing #errors #correctness

https://link.springer.com/chapter/10.1007/978-3-031-52411-0_11

@philosophy

A Friendly Introduction to Zero Knowledge https://zkintro.com/articles/friendly-introduction-to-zero-knowledge
#zero #knowledge #proofs #zk #anonymous

There is something very satisfying about getting that "#Proofs of your paper are ready" email. There is also something very exhausting about it as you think, "Haven't I finished with that one?"
(and it's not like most #ScientificJournals provide with any real editing support)
#academicchatter

TNFISHKEEPER.COM™ 🐠 2007 STATE QUATERS PROOF SET #COINS #PROOFS #TNFISHKEEPER - https://www.youtube.com/watch?v=nFGuyD2z3n4

How Is Science Even Possible?
https://www.quantamagazine.org/how-is-science-even-possible-20240620/ #podcast #transcript #ArtificialIntelligence #Biology #Complexity #Emergence #MathematicalBiology #MathematicalPhysics #Mathematics #Physics #Proofs #TheJoyOfWhy

This support some suspicions I've had about there being a use for formal specification/verification techniques, even if you aren't a PhD, and even if you don't have a ton of time to spend on it:

https://medium.com/koodoo/tla-for-startups-part-1-8b162863824b

I think I'm going to do some experimenting and learning TLA+ to have the knowledge on hand if I run into the use for it.

#proofs #tla #specification

First author paper out in the wild. It's challenging as an independent researcher, but it can be done. This has been a long time coming. Maybe more in the future
https://zenodo.org/records/11214976
#paper #math #matheducation #proofs
Should show up in a couple other locations as well hopefully (pending reviews)

Cheers @rzeta0, was this the book about proofs you have been reading? Or is it another one?

https://www.people.vcu.edu/~rhammack/BookOfProof/

#Mathodon #Math #Maths #Proofs

#Math #Proofs

Ho ripubblicato un #repo GitHub circa delle #dimostrazioni di #matematica: qualcuno che si senta coraggioso e mi voglia dare una mano a controllarle?

https://github.com/senzanome75/Math-Proofs