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@benleis Here is a visual proof of Ptolemy's theorem I just draw.
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#proofs
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Dimension 126 Contains Twisted Shapes, Mathematicians Prove
Quanta Magazine · Dimension 126 Contains Strangely Twisted Shapes, Mathematicians Prove | Quanta MagazineA new proof represents the culmination of a 65-year-old story about anomalous shapes in special dimensions.
Source : Quanta Magazine / Jordana Cepelewicz
https://www.quantamagazine.org/mathematical-beauty-truth-and-proof-in-the-age-of-ai-20250430/
#mathematics #maths #math #proofs
Quanta Magazine · Mathematical Beauty, Truth and Proof in the Age of AI | Quanta MagazineMathematicians have started to prepare for a profound shift in what it means to do mathematics.
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@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.
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
SpringerLinkHandling Mobility Failures by Modal TypesCorrectness is a major concern for logical systems, especially for its significance in computational settings. While establishing a norm for the correctness of computational procedures is a standard requirement, defining errors is a less investigated formal problem....
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
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)
ZenodoApplicability Operator Approach to Mathematical ProofsTeaching proofs of theorems and encouraging students to both comprehend written proofsand originate their own can at times be a difficult undertaking. This, is due, in partto the lack of a single unifying process by which one can approach mathematical proofs.In this paper a method using set theory as a foundation is presented.
here's a fun question that I have my own answer to, but would like to know what others think: what is, in your mind, the most (or one of the most) accessible mathematical proofs? as in, you could take this and show it to someone with barely any maths education, or even a child, and they'd be able to understand it and see why proofs can be fun and useful without all of the baggage of our existing, terrible maths education system
Cheers @rzeta0, was this the book about proofs you have been reading? Or is it another one?
www.people.vcu.eduBook of Proof
Ho ripubblicato un #repo GitHub circa delle #dimostrazioni di #matematica: qualcuno che si senta coraggioso e mi voglia dare una mano a controllarle?
GitHubGitHub - senzanome75/Math-Proofs: Attempt at Mathematical ProofsAttempt at Mathematical Proofs. Contribute to senzanome75/Math-Proofs development by creating an account on GitHub.
Many years ago, when I went to #law school, the #IRAC structure of legal analysis was pounded into us 1Ls. Long before that, I was an undergrad #EE. We were never taught how to read and write mathematical #proofs, unlike our peers in #Maths. Did we non-maths STEMers get short-shifted during undergrad?
Verifying zero-knowledge #proofs on #Bitcoin?
https://www.cryptologie.net/article/606/verifying-zero-knowledge-proofs-on-bitcoin/
#ZKP
www.cryptologie.netVerifying zero-knowledge proofs on Bitcoin?
A few months ago Ivan told me "how cool would it be if we could verify zero-knowledge proofs on Bitcoin?" A week later, we had a prototype of the best solution we could come up with: a multi-party computation to manage a Bitcoin wallet, and a committee willing to unlock funds only in the presence of valid zero-knowledge proofs. A few iterations later and we had something a bit cooler: stateful ap ...
In #Academics including #Math and #ComputerScience one of the biggest things I learned was to be #Methodical. #Proofs and #ComputerPrograms require clear thought. Knowing #FormalLogic was extremely valuable, one of my favorite classes in #college.
In the #ModernWorld of #AI lending a hand to any possible human #intellectual endeavor, I wonder if people will become less likely to learn and practice formal logic.
Interesting #math video on sparse rulers, which has applications ranging from #stellar #interferometry to #ElectricalEngineering designing voltage taps on transformers (ok, these days we have switchmode PS, but it's still cool).
"Proofs really aren't there to convince you that something is true – they're there to show you why it is true." – Andrew Mattei Gleason (1921–2008)
#quote #mathematics #maths #math #proofs
I am preparing for a 2024 project: writing 50 #poems outlining #proofs of #math concepts. My question is what proofs are worthy of poetry? I expect to start with the Pythagorean Theorem and perhaps end with the Poincaré Conjecture. While I have some definites to include, what would you immortalize in #poetry?
There are literally hundreds of #proofs of #Pythagorus’ #Theorem and this book has about three hundred of them. It was published in the 1920s but my copy was printed to order and bound in #India. I hope it will be both a reference and a talking point.
Ethereum L2 Starknet aims to decentralize core components of its scaling network - Starknet has laid out its road map to begin decentralizing core c... - https://cointelegraph.com/news/ethereum-l2-starknet-to-decentralize-scaling-network #decentralization #computation #consensus. #ethereum #starknet #scaling #blocks #proofs
Cointelegraph · Ethereum L2 Starknet aims to decentralize core components of its scaling network