Live and recent posts from across the Fediverse tagged #proofs, aggregated by home.social.
The Proof Economy
Across my career, from medicine and life sciences into structural biology, higher education and later semiconductor verification, I…
#Economy #AI #Axiomise #Formal #formalverification #proofs #verification
https://www.europesays.com/3284859/
Why Sending #Humans to #Venus Is Not as #Mad as It Sounds : Medium
#Mystery #Hominin left big #Footprints at #Ancient #Lake in #Africa : New Sci
#AI helped produce two #Proofs for the same #Cryptography problem : Sci Am
Latest #KnowledgeLinks
The k-server conjecture is true
https://arxiv.org/abs/2609.15979
Comments: https://news.ycombinator.com/item?id=49709129
#HackerNews #kserver #conjecture #math #proofs #arxiv #research #HackerNews
#today is meant to be open 'eco' home day, but with non-responses and a cancellation I may be down to just one or two visitors. I'd hate to think that a few days of cooler weather have made people forget global warming entirely...
I am taking the opportunity to work on my #paper #proofs, and it is going faster and better than yesterday at this point!
The four-colour theorem gets a rare new proof — and offers mathematicians important new insights into graphs
https://www.quantamagazine.org/the-four-color-theorem-gets-a-rare-new-proof-20260910/
By revisiting a famous problem first controversially solved with computer assistance in the 1970s, mathematicians have developed a rare new proof of the four-colour theorem and deepened understanding
#science #mathematics #proofs
By revisiting a famous problem first controversially solved with computer assistance in the 1970s, mathematicians have developed a rare new proof of the four-colour theorem and deepened understanding #science #mathematics #proofs
Posted into FLIPBOARD EXCHANGE FEED 🗞️ @flipboard-exchange-feed-Econopass
The purpose of mathematical sciences isn't merely to figure out whether hypotheses or conjectures hold or not; the reward is what we learn while solving these problems. A yes/no answer to the Collatz conjecture or the P=NP problem would not be particularly helpful if we do not understand the reason behind it. Agentic AI (in combination with interactive theorem proving) can be a tremendously helpful tool, but we will need to figure out how to learn something interesting from these humongous proofs.
"Fermat’s last theorem, one of the most celebrated mathematical results of the last half-century, has been turned into computer-verified code for the first time, using an advanced prototype of the artificial-intelligence (AI) chatbot Claude."
"On the morning of Tuesday, September 8, mathematicians at OpenAI announced that a group of 10,000 autonomous AI agents under their direction, running on an advanced model […] had found a “singularity” in the Navier-Stokes equations in three dimensions — thus resolving one of the six remaining Millennium Prize Problems posed in 2000 by the Clay Mathematics Institute, each of which carries a $1 million prize."
Confession time. I've always had a problem with limit proofs that are based on the formal definitions of the limit.
For instance, when using the epsilon delta definition, the choice of delta very often looks like magic to me. If you magically happen to pick the right delta, then the proof works. Yay!
Except that this is math, not magic. I've used the following video to help myself understand how to pick delta, and OMG what a boon it has been to my understanding.
OpenAI Astra Solves 10 Open Math Problems for $2,000 in Compute
OpenAI's Astra model resolves ten decade-old math problems with machine-checkable Lean 4 proofs for roughly $2,000 in compute cost
https://pulseofnations.lol/openai-astra-solves-10/
#AiResearch #Astra #Breakthrough #Computation #Lean4 #Mathematics #OpenAI #Proofs
An anecdote from Paul Halmos's autobiography:
In class. The lecturer works through a proof, on the blackboard. At some point he says "It is obvious that ..." and then states the relationship he relies on in his proof.
One student asks: Excuse me, Professor, I don't see why this is obvious. I don't understand it.
The lecturer nods, turns back to the blackboard, looks at the previous steps, thinks, chalks up some calculations in a corner, thinks some more.
Then he turns back to class. "Yes, as I said, it is obvious."
[Quoted from memory, details in the book will differ.]
‘Crucially, while in model-theoretic semantics the base case
of the judgment is given by truth (i.e., in the model M with interpretation
I, the judgment w ||- p obtains iff w ∈ I(p)), in proof-theoretic semantics it
is instead given by provability in an atomic system; that is, by the following
clause in which B is an arbitrary atomic system:
||- B p iff p is provable in B’
Categorical proof-theoretic semantics
David Pym, Eike Ritter, Edmund Robinson
Studia Logica 113 (1), 125-162, 2025’
What is an arbitrary atomic system? In the Neo-Nazi model of an ideal world all is interpreted to be a p: ‘the only value to be obtained is by financing the cult of nihilistic fatalism, so as not to hurt the hubris and addiction to power that spawns the craving of psychopaths!’ #NeoNazis #NaziLogic #CultsOfHateAndFear #FascistsFinance #FinancingEcocide #Logic #Models #BetterWorlds #TranscendingFascistLogic #Freedom #FreedomFromFascists #Intuitionism
#FascistsFinanceNeoNazis #proofs #proof #philosophy #atomicsystem
SeL4 security proofs now complete on AArch64
https://proofcraft.systems/news-2026/#2026-08-21
Comments: https://news.ycombinator.com/item?id=49418255
#HackerNews #SeL4 #AArch64 #security #proofs #ProofCraft #cybersecurity #technews
🎉 "Palomar" by Terence Tao: where mathematics finally meets its match in an AI-generated jargon jungle. 🤖✨ Dive into this head-spinning registry of Lean-verified #proofs that promise to make #math so exciting you'd rather reorganize your sock drawer. 🧦📚
https://terrytao.wordpress.com/2026/08/18/palomar-a-registry-of-lean-verified-mathematics/ #Palomar #TerenceTao #AI #Innovation #LeanVerified #MathExcitement #HackerNews #ngated
Why are some #proofs #human-readable and others aren’t?
Why do I understand my own proofs when writing them, but am struggling to understand them when reading them after a long break?
There are many tiny inference steps that are implicit in the write-up and need to be rediscovered by the reader.
My feeling is that natural language facilitates these implicit inferences if the proof is written in a suitable way.
So a #human-readable proof needs to trigger natural language inferences!
Dungeon Proof Crawler: learn how to write proofs with RPG
https://dhilst.github.io/algae/game/index.html
#HackerNews #DungeonCrawler #RPG #Learning #Proofs #Game #Development
At CDIS at KTH and listening to June Andronick on seL4 and I'm left wondering how scalable relying on global axiom of choice is in the era of vibe coders. Perhaps nothing has changed? We just commit to to do MORE proofs by vibe proving? As Terrence Tao (@tao) has pointed out, in this era it is not important who produces an artifact, it is however important to ingest the artifact in such a way that we collectively can build trust against said artifact. Personally I feel that, in this era, it is time to outlaw weak programming languages and require formal verification for any operating software, vibe coded or not. #proofs #formal #verification #vibecoding
We have created two mini apps: Fantastic Fractals and Triangular Geometry. The web versions are available at https://driota.xyz. Android versions are also currently in preview (see the webpage for information). Comments and suggestions are greatly appreciated.
Tutorial videos are available on YouTube:
https://www.youtube.com/watch?v=1p4UONYYCo8
https://www.youtube.com/watch?v=Cawd_Qzz2yQ
#math #geometry #proofs #triangle #fractal #interactive #animated
AI could destroy mathematics and barely touch it
https://davidbessis.substack.com/p/the-fall-of-the-theorem-economy
#AI challenges the "theorem economy" by automating #proofs while overlooking human intuition. Bessis argues that math's true product is understanding, not just results, which AI cannot yet replicate. The discipline's focus on theorems over concepts makes it vulnerable to machines that solve problems without building meaning. To remain relevant, mathematicians must emphasize the field's role in human sense-making rather than competitive symbol-pushing. Success depends on valuing the process of cognitive elevation and the creation of shared conceptual language.
#mathematics #philosophy
Season 2, Episode 9 is live.
Estimates behave, contours close, and a late‑night mistake gets fixed the right way.
Mathematics in motion not just results, but refinement.
#Mathematics #Proofs #LearningInPublic
https://cortexdrifter.blogspot.com/2026/04/a-small-taste-from-my-new-book-season-2_17.html
In Math, Rigor Is Vital. But Are Digitized Proofs Taking It Too Far?
#HackerNews #Math #Rigor #Digitized #Proofs #Mathematics #Education #Digital #Innovations
"How do we balance the creativity needed to discover new mathematical connections with the rigor needed to ensure that every logical step is undeniable?"
@urlyman Others might hold that there is a confluence between the limits of Algorithmic Information; the modelling of digital and analogue processes and Information Algorithms; the reasons for the effective and beneficial processing of properties states. With no proof, are LLMs and quantum computers not just the projection and gaslighting of abstract relations and the reductionist predication of presuppositions? #Models #Proofs #Algorithms #Information #QuantumComputers #LLM #PhilosophyOfAlgorithms
Phew, managed to read through the proofs of an article today. Was a bit tight, only had 15 mins of working time left. It always tends to take longer than expected.
#proofs #publishing #AcademicChatter #AcademicFedi #manuscript #science #research
Blocked by person refusing to believe a #Mathematics #textbook and #proofs because of a random #Wikipedia article that doesn't cite any Maths textbooks, and in fact has proofs in it that actually contradict the conclusion! (the series 0.1, 0.01, 0.001, 0.0001,... never reaches zero, even as the series approaches infinity - it's a hyperbola with an asymptote of 0 - which you think would be self-evident, and yet here we are) Welcome to the #disinformation age! 😡
Lies, Damned Lies and Proofs: Formal Methods Are Not Slopless
#HackerNews #Lies #Damned #Lies #Formal #Methods #Proofs #Technology
