# Mathematics Mathematics is a discipline whose discrete methods are used in computer science. This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles. ## Quoting Terence Tao DevFeed: [Quoting Terence Tao]() Original publisher: [Read original article]() Author: Simon Willison Published: 2026-09-09T00:20:17Z Content type: opinion Language: en Sources: [Simon Willison's Weblog]() Topics: [ai-ethics](), [Mathematics](), [Artificial Intelligence]() Tags: [ai](), [ai-2-236](), [ai-ethics](), [ai-ethics-343](), [ethics](), [mathematics](), [mathematics-22]() ### AI overview The article quotes Terence Tao on the risk that AI-powered efforts could rapidly exhaust promising open mathematical problems after even rumors of active research become public. It argues that these incentives may discourage researchers from sharing directions openly, potentially harming long-standing traditions of open science and the future of the field. ### Source excerpt I wrote recently about how the collection of good, fruitful open problems is now being mined in a non-renewable fashion, leading to the potential scenario of these problems becoming scarce. [...] We have now seen that even the rumor of someone working on a problem can trigger a massive amount of AI-powered effort to flatten it before the original research project has time to reach its full potential. The incentives may now be pointing in the direction of no longer sharing any promising research directions with the broader community, which would reverse centuries of traditions of open science and do serious long-term damage to the future of the field. -- Terence Tao Tags: ai-ethics, mathematics, ai ## Some thoughts on the Navier-Stokes Millennium Prize Problem DevFeed: [Some thoughts on the Navier-Stokes Millennium Prize Problem]() Original publisher: [Read original article]() Author: Simon Willison Published: 2026-09-08T23:55:12Z Content type: opinion Language: en Sources: [Simon Willison](), [Simon Willison's Weblog]() Topics: [OpenAI](), [Mathematics](), [Claude](), [codex](), [Math and Logic](), [Lean]() Tags: [agents](), [ai](), [ai-2-235](), [ai-ethics](), [ai-ethics-342](), [claude](), [codex](), [generative-ai](), [generative-ai-1-981](), [llms](), [llms-1-947](), [mathematics](), [mathematics-22](), [openai](), [openai-463](), [paper](), [training-data](), [training-data-68]() ### AI overview This commentary examines OpenAI's reported resolution of the Navier-Stokes existence and smoothness problem with an unreleased model, alongside accusations that the effort may have drawn on information from related work by mathematicians using Claude and Codex. It also describes questions about timing, data access, authorship, and OpenAI's subsequent use of agents and Lean formalization. ### Source excerpt On the Navier-Stokes Millennium Prize Problem introduces an impressive result from OpenAI, who used an unreleased model to produce a resolution to the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize Problems that have been subject to a $1,000,000 prize since May 24th, 2000. The discovery is somewhat overshadowed by accusations of skulduggery from Tristan Buckmaster, an NYU mathematics professor who was collaborating on related problems with Levent Alpöge, an accomplished mathematician who currently works for Anthropic. Tristan's complaint accompanied a hastily published version of their own results. Here's the PDF describing what happened. The very short version is that Tristan and Levent worked on the problem for almost a year, making extensive use of Claude and Codex (mainly GPT-5.6 Sol), then had a breakthrough on August 15th. The mathematical rumour mill kicked into gear and Tristan and Levent heard that OpenAI had heard that Anthropic had resolved "a major open problem", so they reached out and learned that OpenAI had a team working on a related problem, with a similar approach. Quoting Tristan: I asked when the first prompt had been sent by them. This question was not answered directly by OpenAI for some time. Eventually it was agreed that it had been sent in the past few days, after information about our work had reached OpenAI. I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer. It gets more complicated from there. The OpenAI team offered to wait for Tristan to publish, or to have him author a paper about their result, but were clear that Levent would not be invited as a co-author due to OpenAI's competitive relationship with his employer. Here's how OpenAI described their work: On Tuesday, September 1, we h ## OpenAI's Claimed Navier-Stokes Result Covered Alternatives Fefferman Included in the Official Problem DevFeed: [OpenAI's Claimed Navier-Stokes Result Covered Alternatives Fefferman Included in the Official Problem]() Original publisher: [Read original article]() Published: 2026-09-08T00:00:00Z Content type: opinion Language: en Sources: [Alex Korbonits]() Topics: [OpenAI](), [Mathematics](), [Math and Logic]() Tags: [mathematics](), [openai](), [statement]() ### AI overview The article argues that OpenAI did not prove the standard Navier-Stokes existence and smoothness problem, but did prove alternatives (C) and (D) included in Charles Fefferman's official 2000 problem statement. It distinguishes that result from the unresolved alternatives (A) and (B), which concern existence and smoothness on ℝ³ and the torus with zero force. ### Source excerpt OpenAI did not prove Navier-Stokes, and it also did not solve the wrong problem. It proved alternatives (C) and (D), which Fefferman put in the official statement on purpose in 2000, using theorem statements DeepMind had already written. ## Why Two Similar Compiler Cases Cannot Share One Calling Convention DevFeed: [Why Two Similar Compiler Cases Cannot Share One Calling Convention]() Original publisher: [Read original article]() Author: Brendan Sechter Published: 2026-08-07T09:00:00Z Content type: article Language: en Sources: [Brendan A R Sechter's Development Blog]() Topics: [Compiler](), [interface](), [Back end](), [test](), [Mathematics]() Tags: [article](), [backend](), [case-study](), [class](), [compiler](), [compilers](), [engineering](), [interface](), [mathematics](), [measurement](), [verification]() ### AI overview This compiler backend case study argues that two similar cases cannot be unified when one must report two values through an interface with only one available slot. A counting argument shows that the apparent similarity of nine measured occurrences is irrelevant to the shared interface design. The article also identifies an earlier rule that unnecessarily excluded ten of twenty-four cases. ### Source excerpt A system had grown two ways of doing what looked like one thing. The obvious move was to tidy them into one. The tidying turns out to be impossible, and the reason it is impossible is the reason the two ways exist. The argument that settles it needs no specialist knowledge and fits in a sentence. One of the two cases has two things to report and only one slot to report them in. Whichever thing the slot is given, the other is lost. The other case has only one thing to report, so the single slot is exactly enough. That is a counting argument, it is decided before any code is written, and it is not the argument an engineer reaches for by default. The engineer's instinct is to look at the cases and ask whether they resemble one another. They did. Every one of the nine measured occurrences had exactly the shape that invited the tidy-up, and the measurement encouraged precisely the wrong conclusion. The resemblance was real and it was irrelevant, because the defect was never in the instances. It was in the interface they would have had to share. This article is about that distinction, which is between evidence about members of a class and evidence about the channel the class must pass through. The second dominates the first and is cheaper to check. The article reports the measurement, the way the measurement pointed the wrong direction, and the argument that settled it. It also reports a rule this author shipped one increment earlier which turns out to be stricter than the property it enforces, excluding ten of twenty-four cases for no reason. No test found that. It surfaced while gathering data for this article. How to read this The general argument is in the opening, in the section called The Argument That Settled It, and in Pattern Extraction. Those three need nothing but attention. The sections between them work the argument through a real case with real numbers, and they use the vocabulary of the trade. Every term is glossed at first use, but a reader who wants the r ## 1096 Pages of Mathematics and Machine Learning DevFeed: [1096 Pages of Mathematics and Machine Learning]() Original publisher: [Read original article]() Author: Tivadar Danka Published: 2026-07-16T16:38:57Z Content type: opinion Language: en Sources: [The Palindrome]() Topics: [Machine learning](), [Mathematics](), [Learning]() Tags: [essays](), [machine-learning](), [mathematics](), [tutorials]() ### AI overview The author compiled three and a half years of essays, tutorials, and deep dives on mathematics and machine learning into a 1,096-page book. ### Source excerpt I compiled three and a half years of essays, tutorials, and deep dives into a single book ## Towards demystifying the creativity of diffusion models DevFeed: [Towards demystifying the creativity of diffusion models]() Original publisher: [Read original article]() Published: 2026-07-15T18:06:00Z Content type: article Language: en Sources: [The latest research from Google]() Topics: [Generative AI](), [Mathematics](), [Neural Network](), [Algorithms & Theory](), [Training AI Models](), [datasets](), [Google]() Tags: [algorithms-theory](), [data](), [datasets](), [diffusion](), [generation](), [generative-ai](), [google](), [iclr](), [iclr-2026](), [images](), [machine-intelligence](), [model](), [models](), [research](), [retrieval](), [training]() ### AI overview Google Research explains that diffusion models can generate novel data rather than merely memorize training examples. It attributes this creativity to neural networks learning a smoothed score function, which causes denoising to interpolate between training data points along a hidden data manifold. ### Source excerpt Algorithms & Theory ## 3 Questions: Beyond data-driven aesthetics DevFeed: [3 Questions: Beyond data-driven aesthetics]() Original publisher: [Read original article]() Author: School of Architecture and Planning Published: 2026-06-29T18:00:00Z Content type: news Language: en Sources: [MIT AI News]() Topics: [Artificial Intelligence](), [Data visualization](), [Algorithms](), [Mathematics](), [Computer science](), [Machine learning]() Tags: [3-questions](), [aesthetic-judgment](), [ai](), [ai-and-aesthetics](), [alexandros-haridis](), [algorithms](), [alumni-ae](), [applied-arts](), [architecture](), [artificial-intelligence](), [beyond-data-driven-aesthetics](), [computational-aesthetics](), [computer-science-and-technology](), [data](), [data-visualization](), [design](), [design-computation](), [exhibits](), [interactive-installations](), [interview](), [machine-learning](), [mit-architecture](), [mit-exhibits](), [mit-keller-gallery](), [mit-sa-plus-p](), [philosophy](), [research](), [school-of-architecture-and-planning](), [shape-grammars](), [special-events-and-guest-speakers]() ### AI overview An MIT Keller Gallery exhibition by Alexandros Haridis examines the history of aesthetic judgment and creative production in computing, connecting architecture, design computation, algorithms, and machine-learning systems. ### Source excerpt In a new Keller Gallery exhibition, Alexandros Haridis SM '17, PhD '22 traces centuries of ideas about aesthetic judgment and explores how design can make complex computational systems visible. ## Verification Matters When AI Claims to Solve Mathematics Problems DevFeed: [Verification Matters When AI Claims to Solve Mathematics Problems]() Original publisher: [Read original article]() Published: 2026-05-23T00:00:00Z Content type: opinion Language: en Sources: [Alex Korbonits]() Topics: [Artificial Intelligence](), [math](), [OpenAI](), [Mathematics]() Tags: [ai](), [mathematics](), [openai](), [verification]() ### AI overview The article contrasts an unverified OpenAI claim about solving Erdős problems with a later result on the planar unit-distance conjecture that was accompanied by a paper and reviewed by mathematicians. It argues that verification, rather than simply generating proofs, is the central challenge as AI-produced mathematics becomes cheaper. ### Source excerpt An AI disproved one of Erdős's favorite conjectures. The interesting part isn't the proof -- it's who read it, and what happens when nobody can. ## An OpenAI model has disproved a central conjecture in discrete geometry DevFeed: [An OpenAI model has disproved a central conjecture in discrete geometry]() Original publisher: [Read original article]() Published: 2026-05-20T00:00:00Z Content type: article Language: en Sources: [OpenAI News]() Topics: [Artificial Intelligence](), [Mathematics](), [OpenAI](), [math]() Tags: [ai](), [math](), [model](), [models](), [openai](), [reasoning](), [research]() ### AI overview An OpenAI model disproved a longstanding conjecture in the planar unit distance problem, producing an infinite family of examples with a polynomial improvement. External mathematicians checked the proof, which uses ideas from algebraic number theory and represents a milestone for AI-assisted mathematical research. ### Source excerpt An OpenAI model solved the 80-year-old unit distance problem, disproving a major conjecture in discrete geometry and marking a milestone in AI-driven mathematics. ## Five Minutes of Prime Time DevFeed: [Five Minutes of Prime Time]() Original publisher: [Read original article]() Published: 2026-05-16T00:00:00Z Content type: opinion Language: en Sources: [Susam Pal]() Topics: [Mathematics]() Tags: [games](), [mathematics](), [mobile](), [number](), [puzzles](), [rsa]() ### AI overview A personal story about nerd culture at RSA, including mathematics and physics forums, monthly team challenges, and a five-minute contest to write as many prime numbers between 1 and 1000 as possible. ### Source excerpt Let me share a very silly story from roughly 18 years ago! In 2008, I joined RSA, the network security company named after the initials of the inventors of the RSA algorithm, Rivest, Shamir and Adleman, who were also the founders of RSA, the company. There was a bit of a nerd culture in the workplace where topics like prime numbers, combinatorics, probability theory, etc. were discussed fervently. A prime-number employee number was considered a lucky charm. I had a rather nice large five-digit prime number as my employee number, which I remember being quite pleased about. There were internal forums for almost all kinds of topics. A few I remember fondly were a mathematics forum where colleagues would challenge each other with mathematical puzzles and a similar physics forum where, for some reason, crafting contrived paradoxes using special and general relativity and putting them up for debate was a common activity. The participants would analyse each paradox to determine if it truly was one or if it could be resolved into something that was no longer a paradox. I loved hanging out on those forums and made many friends there. The mathematics forum, in particular, gave me plenty of fun problems to think about. In fact, my Langford Pairing (2011) post was the result of a question I had stumbled upon there. The human resources (HR) department used to organise afternoon games once every month where people would self-organise into teams and solve a small challenge. There was a cash prize for the winning team each time. The HR folks were very well aware of the nerd culture and the fascination with prime numbers, but they probably did not know enough about exactly what type of problems we were fascinated with. So in one of the monthly game events, the HR team gave us this challenge. Write as many prime numbers between 1 and 1000 as you can in 5 minutes. The 5-minute timer started immediately. Really, that was the challenge. We all looked at each other in surprise, wondering ## The Problem of Pedagogy in Advanced Mathematics DevFeed: [The Problem of Pedagogy in Advanced Mathematics]() Original publisher: [Read original article]() Published: 2026-05-11T00:00:00Z Content type: opinion Language: en Sources: [Susam Pal]() Topics: [Mathematics](), [Math and Logic]() Tags: [advanced](), [mathematics](), [opinion](), [students](), [theory]() ### AI overview The article argues that pedagogy remains a serious problem in advanced mathematics. It focuses on graduate-level textbooks whose proofs are often presented as high-level outlines, leaving students and even professional mathematicians to reconstruct omitted intermediate steps. It advocates explanations that are correct, complete, and accessible to reasonably motivated students. ### Source excerpt It is a commonly held opinion that educational institutions could do more to improve the pedagogy of mathematics. This is especially applicable to primary and secondary schools, where students are first exposed to mathematics as a formal subject, along with other new subjects. Poor exposition can turn students away from mathematics for a lifetime. Only the highly motivated ones continue to engage with the subject. This is very unfortunate because mathematics is a beautiful subject and it is filled with wonder. It also teaches rigour in reasoning, clarity of thought and the discipline of constructing arguments from first principles to obtain intricate and often beautiful results. What is perhaps less known is that pedagogy is a problem even for graduate-level mathematics students and professional mathematicians. The proofs in many graduate-level mathematics textbooks are, in my humble opinion, not really proofs at all. They are closer to high-level outlines of proofs. The authors simply do not show their work. The student then has to put in an extraordinary amount of effort to understand and justify each line. Sometimes a 10-line argument in a textbook might expand into a 10-page proof if the student really wants to convince themselves that the argument works. I am not a mathematician, but out of personal interest, I have worked with professional mathematicians in the past to help refine notes that explain certain intermediate steps in textbooks (for example, Galois Theory by Stewart, in a specific case). I was surprised to find that it was not just me who found the intermediate steps of certain proofs obscure. Even professional mathematicians who had studied the subject for much of their lives found them obscure. It took us two days of working together to untangle a complicated argument and present it in a way that satisfied three properties: correctness, completeness and accessibility to a reasonably motivated student. There is a reason why jokes like 'proof by obv ## CKKS -- Polynomials, the Canonical Embedding, and Encoding DevFeed: [CKKS -- Polynomials, the Canonical Embedding, and Encoding]() Original publisher: [Read original article]() Published: 2026-04-29T12:25:44Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [homomorphic encryption](), [Cryptography](), [Mathematics](), [Math and Logic]() Tags: [ckks](), [ckks-tutorial](), [cryptography](), [encoding](), [encryption](), [homomorphic-encryption](), [mathematics](), [neural-network](), [polynomial-ring](), [polynomials](), [programming](), [python](), [technical](), [tutorial]() ### AI overview This tutorial introduces the CKKS homomorphic encryption scheme and develops mathematical background on the polynomial ring used in its basic formulation and the canonical embedding used to encode cleartext messages as plaintexts. It also outlines CKKS's history, including its support for approximate arithmetic and later bootstrapping improvements. ### Source excerpt Table of Contents In this tutorial series, I will introduce the CKKS homomorphic encryption scheme from the ground up, in rather intricate detail. Each article in this series corresponds to a pull request on a GitHub repository. The code for this article is in this pull request. Follow along by cloning the repository and checking out the code at the relevant commit. This first article will cover some of the mathematical background necessary in the formulation of the CKKS encryption scheme, specifically the polynomial ring used in the most basic version of CKKS, and the canonical embedding used to encode cleartext messages as plaintexts. ## Deterministic Primality Testing for Limited Bit Width DevFeed: [Deterministic Primality Testing for Limited Bit Width]() Original publisher: [Read original article]() Published: 2026-04-07T13:00:00Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Algorithms](), [C++](), [Mathematics](), [Cryptography](), [homomorphic encryption]() Tags: [algorithm](), [c-plus-plus](), [code](), [cryptography](), [homomorphic-encryption](), [mathematics](), [miller-rabin](), [oeis](), [primes](), [programming](), [randomized-algorithm]() ### AI overview This article explains how to perform deterministic Miller-Rabin primality testing for 32-bit integers. It presents C++ code using the bases 2, 3, 5, and 7, which the article states is deterministic for all 32-bit inputs, and discusses strong pseudoprimes and related research. ### Source excerpt Problem: Determine if a 32-bit number is prime (deterministically) Solution: (in C++) // Bases to test. Using the first 4 prime bases makes the test deterministic // for all 32-bit integers. See https://oeis.org/A014233. int64_t bases[] = {2, 3, 5, 7}; inline int countTrailingZeros(uint64_t n) { if (n == 0) return 64; return __builtin_ctzll(n); } int64_t modularExponentiation(int64_t base, int64_t exponent, int64_t modulus) { int64_t res = 1; int64_t b = base % modulus; int64_t e = exponent; while (e > 0) { if (e & 1) { // Doesn't overflow because we assume 32-bit integer inputs res = (res * b) % modulus; } b = (b * b) % modulus; e >>= 1; } return res; } bool isPrime(int64_t n) { if (n < 2) return false; if (n < 4) return true; if (! ## From games to biology and beyond: 10 years of AlphaGo's impact DevFeed: [From games to biology and beyond: 10 years of AlphaGo's impact]() Original publisher: [Read original article]() Author: Demis Hassabis Published: 2026-03-09T13:52:36Z Content type: article Language: en Sources: [Google DeepMind News]() Topics: [Artificial Intelligence](), [Algorithms](), [Algorithms, Complexity](), [Programming](), [Optimization](), [Open Source](), [Reinforcement learning](), [Language models](), [Mathematics](), [Quantum Computing]() Tags: [ai](), [algorithms](), [code](), [coding](), [data](), [language-models](), [model](), [models](), [open-source](), [optimization](), [quantum-computing](), [reasoning](), [reinforcement-learning](), [research](), [science]() ### AI overview AlphaGo's search-based approach is presented as a catalyst for scientific discovery beyond Go. The article highlights AlphaFold 2's impact on protein-structure prediction, AlphaProof and AlphaGeometry 2's mathematical reasoning, Gemini's performance at the IMO, and AlphaEvolve's use of code search for algorithm discovery and optimization. ### Source excerpt Ten years since AlphaGo, we explore how it is catalyzing scientific discovery and paving a path to AGI. ## Accelerating Mathematical and Scientific Discovery with Gemini Deep Think DevFeed: [Accelerating Mathematical and Scientific Discovery with Gemini Deep Think]() Original publisher: [Read original article]() Author: Thang Luong; Vahab Mirrokni Published: 2026-02-09T16:12:06Z Content type: article Language: en Sources: [Google DeepMind News]() Topics: [Artificial Intelligence](), [Machine Learning & Artificial Intelligence](), [Combinatorial optimization](), [Algorithms](), [Mathematics](), [Optimization](), [Computer science](), [Training AI Models](), [Streams](), [data](), [Network]() Tags: [ai](), [algorithms](), [combinatorial-optimization](), [data](), [gemini](), [optimization](), [physics](), [research](), [science](), [streams](), [training]() ### AI overview An advanced version of Gemini Deep Think helped researchers resolve long-standing problems across algorithms, machine learning optimization, combinatorial optimization, economics, and physics. The article highlights new counterexamples, mathematical explanations for AI training techniques, an extension of an auction theorem to real-valued bids, and a closed-form solution for integrals involving cosmic-string singularities. ### Source excerpt Research papers point to the growing impact of Deep Think across fields ## \[Math\] Intervals: examples of closed intervals DevFeed: [\[Math\] Intervals: examples of closed intervals]() Original publisher: [Read original article]() Published: 2025-12-17T23:00:00Z Content type: article Language: en Sources: [Dennis Yurichev]() Topics: [math](), [Mathematics]() Tags: [examples](), [math]() ### AI overview An examples-focused explanation of closed intervals, including their inclusive notation and uses in mathematics, Wolfram Mathematica, Fortran, algorithms, Unix shell patterns, rounded ratings, and everyday ranges. ### Source excerpt [Math] Intervals: examples of closed intervals ## On the success of 'natural language programming' DevFeed: [On the success of 'natural language programming']() Original publisher: [Read original article]() Author: Marc Brooker Published: 2025-12-16T00:00:00Z Content type: opinion Language: en Sources: [Marc Brooker's Blog](), [Marc Brooker's Blog]() Topics: [Programming](), [Code](), [Protocol (disambiguation)](), [Mathematics](), [Refactoring]() Tags: [algorithms](), [programming](), [reasoning](), [software](), [writing]() ### AI overview The article argues that programming has increasingly become specification: developers describe what software should do while implementation details are hidden behind layers of abstraction. It proposes that natural language may become central to future programming languages, while acknowledging that ambiguity makes natural-language specifications difficult to use precisely. The discussion references bugs in distributed-protocol implementations and argues that formal mathematical and symbolic tools remain powerful for precise reasoning. ### Source excerpt On the success of 'natural language programming' Specifications, in plain speech. I believe that specification is the future of programming. Over the last four decades, we've seen the practice of building programs, and software systems grow closer and closer to the practice of specification. Details of the implementation, from layout in memory and disk, to layout in entire data centers, to algorithm and data structure choice, have become more and more abstract. Most application builders aren't writing frameworks, framework builders aren't building databases, database builders aren't designing protocols, protocol designers aren't writing kernels, and so on. Our modern software world is built on abstractions. Significant advancements are made, from time to time, by cutting through these abstractions. But still, the abstractions dominate, and will continue to. The practice of programming has become closer and closer to the practice of specification. Of crisply writing down what we want programs to do, and what makes them right. The how is less important. I believe that natural language will form the core of the programming languages of the future. The Ambiguity Problem The most common objection to this view is that natural language is ambiguous. It's exact meaning is potentially unclear, and highly dependent on context. This is a real problem. For example, in The Bug in Paxos Made Simple, I look at a common bug in implementations of Paxos caused directly by the ambiguity of natural language. Pointing out this ambiguity isn't criticizing [Lamport's] writing, but rather reminding you about how hard it is to write crisp descriptions of even relatively simple distributed protocols in text. As Lamport says: Prose is not the way to precisely describe algorithms. Perhaps the most famous statement of this problem is Dijkstra's from On the foolishness of "natural language programming": When all is said and told, the "naturalness" with which we use our native tongues boils down ## How Lean Propositions Differ from TypeScript Booleans DevFeed: [How Lean Propositions Differ from TypeScript Booleans]() Original publisher: [Read original article]() Published: 2025-08-16T00:00:00Z Content type: tutorial Language: en Sources: [Dan Abramov]() Topics: [Lean](), [Programming](), [Mathematics](), [Code](), [TypeScript]() Tags: [mathematics](), [programming](), [programming-languages](), [types](), [typescript]() ### AI overview This tutorial compares logical expressions in TypeScript with propositions in Lean. It explains that Lean treats propositions as distinct values and types, and that proving a proposition requires supplying a proof rather than simply computing a Boolean result. ### Source excerpt What is the type of 2 + 2 = 4? ## Book Notes: The Dark Art of Linear Algebra by Seth Braver -- Chapter 1 Review DevFeed: [Book Notes: The Dark Art of Linear Algebra by Seth Braver -- Chapter 1 Review]() Original publisher: [Read original article]() Author: Ruslan Spivak Published: 2025-07-15T14:38:00Z Content type: opinion Language: en Sources: [Ruslan Spivak]() Topics: [Mathematics](), [math]() Tags: [addition](), [arrow](), [blog](), [book](), [mathematics](), [review](), [vector]() ### AI overview A review of Chapter 1 of Seth Braver's The Dark Art of Linear Algebra, focusing on geometric interpretations of vectors, vector addition, subtraction by addition, and the roles of commutativity and associativity. ### Source excerpt "Mathematics is the art of reducing any problem to linear algebra." -- William Stein If you've ever looked at a vector and thought, "Just a column of numbers, right?", this chapter will change that. The Dark Art of Linear Algebra (aka DALA) by Seth Braver opens with one of the ... ## Efficient MultiModal Data Pipeline DevFeed: [Efficient MultiModal Data Pipeline]() Original publisher: [Read original article]() Author: Aritra Roy Gosthipaty; Luis; Andres Marafioti; Sergio Paniego; Pedro Cuenca Published: 2025-07-08T00:00:00Z Content type: article Language: en Sources: [Hugging Face - Blog]() Topics: [multimodal](), [data](), [datasets](), [GPU](), [Mathematics](), [Open Source]() Tags: [artificial-intelligence](), [batching](), [community](), [data](), [data-pipeline](), [gpu](), [hardware](), [multimodal](), [nanovlm](), [open](), [open-source](), [pipeline](), [research](), [vlm]() ### AI overview This article explains how to build an efficient multimodal data pipeline for nanoVLM training. It examines waste caused by idle GPUs and excessive padding, then introduces progressively improved data preparation and batching strategies, including a knapsack-based approach to fit more useful data into each batch. ### Source excerpt We're on a journey to advance and democratize artificial intelligence through open source and open science. ## My Graduate Career in Math DevFeed: [My Graduate Career in Math]() Original publisher: [Read original article]() Published: 2025-05-12T18:35:57Z Content type: opinion Language: en Sources: [Jeremy Kun]() Topics: [Mathematics](), [Computer science](), [graph theory]() Tags: [computer-science](), [education](), [essay](), [essays](), [game-theory](), [graph-theory](), [group-theory](), [linear-algebra](), [math](), [mathematics](), [retrospective](), [topology](), [university]() ### AI overview An autobiographical essay about the author's transition from computer science to mathematics at Cal Poly, including university coursework, study abroad in Budapest, and reflections on the intellectual environment and an early group theory project. ### Source excerpt Editor's note: This essay was originally published on Medium on 2016-03-05. I have made minor edits in this republishing and added a few small retrospective notes. 2010-2011 (Year 0) I had just switched my major at Cal Poly State University from computer science to math. I wanted to double major but California was in a budget crisis and a few weeks before I tried submitting my double-major request the Provost for the CSU system put a blanket ban on double majors. ## Image formats: Color models for humans and devices DevFeed: [Image formats: Color models for humans and devices]() Original publisher: [Read original article]() Author: polina-gurtovaia Published: 2025-05-06T00:00:00Z Content type: article Language: en Sources: [MDN Blog]() Topics: [Web](), [Mathematics]() Tags: [developer](), [devices](), [image](), [images](), [models](), [vision](), [web]() ### AI overview This article introduces a series on the core principles behind image formats and color models. It explains how humans perceive light and color through the eye and brain, and how devices represent and reproduce color across screens. ### Source excerpt Images help bring more color and life to the web. This post describes how images are represented by humans and on different devices, with details about color spaces and vision theory. ## How NuminaMath Won the 1st AIMO Progress Prize DevFeed: [How NuminaMath Won the 1st AIMO Progress Prize]() Original publisher: [Read original article]() Author: Yann Fleureau; LI Jia; Edward Beeching; Lewis Tunstall; Ben Lipkin; Roman Soletskyi; Shengyi Costa Huang; Kashif Rasul Published: 2024-07-11T00:00:00Z Content type: article Language: en Sources: [Hugging Face - Blog]() Topics: [Mathematics](), [Artificial Intelligence](), [Open Source](), [AI Models](), [Fine-tuning](), [hugging face]() Tags: [ai-models](), [ai4math](), [artificial-intelligence](), [blog](), [blog-post](), [community](), [fine-tuning](), [hugging-face](), [leaderboard](), [math](), [maths](), [nlp](), [number-theory](), [open-science-collab](), [open-source](), [research](), [science]() ### AI overview This article introduces the Numina initiative and describes the technical work behind its winning solution for the 2024 AIMO progress prize. It focuses on open development of AI models for mathematical reasoning, including the role of LLM fine-tuning and support from Hugging Face and other organizations. ### Source excerpt We're on a journey to advance and democratize artificial intelligence through open source and open science. ## Fixing the iterative damping interpolation in video games DevFeed: [Fixing the iterative damping interpolation in video games]() Original publisher: [Read original article]() Published: 2024-05-18T12:22:15Z Content type: article Language: en Sources: [The Last Static Blog RSS]() Topics: [Game Development](), [Godot](), [callback](), [function](), [Mathematics]() Tags: [callback](), [fps](), [game](), [game-development](), [games](), [math](), [physics](), [prog]() ### AI overview This article explains why repeatedly applying linear interpolation for damping can make game behavior depend on the refresh rate. Using Godot examples, it analyzes the iterative formula and motivates a frame-rate-independent solution. ### Source excerpt As I'm exploring the fantastic world of indie game development lately, I end up watching a large number of video tutorials on the subject. Even though the quality of the content is pretty variable, I'm very grateful to the creators for it. That being said, I couldn't help noticing this particular bit times and times again: a = lerp(a, B, delta * RATE) Behind this apparent banal call hides a terrible curse, forever perpetrated by innocent souls on the Internet. In this article we will study what it's trying to achieve, how it works, why it's wrong, and then we'll come up with a good solution to the initial problem. The usual warning: I don't have a mathematics or academic background, so the article is addressed at other neanderthals like myself, who managed to understand that pressing keys on a keyboard make pixels turn on and off. What is it? Let's start from the beginning. We're in a game engine main loop callback called at a regular interval (roughly), passing down the time difference from the last call. In Godot engine, it looks like this: func _physics_process(delta: float): ... If the game is configured to refresh at 60 FPS, we can expect this function to be called around 60 times per second with delta = 1/60 = 0.01666.... As a game developer, we want some smooth animations for all kind of transformations. For example, we may want the speed of the player to go down to zero as they release the moving key. We could do that linearly, but to make the stop less brutal and robotic we want to slow down the speed progressively. Linear (top) versus smooth/exponential (bottom) animation Virtually every tutorial will suggest updating some random variable with something like that: velocity = lerp(velocity, 0, delta * RATE) At 60 FPS, a decay RATE defined to 3.5, and an initial velocity of 100, the velocity will go down to 0 following this curve: Example curve of a decaying variable Note velocity is just a variable name example, it can be found in many other contexts If you [Next page]()