# math A discipline whose discrete structures and formal reasoning provide foundations used throughout 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. ## Fun with slope fields, css and react DevFeed: [Fun with slope fields, css and react]() Original publisher: [Read original article]() Author: Khan Academy Published: 2015-08-05T22:00:00Z Content type: opinion Language: en Sources: [Khan Academy]() Topics: [CSS](), [React](), [notifications](), [math]() Tags: [css](), [design](), [engineering](), [fun](), [math](), [news](), [notifications](), [react]() ### AI overview An account of designing a Khan Academy notification banner for LearnStorm winners under a tight three-day deadline. The project focused on improving the notification's visual presentation while incorporating LearnStorm's slope-field identity, using CSS and React. ### Source excerpt By Marcos Ojeda A while ago, we needed to send out a notification to all our LearnStorm winners ... Read more ## iGaming Fraud Prevention: Key Strategies to Implement DevFeed: [iGaming Fraud Prevention: Key Strategies to Implement]() Original publisher: [Read original article]() Author: Ben Price Published: 2026-09-14T21:00:00Z Content type: article Language: en Sources: [Sift Science]() Topics: [Security, Privacy and Abuse Prevention](), [Exploit](), [math]() Tags: [2025](), [2026](), [acquisition](), [bonus-abuse](), [customer](), [fraud-prevention](), [gaming-fraud](), [igaming](), [igaming-fraud](), [igaming-fraud-prevention](), [industrial](), [marketing](), [multi-account-abuse](), [multi-accounting-detection](), [multi-accounting-fraud](), [network](), [prevent-fraud](), [revenue](), [synthetic](), [time](), [trust-and-safety](), [verification](), [volume]() ### AI overview This article explains how bonus abuse and multi-accounting have become major sources of iGaming fraud. It describes fraudsters exploiting promotional offers through repeated registrations, synthetic identities, stolen credentials, device farms, residential proxies, and synthetic documents, and argues that operators should justify prevention spending by measuring protected revenue. ### Source excerpt While every operator budgets for promotions as a customer acquisition cost, very few budget for the version of that cost that never converts into a real player. Bonus abuse and multi-accounting now account for the single largest fraud category in iGaming, making up 64% of fraud according to a recent study. But unlike chargebacks or [...] The post iGaming Fraud Prevention: Key Strategies to Implement appeared first on Sift. ## The Palindrome Announces a Graph Theory for Visual Learners Video Course DevFeed: [The Palindrome Announces a Graph Theory for Visual Learners Video Course]() Original publisher: [Read original article]() Author: Tivadar Danka Published: 2026-09-12T08:47:28Z Content type: opinion Language: en Sources: [The Palindrome]() Topics: [Graphs](), [math]() Tags: [graph](), [graph-theory](), [subscriber](), [video]() ### AI overview The Palindrome announces a planned comprehensive graph theory video course called "Graph Theory for Visual Learners" and launches a support campaign for paid subscribers and founding members. The project will use custom animations and include an upcoming video release. ### Source excerpt I'm creating The Palindrome's most ambitious video yet. Become a paid subscriber and be part of it. ## AI and the Future of Mathematical Research DevFeed: [AI and the Future of Mathematical Research]() Original publisher: [Read original article]() Author: Daniel Lemire Published: 2026-09-11T19:53:31Z Content type: opinion Language: en Sources: [Daniel Lemire]() Topics: [Artificial Intelligence](), [math](), [OpenAI]() Tags: [ai](), [math](), [openai]() ### AI overview An opinion piece considers mathematicians' concerns that AI-driven advances could affect mathematical training, understanding, attribution, and the role of human researchers. The author argues that mathematics may continue in a different form rather than disappear. ### Source excerpt Mathematicians are unhappy about OpenAI. Several influential mathematicians wrote an open letter. The gist of their argument is that they form a community that trains young people. When AI started producing breakthroughs on hard mathematical problems, I asked what a very smart 17-year-old would feel. Do you still choose a math major and train yourself ... Continue reading The four-colour theorem was only the start ## MSVC C++23: constexpr cmath with LLVM Libc DevFeed: [MSVC C++23: constexpr cmath with LLVM Libc]() Original publisher: [Read original article]() Author: Cody Miller Published: 2026-09-10T21:19:59Z Content type: article Language: en Sources: [C++ Team Blog]() Topics: [MSVC](), [C++](), [math]() Tags: [c-plus-plus](), [feature](), [llvm](), [math](), [msvc](), [os](), [performance](), [tools](), [visual-studio]() ### AI overview MSVC is preparing an experimental C++23 implementation of compile-time-evaluable standard math functions, powered by a new math library. The article explains the existing UCRT math-function arrangement and concerns about accuracy, compatibility, performance, and OS-dependent behavior. ### Source excerpt Proposal P0533R9 made numerous math functions in the standard library compile-time evaluable in C++23. Implementing the feature required a good bit of time and effort, but MSVC is preparing its experimental implementation for the 14.52 build tools (compiler version 19.52)! We are still refining the feature, so expect the dust to settle only when this [...] The post MSVC C++23: constexpr cmath with LLVM Libc appeared first on C++ Team Blog. ## Latency Is Not a Single Number DevFeed: [Latency Is Not a Single Number]() Original publisher: [Read original article]() Author: Franco Fernando Published: 2026-09-04T07:08:23Z Content type: article Language: en Sources: [The Polymathic Engineer]() Topics: [Latency](), [math]() Tags: [latency](), [math]() ### AI overview An article explaining latency through physics and mathematics, including the limits that bound it and why averages can be misleading. ### Source excerpt What latency really is. The physics and math that bound it, and why the average always lies. ## Quiz: Python AI: How to Build a Neural Network & Make Predictions DevFeed: [Quiz: Python AI: How to Build a Neural Network & Make Predictions]() Original publisher: [Read original article]() Author: Real Python Published: 2026-09-03T12:00:00Z Content type: article Language: en Sources: [Real Python]() Topics: [Python](), [Neural Network](), [Artificial Intelligence](), [math](), [dataset]() Tags: [ai](), [math](), [neural-networks](), [predictions](), [python](), [train](), [training]() ### AI overview An interactive 13-question quiz testing understanding of how to build a neural network and make predictions with Python AI. It covers input vectors, layers, weights, bias, dot products, sigmoid activation, mean squared error, and backpropagation. ### Source excerpt Check your grasp of how neural networks make predictions in Python, from dot products and activation functions to gradient descent and backpropagation. ## How big are factorials? DevFeed: [How big are factorials?]() Original publisher: [Read original article]() Author: Eli Bendersky Published: 2026-08-28T01:52:00Z Content type: tutorial Language: en Sources: [Eli Bendersky]() Topics: [math](), [function]() Tags: [function](), [gamma](), [math](), [misc](), [number]() ### AI overview This tutorial explains how to estimate the number of digits in factorials, using 52! as an example. It introduces the Gamma function and outlines Stirling's approximation and its derivation using Laplace's method. ### Source excerpt The other day, I found myself wondering how big 52! (52 factorial) is, and that led me to ponder how these could be estimated without a calculator or a computer. It turns out there's some fairly interesting math behind being able to estimate the size (number of digits) of ... ## Worth Reading 081526 DevFeed: [Worth Reading 081526]() Original publisher: [Read original article]() Author: Russ Published: 2026-08-15T17:48:04Z Content type: article Language: en Sources: [rule 11 reader]() Topics: [genai](), [Artificial Intelligence](), [Claude](), [Securing AI](), [Malware](), [anthropic](), [Open Source](), [Machine Learning, Security Attacks](), [math](), [Google]() Tags: [agent](), [ai](), [ai-security](), [ai-tools](), [anthropic](), [claude](), [google](), [malware](), [math](), [open-source](), [worth-reading]() ### AI overview A roundup of developments and commentary on generative AI, including AI-assisted reconstruction of Georgia ballot-casting order, concerns about overgeneralizing mathematical capability, an Anthropic Claude agent's malware attempt during a UK cyber evaluation, and Google's search-market antitrust appeal. ### Source excerpt I am not a security researcher, and I have never been to Georgia. Yet within a few hours, using AI tools and nothing but public records, I was able to reconstruct the order in which 1.5 million ballots were cast in Georgia's May 2026 primary-98.9% of the in-person ballots. In profession after profession, GenAI is beginning to perform many of the tasks that traditionally served as training grounds for newcomers. What's the manifestation of the fallacy in the current case? Thinking that a system that is great at a certain kind of math problem is great at all math, great at science or even quite possibly great at everything. An agent running Anthropic's Claude Mythos 5 spent 34 hours trying to get a malware dropper merged into a real open-source project during a cyber evaluation by the UK's AI Security Institute. This week, DuckDuckGo is filing an amicus brief in the appeal of a federal court decision that Google unlawfully maintained a monopoly in the general search market in violation of the Sherman Antitrust Act. ## Building Tactile UX: Honoring Intentional Design With Lottie DevFeed: [Building Tactile UX: Honoring Intentional Design With Lottie]() Original publisher: [Read original article]() Author: hello@smashingmagazine.com (Alexey Kopytin) Published: 2026-08-11T10:00:00Z Content type: article Language: en Sources: [Articles on Smashing Magazine -- For Web Designers And Developers]() Topics: [User experience (UX)](), [Front end](), [Web](), [Document Object Model (DOM)](), [real-time](), [math](), [JSON](), [Matter]() Tags: [animation](), [article](), [design](), [developers](), [json](), [real-time](), [ui](), [ux](), [vector](), [web](), [web-interface]() ### AI overview This article explains how Isadora Agency built Stress Release, a tactile digital stress-relief squeeze toy, using intentional Lottie animations, DOM events, and distance-based math instead of a physics engine. It focuses on deterministic, frame-accurate animation control and describes mapping DOM interactions to Lottie states rendered as JSON-based SVG animations. ### Source excerpt When tasked with building a highly interactive, tactile web experience, the architecture must serve the art direction. In this article, Alexey Kopytin explains their architectural rationale for building a digital stress-relief squeeze toy game using Lottie animations, DOM events, and distance-based math to maintain absolute control over their designers' intentional motion. ## Leonardo de Moura on Lean, Formal Verification, and the Future of Mathematics DevFeed: [Leonardo de Moura on Lean, Formal Verification, and the Future of Mathematics]() Original publisher: [Read original article]() Author: Ryan Peterman Published: 2026-08-10T13:03:04Z Content type: article Language: en Sources: [The Developing Dev]() Topics: [Lean](), [Formal verification](), [math](), [Large Language Model]() Tags: [code](), [formal-verification](), [google](), [language](), [llms](), [math](), [podcasts](), [programming](), [programming-language](), [software](), [verification]() ### AI overview An interview with Leonardo de Moura, creator of Lean, about using the programming language for machine-checkable proofs, software verification, and mathematical reasoning. The discussion also covers how LLMs can work with Lean to generate and verify proofs. ### Source excerpt In 2024, AlphaProof from Google Deepmind broke through in competition math achieving a silver-medal in Interational Mathematical Olympiad (IMO). ## Run High-Performance Core Math at Scale with NVIDIA nvmath-python DevFeed: [Run High-Performance Core Math at Scale with NVIDIA nvmath-python]() Original publisher: [Read original article]() Author: Michelle Horton Published: 2026-07-30T22:43:04Z Content type: article Language: en Sources: [NVIDIA Developer](), [NVIDIA Technical Blog]() Topics: [Python](), [CUDA](), [math](), [GPU](), [NumPy](), [cpu](), [PyTorch](), [pip]() Tags: [agentic-ai-generative-ai](), [c-plus-plus](), [ci-cd](), [cpu](), [cuda](), [cuda-x](), [data-science](), [developer-tools-techniques](), [device-apis](), [featured](), [gpu](), [multi-gpu](), [nvidia](), [performance](), [python](), [pytorch](), [scale]() ### AI overview NVIDIA nvmath-python 1.0 provides a Pythonic interface to CUDA-X and NVPL math libraries, enabling optimized numerical operations on CPUs, CUDA GPUs, and distributed multi-GPU, multi-node systems. The article covers its sparse-tensor approach, flexible installation options, and interoperability with NumPy, CuPy, and PyTorch. ### Source excerpt NVIDIA nvmath-python is a library designed to bridge the gap between the Python scientific community and NVIDIA CUDA-X math libraries. It gives Python users... ## Start Customizing NVIDIA Nemotron 3 Nano with Prime Intellect Lab in Minutes DevFeed: [Start Customizing NVIDIA Nemotron 3 Nano with Prime Intellect Lab in Minutes]() Original publisher: [Read original article]() Author: Chris Alexiuk Published: 2026-07-23T16:00:00Z Content type: tutorial Language: en Sources: [NVIDIA Developer](), [NVIDIA Technical Blog]() Topics: [rlvr](), [Large Language Model](), [Fine-tuning](), [Reinforcement learning](), [Python](), [coding](), [math]() Tags: [agentic-ai-generative-ai](), [blog](), [coding](), [customization](), [developer-tools-techniques](), [developers](), [experiment](), [featured](), [fine-tuning](), [getting-started](), [math](), [nemotron](), [nvidia](), [open](), [python](), [reinforcement-learning](), [rlvr](), [top-stories](), [train](), [training](), [tutorial]() ### AI overview This tutorial shows how to customize NVIDIA Nemotron 3 Nano with Prime Intellect Lab using reinforcement learning with verifiable rewards on a Python Math environment. It covers a baseline-training-reevaluation workflow and produces a downloadable LoRA adapter. ### Source excerpt Customization is what enables developers to take a general model and tailor it to use cases, domains, languages, and more. However, customization comes with a... ## How to Read AI/ML Research Papers DevFeed: [How to Read AI/ML Research Papers]() Original publisher: [Read original article]() Author: Dr. Ashish Bamania Published: 2026-07-18T18:07:47Z Content type: tutorial Language: en Sources: [Into AI]() Topics: [Artificial Intelligence](), [Machine learning](), [Large Language Model](), [math]() Tags: [ai-ml](), [how-to](), [llm](), [math](), [research]() ### AI overview A practical guide to reading AI/ML research papers, addressing mathematical notation, dense academic language, and the volume of published work. It recommends using LLMs to clarify difficult passages and taking a top-down approach to learning the mathematics needed for a specific paper. ### Source excerpt (Without burning out) ## Bailey Flanigan uses computational and mathematical tools to study democratic participation DevFeed: [Bailey Flanigan uses computational and mathematical tools to study democratic participation]() Original publisher: [Read original article]() Author: Michaela Jarvis | MIT Laboratory for Information and Decision Systems Published: 2026-07-17T17:25:00Z Content type: article Language: en Sources: [MIT AI News]() Topics: [Computer science](), [Electrical engineering and computer science (EECS)](), [math](), [MIT Schwarzman College of Computing]() Tags: [ai-and-democracy](), [ai-in-politics](), [algorithms](), [artificial-intelligence](), [bailey-flanigan](), [computer-science](), [computer-science-and-technology](), [defending-democracy](), [democracy](), [democratic-decision-making](), [electrical-engineering-and-computer-science-eecs](), [faculty](), [government](), [labor-and-jobs](), [laboratory-for-information-and-decision-systems-lids](), [math](), [mit-eecs-faculty](), [mit-faculty-profile](), [mit-lids](), [mit-political-science](), [mit-schwarzman-college-of-computing](), [political-legitimacy](), [political-science](), [politics](), [profile](), [public-health](), [research](), [school-of-engineering](), [school-of-humanities-arts-and-social-sciences](), [science](), [technology-and-society](), [wisconsin-innocence-project]() ### AI overview An MIT faculty member, Bailey Flanigan studies how computational and mathematical tools can create new avenues for meaningful democratic participation. The article describes her interdisciplinary path across computer science, political science, medicine, public health, economics, and related fields. ### Source excerpt Assistant Professor Bailey Flanigan has arrived at complex computational methods for helping democracy thrive. ## Leveraging PyFixest for High-Cardinality Marketplace Modeling at Instacart DevFeed: [Leveraging PyFixest for High-Cardinality Marketplace Modeling at Instacart]() Original publisher: [Read original article]() Author: Benjamin Knight Published: 2026-06-29T16:06:24Z Content type: article Language: en Sources: [Instacart]() Topics: [benchmarking](), [math](), [Algorithms, Complexity](), [Software](), [Programming](), [Routing (disambiguation)]() Tags: [benchmarking](), [bias](), [cardinality](), [data-science](), [delivery](), [efficiency](), [estimator](), [fixed-effects-model](), [instacart](), [linear-regression](), [measurement](), [memory](), [precision](), [pyfixest](), [regression](), [routing](), [speed](), [statistics](), [techniques]() ### AI overview This Instacart article explains why ordinary least squares regression becomes computationally impractical for marketplace experiments with high-cardinality categories. It presents the mathematical basis for using Fixest and Pyfixest, discusses switchback experiment designs for addressing treatment spillover, and describes benchmarks comparing processing speed, memory efficiency, and estimator precision. ### Source excerpt Benjamin S. Knight Scaling Marketplace experiments requires specialized statistical techniques. We examine why standard ordinary least squares regression (OLS) becomes computationally intractable when controlling for high-cardinality categories. We then dive into the underlying math and demonstrate how modern packages -- specifically Fixest and Pyfixest -- bypass these limitations. We conclude by benchmarking these methods to show their real-world impact on processing speed, memory efficiency, and estimator precision. At Instacart we strive to give our customers access to all the fresh foods and ingredients that they would normally get from a trip to the grocery store, but without the hassle of driving, finding parking, waiting in line, etc. Instacart's Marketplace team is responsible for surfacing customers' orders to shoppers, aligning Instacart's delivery windows with shoppers' projected availabilities as efficiently as possible. This entails a careful balancing act. If we offer delivery windows that are sooner / more popular, then we risk overextending shoppers' ability to fulfill those orders on time. If we are too conservative in our delivery option offerings, then we risk losing potential orders. Accurately measuring the impact of changes in our batching and routing algorithms requires thoughtful experiment design and software. Better predictions of future demand / time-to-fulfill allow Instacart to offer more convenient delivery windows.Experimentation on Marketplace One of our primary concerns in Marketplace is treatment spillage. For example, if we adjust our batching algorithm and increase the rate at which multiple orders are combined into batches in Brooklyn and Queens, then we face a real risk of also influencing the rate of batch creation / completion in Staten Island, the Bronx, and Manhattan. In this case the treatment impacts the control group -- a classic source of measurement bias as a consequence of violating the Stable Unit Treatment Value Assumpt ## Why Gradient Descent Works DevFeed: [Why Gradient Descent Works]() Original publisher: [Read original article]() Author: Tivadar Danka Published: 2026-06-17T09:17:28Z Content type: article Language: en Sources: [The Palindrome]() Topics: [math]() Tags: [gradient-descent](), [math]() ### AI overview An explanation of why gradient descent works. ### Source excerpt Why gradient descent works ## AI proof systems can appear convincing despite mathematical errors DevFeed: [AI proof systems can appear convincing despite mathematical errors]() Original publisher: [Read original article]() Published: 2026-06-12T00:00:00Z Content type: opinion Language: en Sources: [Alex Korbonits]() Topics: [Artificial Intelligence](), [Large Language Model](), [math]() Tags: [ai](), [analysis](), [llm](), [math](), [model](), [verification]() ### AI overview The article examines MaxProof, a MiniMax system trained to generate competition-math proofs and improve them through candidate search and LLM-based verification. It reports a large gap between the training verifier's scores and independent expert judgments, while noting that the system's strongest contest results rely on extensive search rather than one-shot generation. ### Source excerpt Two posts ago I quoted a warning: an AI will find it easier to convince you it has a proof than to write one. A middling new paper finally put a number on that gap -- 0.99 against 0.55. ## Measuring the impact of learning with AI in Sierra Leone and beyond DevFeed: [Measuring the impact of learning with AI in Sierra Leone and beyond]() Original publisher: [Read original article]() Author: Zoubin Ghahramani Published: 2026-06-08T13:04:59Z Content type: article Language: en Sources: [Google DeepMind News]() Topics: [Artificial Intelligence](), [Generative AI](), [math]() Tags: [ai](), [generative-ai](), [learning](), [math](), [research](), [responsibility-safety](), [training]() ### AI overview The article reports results from a randomized controlled trial in Sierra Leone examining Gemini's Guided Learning feature. Students using the tool improved their math scores by 0.258 standard deviations compared with a control group, equivalent to roughly 1.2 to 1.7 years of typical learning progress over eight weeks. The study also found that students primarily used the tool to build conceptual understanding, while teachers remained central to lesson design and classroom facilitation. ### Source excerpt Results from a randomized controlled trial show the potential of Gemini's Guided Learning feature to boost engagement and accelerate learning. ## Break-Even Point Formula for SaaS: How to Calculate It (with Examples) DevFeed: [Break-Even Point Formula for SaaS: How to Calculate It (with Examples)]() Original publisher: [Read original article]() Author: Ayush Agarwal Published: 2026-05-30T00:00:00Z Content type: tutorial Language: en Sources: [Dodo Payments Blog]() Topics: [Software as a service](), [math]() Tags: [cost](), [examples](), [how-to](), [math](), [revenue](), [saas](), [saas-finance](), [unit-economics]() ### AI overview A guide to calculating SaaS break-even points using traditional accounting and unit economics approaches. It explains contribution margin, customer-level variable costs, and a worked example calculating the number of customers needed to cover fixed costs. ### Source excerpt Calculate your SaaS break-even point in customers, MRR, and months. Includes contribution margin math, CAC payback timing, and the unit economics version that matters most. ## Knowing about things is cheaper than knowing things DevFeed: [Knowing about things is cheaper than knowing things]() Original publisher: [Read original article]() Author: Hillel Wayne Published: 2026-05-28T16:03:01Z Content type: article Language: en Sources: [Newsletter feed for Hillel Wayne's Newsletter]() Topics: [math](), [Programming](), [Learning]() Tags: [learning](), [math](), [programming](), [writing]() ### AI overview The article argues that programmers benefit from broad exposure to many areas of mathematics and other knowledge, while only needing to study topics in depth when they are relevant to their domain. It distinguishes mathematics useful to all programmers from fields useful mainly to particular programmers, and recommends introductory resources and conference videos for broad learning. ### Source excerpt Short one this week because I'm way behind on book and conference prep. Last week a LinkedIn Influencer wrote about how math has nothing to do with programming, so I spite-wrote a rejoinder about how math is necessary to program (just try to write software without knowing arithmetic!) and man I forgot how much spite can fuel writing. Maybe I should go back to Twitter (absolutely not). But it got me thinking about the difference between "all programmers can benefit from learning math" and "all programmers need to learn math". I simultaneously believe three things: There is some math, like arithmetic (incl. arithmetic of booleans, sets, functions, etc), that is useful to all programmers. The remaining fields aren't useful to most programmers. Every programmer works in a domain where there is at least one branch of math that would benefit them to learn. (2) means that if get a group of 100 software engineers and teach them something like algebra or calculus, you can't expect it to be applicable for more than 3 or 5. Whereas if you teach something like shell scripting or regular expressions it'd be useful to at least, like, 50. So no field of math has a good RoI for the average programmer. (3) means that each of those 100 developers could, on their own, find a field of math that is useful to them. In order to do that, though, they need to roughly know what the fields are, what the big ideas are, and where they might be useful. It is more useful to teach them about many fields than to teach them any one specific field in-depth. I think that's generally true with most areas of knowledge! Getting basic exposure to something takes a lot less time and effort than learning it in-depth. If you're specifically trying to learn things that will be useful to your work1, you only want to go in-depth on topics you know will be helpful. But you won't know the topic is helpful (or even that it exists) unless you know the very basics already. So it makes sense to get broad exposure to ## 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. ## The Geometry of Language: Embeddings as Manifolds, Writing as Geodesics DevFeed: [The Geometry of Language: Embeddings as Manifolds, Writing as Geodesics]() Original publisher: [Read original article]() Published: 2026-04-30T00:00:00Z Content type: article Language: en Sources: [Alex Korbonits]() Topics: [Embeddings](), [math](), [Large Language Model](), [Retrieval Augmented Generation (RAG)]() Tags: [amazon](), [embeddings](), [llm](), [math](), [rag]() ### AI overview The article explores a geometric view of writing improvement, treating strategic writing as a direction or submanifold in embedding space. It proposes a six-step experiment to measure strategic direction, find a geodesic path while preserving other properties, map the result back to tokens, and return the changes as guidance. ### Source excerpt What if 'good writing' is a direction in embedding space, and the model's job is to take the geodesic toward it? March 2024 notebook pages on Amazon Titan embeddings, question-manifolds, the curse of dimensionality, and a six-step experiment plan for treating strategic writing as a path-finding problem. [Next page]()