# mathematics Published articles for mathematics. 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. ## Updates on HEIR, the homomorphic encryption compiler project DevFeed: [Updates on HEIR, the homomorphic encryption compiler project]() Original publisher: [Read original article]() Published: 2026-09-04T18:53:40Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [homomorphic encryption](), [Compiler](), [Encryption](), [Cryptography](), [Machine learning](), [Inference](), [GitHub](), [bazel](), [Kaggle]() Tags: [bazel](), [ckks](), [compiler](), [cryptography](), [encryption](), [github](), [homomorphic-encryption](), [inference](), [kaggle](), [mathematics](), [ml](), [programming]() ### AI overview This companion article explains HEIR, a homomorphic encryption compiler that converts programs to operate directly on encrypted data. It discusses compiling pre-trained machine-learning models for private inference, describes the repository and setup, and reports an example involving encrypted credit-card fraud detection. ### Source excerpt On 2026-08-14 I published an article on the Google Security blog with an update on HEIR, our homomorphic encryption (HE) compiler. This is a companion article, in which I have no limits on word count or jargon, and I can feel free to be honest. So strap in. Assuming you won't read the linked corporate blog post, HEIR is a compiler that converts an input program to a program that operates directly on encrypted data. ## 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 ## MIT projects selected for funding under US Department of Energy's Genesis Mission DevFeed: [MIT projects selected for funding under US Department of Energy's Genesis Mission]() Original publisher: [Read original article]() Author: Office of the Vice President for Research Published: 2026-07-23T12:00:00Z Content type: news Language: en Sources: [MIT AI News]() Topics: [Artificial Intelligence](), [Supercomputing](), [systems]() Tags: [administration](), [ai](), [artificial-intelligence](), [center-for-computational-science-and-engineering](), [chemical-engineering](), [department-of-energy](), [department-of-energy-doe](), [doe](), [eaps](), [engineering](), [faculty](), [funding](), [genesis](), [genesis-mission](), [industry](), [initiative](), [laboratory-for-nuclear-science](), [manufacturing](), [mathematics](), [mechanical-engineering](), [mission](), [national-security](), [nuclear-science-and-engineering](), [physics](), [plasma-science-and-fusion-center](), [projects](), [quantum](), [quantum-computing](), [quantum-systems](), [research](), [research-laboratory-of-electronics](), [school-of-engineering](), [school-of-science](), [science](), [supercomputing](), [us]() ### AI overview MIT researchers will contribute to 15 collaborative projects selected for funding under Phase I of the U.S. Department of Energy's Genesis Mission. The projects apply AI, supercomputing, quantum systems, and scientific instruments to research areas including energy, materials, fusion, and national security. Funding remains pending completion of award negotiations. ### Source excerpt Initial research projects advance national priorities across natural resources, manufacturing, nuclear physics, and more. ## 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 ## 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. ## 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 (! ## Bicyclic Matrix-Matrix Multiplication in Fully Homomorphic Encryption DevFeed: [Bicyclic Matrix-Matrix Multiplication in Fully Homomorphic Encryption]() Original publisher: [Read original article]() Published: 2025-11-17T16:41:28Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [FHE](), [Encryption](), [Algorithm](), [Code](), [GitHub]() Tags: [algorithm](), [circuit](), [code](), [cryptography](), [encryption](), [fhe](), [github](), [homomorphic-encryption](), [linear-algebra](), [lwe](), [mathematics](), [programming](), [rlwe]() ### AI overview This article explains the bicyclic method for matrix-matrix multiplication in fully homomorphic encryption. It introduces the method's packing scheme, relates it to Halevi-Shoup diagonal packing, and discusses properties including multiplicative depth, layout invariance, and rotation complexity. The implementation is provided in a GitHub repository in a file named bicyclic.py. ### Source excerpt In an earlier article, I covered the basic technique for performing matrix-vector multiplication in fully homomorphic encryption (FHE), known as the Halevi-Shoup diagonal method. This article covers a more recent method for matrix-matrix multiplication known as the bicyclic method. The code implementing this method is in the same GitHub repository as the previous article, and the bicyclic method is in a file called bicyclic.py. The previous article linked above covers the general concepts behind "FHE packing," which I will assume as background knowledge for this article: ## Integer Set Library (ISL) - A Primer DevFeed: [Integer Set Library (ISL) - A Primer]() Original publisher: [Read original article]() Published: 2025-10-19T20:14:22Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Library](), [Optimization](), [compilers](), [Open Source](), [mlir]() Tags: [code](), [compilers](), [isl](), [library](), [loops](), [mathematics](), [mlir](), [open-source](), [optimization](), [polyhedral-optimization](), [programming](), [set-theory]() ### AI overview This primer introduces the Integer Set Library (ISL), an open-source C library that implements core algorithms for polyhedral optimization. It focuses on representing integer sets and relations, manipulating them, and the relationship between ISL and MLIR's Fast Presburger Library. ### Source excerpt Polyhedral optimization is a tool used in compilers for optimizing loop nests. While the major compilers that use this implement polyhedral optimizations from scratch,1 there is a generally-applicable open source C library called the Integer Set Library (ISL) that implements the core algorithms used in polyhedral optimization. This article gives an overview of a subset of ISL, mainly focusing on the representation of sets and relations and basic manipulations on them. ## 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? ## Frequently Asked Questions about FHE DevFeed: [Frequently Asked Questions about FHE]() Original publisher: [Read original article]() Published: 2025-07-18T17:31:49Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [homomorphic encryption](), [FHE](), [Cryptography](), [math](), [GPU](), [Facial recognition](), [Sorting]() Tags: [cryptography](), [encryption](), [facial-recognition](), [fhe](), [gpu](), [homomorphic-encryption](), [mathematics](), [programming]() ### AI overview A collection of short answers about fully homomorphic encryption (FHE), covering encrypted queries, computation on ciphertexts, sorting, performance, and security against quantum computers. The article explains that FHE can support operations on encrypted data without exposing the underlying plaintext, while computational overhead remains a key limitation. ### Source excerpt I work on homomorphic encryption (HE or FHE for "fully" homomorphic encryption) and I have written a lot about it on this blog (see the relevant tag). This article is a collection of short answers to questions I see on various threads and news aggregators discussing FHE. Facts If a service uses FHE and can respond to encrypted queries, can't the service see your query? How is it possible to operate on encrypted data without seeing it? ## 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 ... ## 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. ## Carnival of Mathematics #233 DevFeed: [Carnival of Mathematics #233]() Original publisher: [Read original article]() Published: 2024-11-01T07:00:00Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [math](), [GPU](), [Nvidia](), [clustering](), [Regular expression](), [Python]() Tags: [carnival](), [clustering](), [fibonacci](), [gpu](), [mathematics](), [nvidia](), [python](), [regex]() ### AI overview A roundup of mathematics news and media from October 2022, including a newly reported largest known prime, mathematical research, discussions of political geography and clustering, and videos about voting paradoxes, polylinks, and prime-recognizing regular expressions. ### Source excerpt Welcome to the 233rd Carnival of Mathematics! Who can forget 233, the 6th Fibonacci prime? Hey, not all numbers are interesting. Don't ask me about the smallest positive uninteresting number. You can't make it interesting with your feeble mind tricks! Anyway, on to the fun. Provers and Shakers The big discovery this month was a new largest known prime number, $2^{136279841} - 1$, as reported by the Great Internet Mersenne Prime Search. ## Packing Matrix-Vector Multiplication in Fully Homomorphic Encryption DevFeed: [Packing Matrix-Vector Multiplication in Fully Homomorphic Encryption]() Original publisher: [Read original article]() Published: 2024-09-07T04:18:09Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [homomorphic encryption](), [FHE](), [Encryption](), [layout](), [parallel](), [Python]() Tags: [arithmetic](), [code](), [cryptography](), [data](), [encryption](), [fhe](), [github-repository](), [homomorphic-encryption](), [layout](), [linear-algebra](), [lwe](), [mathematics](), [packing](), [parallel](), [programming](), [python](), [rlwe](), [simd](), [strategies]() ### AI overview This article explains packing for SIMD-style fully homomorphic encryption. It describes how to arrange plaintext data in RLWE ciphertexts so matrix-vector multiplication requires fewer alignment multiplications and rotations, then introduces two basic packing techniques and a computational model. ### Source excerpt In my recent overview of homomorphic encryption, I underemphasized the importance of data layout when working with arithmetic (SIMD-style) homomorphic encryption schemes. In the FHE world, the name given to data layout strategies is called "packing," because it revolves around putting multiple plaintext data into RLWE ciphertexts in carefully-chosen ways that mesh well with the operations you'd like to perform. By "mesh well" I mean it reduces the number of extra multiplications and rotations required merely to align data elements properly, rather than doing the actual computation you care about. ## Converting Between Packings in SIMD-Style FHE DevFeed: [Converting Between Packings in SIMD-Style FHE]() Original publisher: [Read original article]() Published: 2024-09-02T21:01:03Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [FHE](), [homomorphic encryption](), [data](), [Code]() Tags: [compilers](), [encryption](), [fhe](), [github](), [graph-coloring](), [heir](), [homomorphic-encryption](), [mathematics](), [optimization](), [packing](), [permutation](), [programming](), [rlwe](), [simd]() ### AI overview This article explains packing in SIMD-style fully homomorphic encryption and focuses on converting between established packings. It introduces a computational model involving RLWE ciphertext vectors, elementwise operations, cyclic rotations, and differing operation costs. ### Source excerpt In my recent overview of homomorphic encryption, I underemphasized the importance of data layout when working with arithmetic (SIMD-style) homomorphic encryption schemes. In the FHE world, the name given to data layout strategies is called "packing," because it revolves around putting multiple plaintext data into RLWE ciphertexts in carefully-chosen ways that mesh well with the operations you'd like to perform. By "mesh well" I mean it reduces the number of extra multiplications and rotations required merely to align data elements properly, rather than doing the actual computation you care about. ## MLIR -- Defining Patterns with PDLL DevFeed: [MLIR -- Defining Patterns with PDLL]() Original publisher: [Read original article]() Published: 2024-08-04T14:00:00Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [LLVM](), [Tooling]() Tags: [c-plus-plus](), [compilers](), [heir](), [llvm](), [mathematics](), [mlir](), [optimization](), [patterns](), [primer](), [programming](), [tablegen]() ### AI overview A tutorial on using PDLL to define MLIR patterns. It explains PDLL's relationship to PDL, its intended role as an alternative to TableGen pattern definitions, and how PDLL files are transformed into IR and then C++ code for compilation into a pass. ### Source excerpt Table of Contents In this article I'll show how to use PDLL, a tool for defining MLIR patterns, which itself is built with MLIR. PDLL is intended to be a replacement for defining patterns in tablegen, though there are few public examples of its use. In fact, the main impetus for PDLL is that tablegen makes it difficult to express things like: Operations that return multiple results Operations with regions Operations with variadic operands Arithmetic on static values While not all these features are fully supported in PDLL yet, they are within scope of the language and tooling. ## Fully Homomorphic Encryption in Production Systems DevFeed: [Fully Homomorphic Encryption in Production Systems]() Original publisher: [Read original article]() Published: 2024-07-31T07:00:00Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [homomorphic encryption](), [FHE](), [Encryption](), [Cryptography](), [Edge](), [Microsoft](), [iOS](), [Differential Privacy](), [Embeddings](), [clustering](), [Library]() Tags: [apple](), [clustering](), [cryptography](), [differential-privacy](), [embeddings](), [encryption](), [fhe](), [homomorphic-encryption](), [ios](), [library](), [mathematics](), [microsoft-edge](), [programming](), [systems]() ### AI overview A living document catalogs production systems known to use fully or somewhat homomorphic encryption. It describes deployments and techniques involving Microsoft Edge password checking, Apple's Live Caller ID Lookup, and Apple's private image search, while distinguishing FHE from SHE. ### Source excerpt In this living document, I will list all production systems I'm aware of that use fully homomorphic encryption (FHE). For background on FHE, see my overview of the field. If you have any information about production FHE systems not in this list, or corrections to information in this list, please send me an email with sufficient detail allow the claim to be publicly verified. For all production deployments, I will distinguish between cases where the deployed system does "fully" homomorphic encryption (with bootstrapping), aka FHE, and "somewhat" homomorphic encryption, aka SHE (avoiding bootstrapping). ## Ben Recht on Meehl's Philosophical Psychology DevFeed: [Ben Recht on Meehl's Philosophical Psychology]() Original publisher: [Read original article]() Published: 2024-07-27T18:49:42Z Content type: opinion Language: en Sources: [Jeremy Kun]() Topics: [Data Science](), [Math and Logic]() Tags: [blog-posts](), [mathematics](), [philosophy](), [science](), [shortform](), [social-sciences]() ### AI overview A review of Ben Recht's blog series on Paul Meehl's Philosophical Psychology, which examines philosophy of science, scientific debate, and weaknesses in statistical studies in the social sciences. The series also discusses alternatives to relying on conventional hypothesis testing, including historical experimental examples. ### Source excerpt Ben Recht, a computer science professor at UC Berkeley, recently wrapped up a 3-month series of blog posts on Paul Meehl's "Philosophical Psychology." Recht has a table of contents for his blog series. It loosely tracks a set of lectures that Meehl gave in 1989 at the University of Minnesota. In it, he surveys of the philosophy of science, lays out a framework for scientific debate, and critiques scientific practice. Recht summarizes his arguments, simplifies the ideas, provides examples, and offers his own commentary, considering today's computerized world. [Next page]()