How did a fly on the ceiling shape math as we know it? Come explore the coordinate plane, a simple tool with endless applications.| ChemTalk
It’s been a while. Let me finally wrap up this this series! I’ll show you how we can get the periodic table of elements from a quantum field theory of massless spin-1/2 particles. We’ve been studying the hydrogen atom using Schrödinger’s equation, but still taking the electron’s spin into account. This is more realistic than […]| Azimuth
This article, Part 2 of 'The Inward Spiral of Time', deepens the theoretical foundation laid in the first installment by connecting the spiral model of time to the Fibonacci sequence and golden ratio, revealing recurring mathematical and biological patterns that mirror our proposed cognitive and cosmic spiral framework. It ties together concepts from cosmology, human cognition, AI development, and evolutionary dynamics. This work was written in collaboration with Omni Intelligence AI, continu...| Interalia Magazine
The Tensor Coordinate Generator In CuTe| Lei Mao's Log Book
Understanding CuTe Tiled Copy| Lei Mao's Log Book
On June 30, 2025, Mark Brittenham and Susan Hermiller uploaded a preprint to the arXiv called “Unknotting number is not additive under connected sum” (and an updated version on Septembe…| David Richeson: Division by Zero
I’m a great believer in low-tech math. I don’t like to rely on things a computer tells me; what if there’s a bug in the code? I prefer trusting things that I can check for myself. At the same…| mathenchant.wordpress.com
Decorated rock climber Kerry Scott ’18 flexes her Carolina mathematics degree as an elite problem solver at the crag and in her career. The post Reaching new heights appeared first on Carolina Arts & Sciences Magazine.| Carolina Arts & Sciences Magazine
As a member of the Advisory Council for the National Museum of Mathematics (“MoMath”) over the past decade, I’ve had a number of unique opportunities, such as the thrilling chance to improve the Museum’s datebase via my smartphone and watch exhibit-content update in real-time, and the less thrilling opportunity to break an exhibit on the […]|
“I couldn’t help but wonder…” — Carrie Bradshaw (in every episode of Sex and the City) The best birthday party I ever had as a kid was a trip to the Museum of Natural History in New York City with half a dozen like-minded friends and my indulgent parents. The huge dinosaur skeleton in the […]|
If you ask a person on the street whether 1 is a prime number, they’ll probably pause, try to remember what they were taught, and say “no” (or “yes” or “I don’t remember”). Or maybe they’ll cross the street in a hurry. On the other hand, if you ask a mathematician, there’s a good chance […]|
There are mathematical operations of all kinds with the property that doing the operation twice is tantamount to not doing anything at all. Such operations are called involutions, and you can find them all over the place in math: taking the negative of a number, taking the reciprocal of a number, rotating an object by […]|
“No simplicity of mind, no obscurity of station, can escape the universal duty of questioning all that we believe.” — William K. Clifford “Nobody knew math could be so com…| mathenchant.wordpress.com
Fire vs. Water “All things are water,” says Thales. “All things are fire,” says Heraclitus. “Wait,” says David Hume’s Philo. “You both agree that all things are made up of one substance. Thales, you prefer to call it water, and Heraclitus, you prefer to call it fire. But isn’t that merely a verbal dispute? According … Continue reading Fire, Water, and Numbers| Entirely Useless
Fairy tales and other stories occasionally suggest the idea that a name gives some kind of power over the thing named, or at least that one’s problems concerning a thing may be solved by know…| Entirely Useless
A link has been found between autism, high intelligence, and giftedness. Consequently, some came to call autism a “disorder of high intelligence”.| Embrace Autism
Core Concepts In this article, we will introduce the concept of calculus. We will illustrate its origin, founding principles, and potential applications. What is calculus? Calculus is the study of change! More specifically, it’s the process of using math to model changes. Credit is given to both Issac Newton and Gottfried Leibniz who, independently of … Introduction to Calculus Read More » The post Introduction to Calculus appeared first on ChemTalk.| ChemTalk
If you’re looking for preschool math books, you’re in the right place! Math is everywhere, and the best way to introduce it is through math activities for preschoolers and picture books that make learning fun and relatable. Picture books bring math concepts like numbers, shapes, and patterns to life with colorful illustrations and engaging stories,... The post Best Preschool Math Books for Early Learning appeared first on Stay At Home Educator.| Stay At Home Educator
In which I attempt maths and experience regret.| Diagram Monkey
It’s been over three years since my last post on this blog and I have sometimes been asked, understandably, whether the project I announced in my previous post was actually happening. The ans…| Gowers's Weblog
October is here, and with it the crisp fall air here in the northeast US. No matter where you are, you can get a breath of fresh air with some problem solving in your math classes! Here is the 2015…| Reflections and Tangents
CUDA PTX ldmatrix Instruction and Its CuTe Wrapper| Lei Mao's Log Book
Learning times tables doesn’t have to be a battle. With modern teaching approaches backed by cognitive science, children can master multiplication facts while developing genuine mathematical understanding. This comprehensive guide reveals the most effective, research-based strategies for teaching times tables that transform struggling learners into confident mathematicians. Why Traditional Times Tables Methods Fail (And What ... Read more The post The Complete Guide to Teaching Times Tables...| Special Education and Inclusive Learning
Faculty in The University of Tulsa’s Department of Mathematics are creating hands-on research opportunities for undergraduate students through a unique initiative. Professor Richard Redner, Ph.D., and Assistant Professor Nicholas Cox-Steib, Ph.D., have created a research initiative centered on zero-one matrices – binary matrices that while widely applicable in fields such as signal processing, computer science, […]| The University of Tulsa
A collection of simple, hands-on math activities suitable for 2- and 3- year old toddlers and preschoolers. Great for home or preschool.| Childhood101
Gerardus Mercator warped the world to flatten it. He created a conformal map that helped early navigators hold courses of constant bearing across vast oceans.| Galileo Unbound
Is category theory being co-opted? These authors think so: • Esteban Montero and Brandon Baylor, Category theory is being co-opted, Holon Substack, 7 September 2025. Category theory offers a p…| Azimuth
Using Dynamic Technology to Build Understanding ◊ Episode 7: Pythagorean Squares◊ Today is a “perfect square day” since the date is 9-16-25 (or 16-9-25 if you live somewhere that puts the day first…| Reflections and Tangents
When you talk to a large language model (LLM), it feels like the model understands meaning. But under the hood, the system relies on numbers, vectors, and math to find the relationships between words and sentences. One of the most important tools tha...| freeCodeCamp.org
When Turkish courts sentenced crypto exchange founder Faruk Özer to 11,196 years in prison, they created a mathematical anomaly that reveals fascinating patterns about justice, time, and the limitations of human-scale punishment. Join the Atlas Monkey crew as we decode this temporal enigma through the lens of Clockweave's computational justice algorithms.| Seuros Blog - Navigation Logs from the Ruby Nebula
Designing Tilers for Data Access| Lei Mao's Log Book
Science has made great strides in modeling space, time, mass and energy. Yet little attention has been paid to the precise representation of the information ubiquitous in nature. Introduction to Evolutionary Informatics fuses results from complexity modeling and information theory that allow both meaning and design difficulty in nature to be measured in bits. Built on the foundation of a series of Read More ›Source| Books – Discovery Institute
Star Wars Day is here again and it’s a terrific time to integrate Star Wars| Kelly's Classroom Online
Host page for the first Symposium on the Platonic Space| Forms of life, forms of mind
Preschool math printables and simple math activities for preschoolers make it easy to add hands-on learning to your day. These low-prep printables help kids build key math skills in a way that feels fun and natural. You’ll find a collection of free printable math activities for preschoolers, plus ideas for adding play-based learning into your... The post Free Preschool Math Printables appeared first on Stay At Home Educator.| Stay At Home Educator
Preschool math games bring energy and movement into everyday learning, and math activities for preschoolers help little ones build math skills in ways that feel easy and natural. When kids play games, they stay curious and involved, which means they practice skills without feeling pressure. With print-and-go resources and online math games for preschoolers, it’s... The post The Best Free Preschool Math Games appeared first on Stay At Home Educator.| Stay At Home Educator
Does teaching preschool math numbers feel more like work than fun? Let’s flip that around! With the right math activities for preschoolers, learning numbers can be full of giggles and hands-on play. Even worksheets can be fun, because we’ve added a little bit of tracing, some possible coloring, and a whole lot of playdough! Grab... The post Preschool Math Numbers Playdough Mats appeared first on Stay At Home Educator.| Stay At Home Educator
Thomas Bloom’s erdosproblems.com site hosts nearly a thousand questions that originated, or were communicated by, Paul Erdős, as well as the current status of these questions (about a third of which are currently solved). The site is now a couple years old, and has been steadily adding features, the most recent of which has been […]| What's new
Morava, a member of the Hopkins faculty for nearly four decades, remembered for his warmth, brilliance| The Hub
Sometimes, when I write a post about AI, I’ve been sitting on an idea for a long time. I’ve talked to experts, I’ve tried to understand the math, I’ve honed my points and cleared away clutter. This is not one of those times. The ideas in this post almost certainly have something deeply wrong with […]| 4 gravitons
When bad news gets me down, I often get insomnia. I wake up in the middle of the night, start thinking about how we’re all doomed, and can’t easily stop. To break out of these doom loop…| Azimuth
Did you own a personal computer 40 years ago? How many teachers and students had access to computers in 1983. What if I told you that a 400-page book focused on teaching computer programming to children sold more than 100,000 copies way back then? Well, it’s true. Former engineer, elementary school teacher, and member of […] The post Classic Book Now Available Online (free) appeared first on The Daily Papert.| The Daily Papert
Documents and recollections from the early days of 1:1 computing in schools. The post Laptops appeared first on The Daily Papert.| The Daily Papert
A month or two ago I wrote this post which expressed my frustration with various issues around private datasets as a way of measuring the mathematical abilities of language models. More generally I was frustrated about the difficulty of being … Continue reading →| Xena
Undergraduate mathematicians usually have a hard time defining functions from quotients in Lean, because they have been taught a specific model for quotients in their classes, which is not the model that Lean uses. This post is an attempt to … Continue reading →| Xena
So I'm two months into trying to teach a proof of Fermat's Last Theorem to a computer. We already have one interesting story, which I felt was worth sharing. Continue reading →| Xena
A huge amount happened in the Lean theorem prover community in 2023; this blog post looks back at some of these events, plus some of what we have to look forward to in 2024. Modern mathematics I personally am a … Continue reading →| Xena
I previously had put together analysis that utilized the full name and date of birth information from the Virginia Registered Voter List (“RVL”) in order to look for duplicate registrations, either exact matches or by using a string distance measure (the Levenshtein distance) to accommodate for typos, abbreviations, and mis-spellings. Just prior to the start […]| Digital Poll Watchers (dot) Org
Update: See my daily math streak progress here 👈 I recently passed 100 days of practicing math every single day 💯 I’ve wanted to beef up my math chops for a while, but I needed a good reason that would justify the time investment. Plus, it’s always easier to learn when you have a clear […]| Gabe Mays
In Part 10 we saw that, loosely speaking, the theory of a hydrogen atom is equivalent to the theory of a massless left-handed spin-½ particle in the Einstein universe—a static universe where space is a 3-sphere. Today we’ll ‘second quantize’ both of these equivalent theories and get new theories that again are equivalent. ‘Second quantization’ […]| Azimuth
The poet Blake wrote that you can see a world in a grain of sand. Today we’ll see a universe in an atom! We’ll see that states of the hydrogen atom correspond to states of a massless spin-½ particle in the Einstein universe—a closed, static universe where space is a 3-sphere. The rotational symmetries of […]| Azimuth
Today I want to make a little digression into the quaternions. We won’t need this for anything later—it’s just for fun. But it’s quite beautiful. We saw in Part 8 that if we take the spin of the electron into account, we can think of bound states of the hydrogen atom as spinor-valued functions on […]| Azimuth
I’ve been working with Adittya Chaudhuri on some ideas related to this series of blog articles, and now our paper is done! • John Baez and Adittya Chaudhuri, Graphs with polarities. Abst…| Azimuth
Prof. Olivia Caramello, Coordinator of the Centre for Topos Theory and its Applications (CTTA), gave an invited lecture in Shanghai| Istituto Grothendieck
This is a puzzle with both the computer-puzzle tag and the no-computers tag. We have the following list of five fractions: 11/5, 30/77, 1/11, 21/2, 5/7 Starting with an integer x, we perform the| Puzzling Stack Exchange
A polycube is a three dimensional generalisation of polyomino, i.e., it is formed by gluing unit cubes along their faces. Given a cube of side n, one can easily dissect it into n congruent polycube...| Puzzling Stack Exchange
Recently, I got an IKEA LILLABO train set for my daughter. It has twelve curved segments, each is 1/8th of a circle of radius 1, two straight segments of length 1, and a bridge of length 2 (in top ...| Puzzling Stack Exchange
Last week had a special math-y date: 7-24-25, which is a Pythagorean triple. This means that the sum of the squares of the smaller two numbers equals the square of the largest number. Let’s d…| Reflections and Tangents
Here's an interesting question: given a target integer n,| mathesis
Note: this article| mathesis
There has been an extraordinary participation for the conference "Mathematics as an artistic experience" held on 11 July 2025 in Paris at the Hermite Amphitheatre of the Henri Poincaré Institute, and organised by the Grothendieck Institute in collaboration with the IHP and the MICS Laboratory of Centrale Supélec (Paris-Saclay University).| Istituto Grothendieck
In ordinary math, the infinite decimal .999… is defined to be the limit of the terminating decimals .9, .99, .999, …; that is, it’s defined to be the real number that the fractions 9/10, 99/1…| mathenchant.wordpress.com
We piled into the two cars and headed north to the World Heritage city of Évora for the third conference on Theoretical and Computational Algebra. Arriving in my room, the welcome message on the television informed me that the temperature … Continue reading →| Peter Cameron's Blog
I was looking for information about mathematics programs at other liberal arts colleges, so I put together this collection of links. I thought others might find it helpful, so I’m posting it here. (I actually asked ChatGPT to assemble this list. It did an OK, but not great, job. About 70% of the links were... Read More| David Richeson: Division by Zero
Recently I was made aware of the work Ed Solomon had been doing with data from the 2020 Colorado Cast Vote Records (CVRs), and I’ve taken some time to replicate and validate some of his data observations. I don’t always agree with Ed, but I wanted to take some time and verify the facts of the matter for myself.| Digital Poll Watchers (dot) Org
MuSA_RT 3.1 is out! This latest version features RealityKit-based graphics, support for audio file input, and the ability to stream result analysis to other MuSA_RT clients for local rendering.| ARJF
| ARJF
| ARJF
Nina found the official solution to Dudeney’s “Digital Difficulties” (her article on it is shared here and here). The guess on how they solved it was confirmed in the Strand solut…| Win Vector LLC
Some years ago I speculated that it would nice if a certain mathematical object existed, and even nicer if it were to satisfy an ordinary differential equation of a special sort. I was motivated by a particular physical question, and it seemed very natural to me to imagine such an object... So natural that I was sure that it must already have been studied, the equation for it known. As a result, every so often I'd go down a rabbit hole of a literature dig, but not with much success because it...| Asymptotia
Not too long ago, my math block started the same way every day: students walked in, grabbed their notebooks, and started a warm-up. Some finished quickly.| Region 13's Blog
At a quick glance: 32 is greater than 10. 31/32 is about 0.96875, not near pi ~ 3.141593. 31/10 = 3.1 is a worse approximation of pi than 22/7 ~ 3.142857.| Win Vector LLC
Every summer, the School of Education hosts a Math Teacher Academy, in which math teachers from all over the state can come and learn about techniques that will best help their students succeed. This year, it will be June 23-25 from 9 a.m. to 3 p.m.| The Baylor Lariat - The official student news source
Welcome to the 239th installment of the Carnival of Mathematics, a roundup of interesting mathematics content from April 2025. The Carnival is a monthly post hosted by a different blog each month. Since this is the 239th Carnival, I’ll begin with some interesting facts about the number 239. Fun Facts About 239 239 is a … Continue reading Carnival Of Mathematics→| Reflections and Tangents
I recently watched a great interview of the mathematician and Fields medalist (2022) Hugo Duminil-Copin by Science étonnante (aka David Louapre). At some point, there was an interesting discussion on the role of AI in the discovery of new mathematical findings. I think the arguments generalize far beyond mathematics: AI as a creative sparring partner, AI as a way to have an inner, interactive dialogue with oneself, AI as a tool to automate the boring parts of the process, human fallibility a...| blog.mathieuacher.com
When you teach at a small high school, like I do, you where a lot of different hats. There’s a ton of stuff that needs to get done and are fewer people to do it. Naturally, everybody is asked…| lazy 0ch0
Can chance childhood thoughts shape the whole life? Maybe a lifetime studying the nuanced complexity of humanity alongside the elusive simplicity of mathematics comes down to The Woodentops.| Alan Dix
Using Dynamic Technology to Build Understanding ◊ Episode 6: Quadrilaterals ◊ In Episode 5, we took a brief look at trapezoids, and that got me thinking about the family of quadrilaterals: all the wonderful four-sided polygons that students learn about in geometry. How might Dynamic Geometry (DG) help our learners investigate these shapes? Constructing Parallelograms … Continue reading Go For Geometry! 6→| Reflections and Tangents
So much of mathematics is focused on the end point: the answer, the solution, the proof. We attach so much emphasis on the destination — the more efficient the better. We place such high value on t…| How I teach maths.
A deep dive into DeepSeek’s Multi-Head Latent Attention, including the mathematics and implementation details. The layer is recreated in Julia using Flux.jl.| liorsinai.github.io
A paper from last week with high press visibility that makes claims to climate1 applicability is titled: Topology shapes dynamics of higher-order networks The higher-order Topological Kuramoto dyna…| GeoEnergy Math
The Ultimate Guide to AI Math Solvers: Boosting Your Math Skills with Technology Introduction to AI Math Solvers Mathematics has always been a subject that challenges students, often requiring extra practice and assistance to master. With the rapid advancements in technology, Artificial Intelligence (AI) has stepped in to bridge the gap, offering innovative solutions that […]| Interactive Mathematics - Mathematics, learning, computing, travel - and what...
We are currently seeking a Research Fellow in Eco-epidemiology/Human Ecology to join our team at Flinders University. The successful candidate will develop spatial eco-epidemiological models for the populations of Indigenous Australians exposed to novel diseases upon contact with the first European settlers in the 18th Century. The candidate will focus on: The ideal candidate willContinue reading "New job posting: Research Fellow in Eco-Epidemiology & Human Ecology"| Global Ecology @ Flinders
I love John Mason and although I’ve even quoted it myself a few times, I think I don’t wholeheartedly agree with the statement “it is the ways of thinking that are rich, not the task itself&#…| How I teach maths.
Root Finding| degenerateconic.com
There’s a pretty thought experiment that’s sometimes attributed to Democritus though it’s actually due to a later popularizer of the atomic hypothesis1 and it goes like this: Suppose we use the wor…| mathenchant.wordpress.com
Humans are lazy when thinking about infinity. Usually it doesn’t matter, but sometimes, our imprecision comes with big philosophical implications.| Steve Patterson
For the last several years, I’ve been on the hunt. I’ve been searching for an explanation for the popularity of irrational beliefs. People casually accept contradictions into their worldview; they are convinced that paradoxes exist. I’ve been trying to understand why. Their arguments frequently end up appealing to mistaken interpretations of quantum physics or the […]| Steve Patterson
Using Dynamic Technology to Build Understanding ◊ Episode 2: Draw Vs. Construct ◊ When using Dynamic Geometry technology platforms, a careful distinction must be made between a figure that is DRAWN…| Reflections and Tangents
Stephen Wolfram discusses understanding proofs discovered using automated theorem proving. Based on Wolfram’s proof of the simplest axioms of logic of Boolean algebra.| writings.stephenwolfram.com
The Martinez-Rueda algorithm computes boolean operations between polygons. It can be used for polygon intersections (polygon clipping), unions, differences a...| liorsinai.github.io
THIS POST IS CURRENTLY UNDER CONSTRUCTION| Matthew N. Bernstein
Structural Causal Models (SCMs) and Do-Calculus are foundational to causal reasoning and inference. SCMs formalize causal relationships through mathematical ...| Rehan Guha -Portfolio & Blog
Just in time for the holidays, Colleen Robichaux and I wrote this paper on positivity of Schubert coefficients. This paper is unlike any other paper I had written, both in the content and the way w…| Igor Pak's blog
What happens to ground truth when finding a factoid or photo no longer means consulting an archive but generating one from scratch? That’s the question that drives “Honey, AI Shrunk the Archive,” an essay I wrote for the forthcoming anthology New Directions in Digital Textual Studies.| Still Water Lab
[Needs cleanup… just dumping here for now.] Mark Jason Dominus tweeted and later blogged about this puzzle: From the four numbers [6, 6, 5, 2], using only the binary operations [+, -, *, /], form the number 17. When he tweeted the first time, I thought about it a little bit (while walking from my […]| The Lumber Room
In his wonderful On Proof and Progress in Mathematics, Thurston begins his second section “How do people understand mathematics?” as follows: This is a very hard question. Understanding is an individual and internal matter that is hard to be fully aware of, hard to understand and often hard to communicate. We can only touch on […]| The Lumber Room
(TODO: Learn and elaborate more on their respective histories and goals.) The formula (reminded via this post), a special case at of was found by Leibniz in 1673, while he was trying to find the area (“quadrature”) of a circle, and he had as prior work the ideas of Pascal on infinitesimal triangles, and that […]| The Lumber Room
1. Alphabet Suppose we have an alphabet of size . Its generating function (using the variable to mark length) is simply , as contains elements of length each. 2. Words Let denote the class of all words over the alphabet . There are many ways to find the generating function for . 2.1. We have […]| The Lumber Room
A long time ago, Diophantus (sort of) discussed integer solutions to the equation (solutions to this equation are called Pythagorean triples). Centuries later, in 1637, Fermat made a conjecture (now called Fermat’s Last Theorem, not because he uttered it in his dying breath, but because it was the last one to be proved — in ~1995) […]| The Lumber Room
