4-Dimensional Cross-Polytope | Azimuth
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
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
Place a nonzero digit into some of the white cells of the grid. Shaded cells must remain blank. No digit can repeat in a row or column. In each row, the sum of the digits must be equal to some fixed value R (which you find during the solution). Similarly, in each column, the sum of the digits must be equal to some fixed value C. Circles in the grid give all the digits in the cells that touch the circle. (Including repeats; if two cells touching a circle have the same digit, the circle must co...| Recent Questions - Puzzling Stack Exchange
Note: I created this puzzle. Last year, 2024, when mistyped, can result in the years 22024, 20024, 20224, and 20244. Even if those "years" are very far from now, if you look on a cellphone calendar that supports 5-digit years or on WolframAlpha, you would see that all of them, except for 20224, have the same calendar as 2024. 20024, 20244, and 22024 are all mistyped years of 2024, and all of those start on Monday and are leap years. What are the years N in Gregorian Calendar, such that all mi...| Recent Questions - Puzzling Stack Exchange
Here's a Scrabble puzzle that Nick Ballard and I composed, and recently presented at the MOVES conference. See the diagram below. The game is nearing its end and you’re in dire straits. On your last turn, you bingoed with GROGSHOP, but then your opponent immediately bingoed back with UNUSUAL, taking a commanding lead of 476 points to your 344 points. On your rack, you have MONKYSZ. The tiles unseen to you are DEFJLLLQW, two of which are in the bag and seven of which are on your opponent’s...| Recent Questions - Puzzling Stack Exchange
I was playing around with some ideas for a nice geometry puzzle involving circles on my iPad when my daughter saw it and said it looked like fire. I then added some background elements like the sun, the cloud, the sky, and the land, and now it looks like a tsunami of fire on a sunny day! Anyway, here’s the question. What fraction of the image is covered in fire? And more importantly, can you find it with as little calculation as possible? --- Clarifications: All curves in the fire are circu...| Recent Questions - Puzzling Stack Exchange
Try to make all numbers 1-40 using the digits 2, 0, 2, 6. Rules: Use all four digits exactly once. Allowed operations: +,−,×,÷,! (factorial), $x^y$ (exponentiation), √ (square root). Parentheses and concatenation are allowed. (e.g. 20+2×6). Squaring uses the digit 2. The modulus operator is not allowed. Rounding is not allowed.| Recent Questions - Puzzling Stack Exchange
We have many puzzles to find complete knight's tours – including on 4D boards, irregular boards and nonplanar boards – but few puzzles to find partial tours where only some cells are visited. I present a puzzle of the latter type below. On an 8×7 board, can 26 cells be labelled 0 to 25 inclusive such that 0-1-2-…-25-0 is a closed knight's tour and every even number n is also a knight's move away from (n+7) mod 26? Can the same be done on an 8×6 board? A 7×7 board?| Recent Questions - Puzzling Stack Exchange
Here's a circular chip with three evenly spaced notches. Two such chips can be attached as shown, where the "boundary circle" of each chip goes through the center of the other, and the planes of the two chips are orthogonal. I have been trying to make a closed loop out of such chips but the best I have so far is the following (made in Geogebra). The two red circles at the top intersect nontrivially and the angle between them is about 130º, so this certainly doesn't lead to a closed loop, but...| Recent Questions - Puzzling Stack Exchange
Note: I created this puzzle. A person has a phobia on certain dates - January 15 and February 3. While some dates like April 15 and July 24 also appear unlucky, that person is more afraid of those first two dates. That person does not like evil. Why? Hint:| Recent Questions - Puzzling Stack Exchange
Qwirkle tiles are identically-sized squares. Each has two attributes: one of 6 symbols and one of 6 colors. There are 3 tiles for each combination of symbol and color, thus 6×6×3 = 108 tiles. We want to fit these on a square grid (at most one tile at each position), while respecting standard Qwirkle constraints: Each horizontal or vertical segment of consecutive non-empty grid squares has tiles with either the same symbol and different colors, or the same color and different symbols. It fol...| Recent Questions - Puzzling Stack Exchange
Consider a scenario where an object's world position is x distance in magnitude away from another object's position, naturally you would just use trig to determine the hypotenuse of the vector between them... is it nearby? WRONG. because the overall mesh, that is drawn relative to that translation offset or position, could be very large. So you might have a giant BlackHole instance which has a world position quite far away from the reference object, but its overall mesh could be nearby, or ev...| Recent Questions - Game Development Stack Exchange
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
Visit the post for more.| Frame-Poythress.org
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
The mathematician John Venn was born on this day in 1834. To commemorate the occasion, here’s a poem in the form of a Venn diagram.| Brian Bilston
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
Deriving Inverse Layout Mathematically| Lei Mao's Log Book
Creating Tiled Layouts Using Blocked Product and Raked Product| Lei Mao's Log Book
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
Now comes the really new stuff. I want to explain how the hydrogen atom is in a certain sense equivalent to a massless spin-½ particle in the ‘Einstein universe’. This is the universe Einstein believed in before Hubble said the universe was expanding! It has a 3-sphere for space, and this sphere stays the same […]| Azimuth
Did you know that Lawvere did classified work on arms control in the 1960s, back when he was writing his thesis? Did you know that the French government offered him a job in military intelligence? The following paper should be interesting to applied category theorists—for a couple of different reasons: • Bill Lawvere, The category […]| Azimuth
I’ve explained a cool way to treat bound states of the hydrogen atom as wavefunctions on a sphere in 4-dimensional space. But so far I’ve been neglecting the electron’s spin. Now let’s throw that in too! This will wind up leading us in some surprising directions. So far I’ve just been reviewing known ideas, but […]| Azimuth
In Part 4 we saw that the classical Kepler problem—the problem of a single classical particle in an inverse square force—has symmetry under the group of rotations of 4-dimensional space Since the Lie algebra of this group is we must have conserved quantities and corresponding to these two copies of The physical meaning of these […]| Azimuth
In Part 4 we saw how the classical Kepler problem is connected to a particle moving on a sphere in 4-dimensional space, and how this illuminates the secret 4-dimensional rotation symmetry of the Kepler problem. There are various ways to quantize the Kepler problem and obtain a description of the hydrogen atom’s bound states as […]| Azimuth
The Kepler problem is the study of a particle moving in an attractive inverse square force. In classical mechanics, this problem shows up when you study the motion of a planet around the Sun in the Solar System. In quantum mechanics, it shows up when you study the motion of an electron around a proton […]| Azimuth
The Kepler problem studies a particle moving in an inverse square force, like a planet orbiting the Sun. Last time I talked about an extra conserved quantity associated to this problem, which keeps elliptical orbits from precessing or changing shape. This extra conserved quantity is sometimes called the Laplace–Runge–Lenz vector, but since it was first […]| Azimuth
I’ve been working on a math project involving the periodic table of elements and the Kepler problem—that is, the problem of a particle moving in an inverse square force law. I started in 2021, the year I retired from U. C. Riverside. I had driven my wife across the country to DC, and spent the […]| 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
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
Preschool math number recognition and counting are essential skills in our preschoolers’ early math development. Children, without even realizing it, start developing mathematical skills from the moment they begin to notice numbers all around them. These early experiences with numbers help develop number sense naturally. Preschoolers learn numbers best by doing! Using games, songs, and... The post Preschool Math Numbers: Ways to Build Counting Skills appeared first on Stay At Home Educator.| Stay At Home Educator
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
A circle is a ‘self-referential’ kind of thing, we might say – a circle is a self-referential kind of thing because every point on its circumference has the very same relationship to the centre, which is also the circle, just...| The Negative Psychologist
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
Elucidating CuTe Inner Partition and Local Tile| Lei Mao's Log Book
Elucidating CuTe Outer Partition and Local Partition| Lei Mao's Log Book
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
Summer is conference season for academics, and this week held my old sub-field’s big yearly conference, called Amplitudes. This year, it was in Seoul at Seoul National University, the first t…| 4 gravitons
A puzzle about the surprisingly tight distribution of mathematical constants.| Forms of life, forms of mind
New overseas research has found that gender disparities in maths performance in favour of boys show up as early as after four months of formal schooling. French and US researchers analysed data from more than 2.6 million first and second grade children (ages 5 to 7) in France. There was almost no d| www.sciencemediacentre.co.nz
[B]y its very existence, [mathematics] poses a serious threat to their entire world view that there is no such thing as objective truth and what they have to say on any subject is just as valid as what anyone else says. Imagine a baseball field with a ball resting on the ground. Two teams come […]| Minding The Campus
A series of short videos showcasing the principles of effective maths teaching in action in classes from Year 1 to Year 6| THE EDUCATION HUB
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
Always interested in exploring recursive functions, Stephen Wolfram takes a fresh look using the most modern Wolfram Language tools and finds new surprises.| writings.stephenwolfram.com
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
In another blow to public schools, a majority of House members voted on May 7 to lower the high school mathematics graduation requirements for all public schools. Because the new, lower standards fall below the minimum admissions requirements for UNC system schools, the bill also directs the UNC Board of Governors to lower its standards […]| Public Schools First NC
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
I have a new “crazy theorists” article up: “Working Through A Trivial Algorithm Whose Analysis Isn’t.” It is my notes on reading through Jonassen and Knuth’s ama…| 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
Not only did Scottish mathematician, science writer, and polymath Mary Fairfax Somerville (December 26, 1780–November 28, 1872) defy the era’s deep-seated bias against women in science, she was the very reason the word “scientist” was coined: When reviewing her seminal second book, On the Connexion of the Physical Sciences, which Somerville wrote at the age of 54, English polymath and Trinity College master William Whewell was so impressed that he thought it rendered the term “men o...| The Reconstructionists
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
No, this is not that 21st century skills crap that people keep trying to sell us. It is learning something about 21st century mathematics, as invented/discovered by 21st century mathematicians. Jus…| BAD MATHEMATICS
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
Using Dynamic Technology to Build Understanding ◊ Episode 5: Marvelous Midsegments ◊ Welcome to Episode 5, where we take the scenic route in our geometry journey. What happens when we find midpoints of the sides of various polygons and connect them with a segment (known as a midsegment)? Marvelous properties show up; read on for … Continue reading Go For Geometry! 5→| 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
Before I read The Man from the Future by Ananyo Bhattacharya, I only knew about John von Neumann in two contexts: that computers use the von Neumann architecture, and that he appeared in a story about a mathematical problem I … Continue reading →| Henrik Warne's blog
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
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
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
