The 2025 MathsJam Gathering took place on the weekend of 22-23 November 2025, at Kent's Hill Park in Milton Keynes. Below are links to things people shared at MathsJam.
This is a list of talks which were given at the 2025 MathsJam Gathering, including links to slides where available. If you spot any mistakes on this page, or would like to update the description of your talk, use the 'Edit this page' link at the bottom with a GitHub account to propose changes and make a pull request.
This year, 2025, we, Pedro Freitas, Jorge Nuno Silva, Alexandre Silva, and Tiago Hirth, got our book "Magic, Mathematics, and Playing Cards" published. In this five minute presentation I aim to share four quick effects to hook the audience in wanting to know more about the mathematics that make them work to promote our work.
I don't know any overarching theory of such polyhedra; I suspect there are many wonders in this vicinity waiting patiently to be found.
In the early twentieth century, two Nepali translations were published of Lilavati, a classic Sanskrit maths text. Despite the attribution of one text to Chandrakala Dhananjaya and the other to her husband, Tikaram, the books' contents reveal that both authors contributed to both texts. In the absence of further documentary evidence, we explore why collaboration was needed to translate Sanskrit mathematical poetry into Nepali. This talk is based on research by Dr Deepak Basyal.
An exploration of cell collinearity in polyominoes inspired by a competition from last year called "Dots on a Tiling". Relevant OEIS sequences: A377756 A378169 A377941 A377942 A378014 A378015 A380990 A380991
When Anscombe, Simpson, Berkson, and Lindley team up, reality bends. A fast, funny tour of how graphs, context, selection, and priors all gang up to make statistics weird again.
This is one of a pair of talks about mathematical magic tricks that we saw and fiddled with at this years G4G Europe. This one is a variation of a binary code trick to guess a number, and the result is what happens when someone says "could this be done in base 3?". Rock paper and scissors are used to encode the numbers, and the challenge is to figure out how it works.
There is no knight tour, nor a king tour on a 4x4 square that produces a magic square. But there are some magic squares that you can get when combining the knight and the king movement.
Rational tangles are a way to represent any fraction using two lengths of rope. They were first introduced and studied by John Conway. Every implementation seems to use two standard moves for manipulating the ends of the rope, while also relying on four helpers who have been pre-trained in how to do these. Here, we will show that with eight Lego mini-figures, pre-training is not necessary, and there are an additional nine building blocks for how to move.
I was with two mathematician friends of mine, and we started comparing how we structure our maths notes on our computers. Specifically, the directory structures. This got us thinking: could we quantify the shape of our thinking? Could we come up with metrics to see how differently we all approached our work? As we sketched out our own folder structures, a nice pattern emerged. We were all on a spectrum, and the two extremes were always the same two shapes: the Path Graph and the Star Graph. Instantly, we had a new language. "Oh, you're very path-like in how you approach problem solving," or "That's a very star-like way to organize a course." Maths is a great place to pick up some good vocabulary and metaphors for life, e.g. "progress is not monotonic", "the tasks on my to-do list do not commute". I believe "path-like" and "star-like" can be just as useful, and discuss a few examples.
Inspired by a post on Futility Closet, Katie recreates some of these 'fridge magnet equations' (with thanks to Finite Group member r10pez10 for that name) using real fridge magnets, and demonstrates their equality.
Talk summary : An AI can play set, but at the moment, not honestly or accurately.
The number one law in physics is, of course, Emmy Noether's Law of Conservation - without which - physics wouldn't even be a subject!
An examination of fair coins, Sherlock Holmes, and The Return of the Obra Dinn - to show how some of the ways mathematicians sometimes talk about probability, logic, and conclusions fail at understanding how reasoning applies in the real world.
A look into the world of logic puzzles beyond traditional sudoku, with example puzzles of a variety of types. Let's see some cool puzzles! Highlights included: Toketa Magazine, Pulze Magazine, Sudokuvania
Much of the history of maths is intertwined with its use as a language to describe how the real world works. But why stop there, when we can also use maths to define how we want the world to work, and to make it so? We take a look at the fascinating world of control theory, what it means to be in control, and how to analyse and understand some of the properties of the resulting systems.
Mathematics can be rather siloed; this g'(x) =1/(f'(g (x))) brings calculus and functions tidily together.
Playing one of the games from WikiSim: a platform for making open source games and calculations of complex problems along with a brief walk through of the platform
In a 2-D (conventional) jigsaw, all pieces are first-order (can be removed immediately). 3-D jigsaws are much trickier!
The talk looked at the origin of the dissection of a well-known puzzle known as the Haberdashers' problem. It requires the dissection of an equilateral triangle into a square in the fewest number of pieces. It was proposed by H. E. Dudeney and appeared in the Daily Mail in a puzzle column in February 1905. He published the solution, but some years later, he gave credit to another.
A famous 1503 woodcut in the book Margarita Philosophica shows the transition that was taking place in arithmetic. A smiling Boethius shows off the new method of doing arithmetic with Indo Arabic numerals. He appears to be doing a subtraction, but he gets the wrong answer.
Like the complex numbers, the dual numbers are 2D vectors of real numbers with a rule that allows you to multiply them together. But the multiplication rule is different - instead of i2 = -1, we have ε2 = 0. This means that the "imaginary" part of a dual number behaves like an infinitesimal difference, and obeys the chain and product rules for derivatives. This is behind the magical-seeming trick of automatic differentiation, which makes training modern deep neural networks feasible.
Zoe summarises mathematical fun that she's has with the ONS Baby Names data.
Belgin finds a chronological list of formulae, theorems and other historical mathematical achievements on one side of CERN's metallic sculpture, "Wandering the immeasurable". Timeline includes: - Base 60 calculations, Mesopotamia - Pythagoras' theorems - Chinese/Sanskrit/Arabic calculations & results - Numerous physics equations with famous names attached - Mendeleev and the periodic table - Early estimates of the speed of light - Standard model's Lagrangian
Look at a map of the London Underground and try to find a path through 12 stations that uses all 11 tube lines. Ally first attempted the London "all lines" challenge in 2023, then did it some more until he'd tried every possible route. There are more than you might expect. Here he shares his findings, tips for future challengers, and some fun facts found along the way.
Paul found this StackExchange post in which people were discussing an interesting maths problem... but further down the thread, discovered that the problem is actually based on one of the minigames from the 2010 Nintendo party game Wii Party. (He brought a Wii so we could play a bit ourselves).
This is one of a pair of talks about mathematical magic tricks that we saw and fiddled with at this years G4G Europe. This one is about a set of clown cards where every clown is wearing different coloured clothes. When we first saw this trick the clowns had four different coloured pieces of clothing. We thought it proper to give them a bit more to wear, so we extended the trick, so our clowns have six pieces of clothing. The cards are constructed in such a way that the cards themselves reveal the colours of all the different pieces of clothing a secretly selected clown was wearing.
This talk covered miscellaneous topics in training Alpha Zero style programs to play abstract games at a high level. The talk focused on efficient Monte Carlo Tree Search and pitfalls from getting tricked by randomness when determining which models or algorithms actually play better.
2025 is the sum of the first 9 cube numbers and also the square of the sum of the first nine numbers. You can represent this fact by arranging one 1 by 1 square, two 2 by 2 squares, three 3 by 3 squares, and so on up to nine 9 by 9 squares inside a 45 by 45 square. This talk looked at the general puzzle involving the sum of the first n cubes, showing that it's possible to do the arrangement for n=1, n=8 and n=9, but not possible for 2 to 7, and showed off the interactive thing that Scroggs made.
This talk is about weighing items where all but one of the items have identical weight. My interest in this puzzle was ignited by one of the questions in the Leiden Math Trail.
Paper comes in standard sizes. Most of the world use paper with the irrational aspect ratio of sqrt(2). I explore the reason for that and how to exploit it when folding a piece of paper. Some countries use another rational, but imperial systems and I cover those too. I reveal an amazing coincidence about your credit card.
As a child, I often decorated my unicycle by threading crepe paper through the spokes. When I recently wanted to increase my unicycle's visibility, I figured that must also work with reflective rope. For decorative purposes, I wanted to alternate between different colours of rope. Given that the wheel is a circle, the obvious choice for the pattern was of course dictated by the digits of the circle constant... but which one? Using slightly questionable python code, I analyzed which constant's digits would give me a higher proportion of reflective rope, depending on wheel size and rope thickness.
I tried a few different ways to print the 14th Stellation of the Icosahedron. I will show a few ways that I tried. The final way is very neat - it uses 60 identical tetrahedra (plus 240 magnets!). You can try it yourself here. This is a similar much bigger project by Bob Hearn which I have started and will also show (and for people to play with afterwards).
Ben tried and failed to get a closed form result for the expected number of draws before a collision. But a computer simulation, assuming independence of skittles, gave the same results as resampling from Clare's dataset, thereby not contradicting independence, and produced a much lower numerical estimate for time until collision than the naive birthday approach.
I explored sequences of consecutive odd semi-primes: numbers with exactly two (not necessarily distinct) prime factors. While the maximum length of sequences of consecutive semi-primes is a fairly widely known result, I wondered what would happen if we restricted to the odd-only case. By systematically searching, I found chains of lengths 2 through 8, but none longer, and for good reason. In any run of nine or more consecutive odd numbers, one must be divisible by 9, which means it contains the factor 3×3, and so it can't be semi-prime. Therefore, the longest possible chain of consecutive odd semi-primes is of length eight. The talk also touched on why the smallest example of the longest chain isn't the largest and posed some questions about generalising to other spacings between semi-primes.
If you glue a Square based pyramid (S) and a Triangular based pyramid (T) together at one of the triangular faces, the resulting shape still has just five faces! How is this possible? What's more, the volume of S is exactly twice that of T. This talk demonstrates two ways to see this result simply and intuitively (no trig!).
A talk on creating stitch diagrams using Haskell.
Mathematical magic has its own curious charm. It delights, confounds, and entices audiences to think about how the trick works. I presented a trick called "Cat, Dog, and Mouse Magic" and a variation of it. The beauty of this trick is that it can be accomplished in multiple ways. After I demonstrate my method, spectators are eager to stage it themselves. When they perform the trick, they inadvertently practice and develop their mathematical skills. For the Cat, Dog, and Mouse Magic cards and a video or two of the magic trick, visit jrmf.org/puzzle/cat-dog-mouse-magic/.
We can easily find a compass and straight-edge construction of regular pentagon, but how do you know it is exact?
