The Rapper, The Canadian Academics, And The Secret Behind The Earworm

April 4, 2026 by Jenny List 10 Comments

There are many events so far in 2026 that could reasonably have been predicted, but perhaps one which couldn’t is a Hackaday scribe in Europe unexpectedly finding herself with a constant earworm from Afroman. The rapper, who most of us know only from his year 2000 hit single about getting high, made the news after an inept police raid on his house, and in turn a court case over his musical denunciations of the authorities.

It’s fair to say they picked on the wrong guy, but in thinking about why, the answer is in the earworm. He has the unique skill of making a song irritatingly catchy, which led us to the question of how a catchy song works. As luck would have it a team from the University of Waterloo have recently released a paper in which they explain it all in terms of maths, giving the rest of us a formula where the likes of Afroman are presumably born with it.

We won’t pretend that Hackaday’s mathematical expertise stretches beyond that needed for engineering, but for the more advanced numberphiles among us the university’s write-up goes into some detail about their use of group theory to study the patterns and symmetry in a given piece of music. It’s a new approach that joins other more famous guides to musical success, so perhaps if you couple it with the stuff your music teacher failed to tell you in school, you could be on your way to the top of the charts. Meanwhile here at Hackaday we’ll stick to more conventional inspiration.

Header: Chris Gilmore, CC BY-SA 2.0.

Momentus Clock Aims To Find Meaning

March 26, 2026 by Lewin Day 8 Comments

A lot of the time, we must assign our own meaning to the numbers on the clock. 8:30 AM is work kicking off, 12 PM is lunch, and 5PM is when the corporate chains release us to what’s left of the day. If you’d rather the clock tell you what’s special about the current time, though, you might like this project from [Andy Isaacson].

It’s called Momentous—”a clock to make every minute meaningful” in [Andy’s] own words. The concept is simple—for each minute, the clock digs up some random mathematical fact relevant to the current time. For example, you might think of 3:14 as Pi o’clock, but Momentous also notes that the sequence “314” shows up at the 856th decimal of e. Useful? Probably not. Fun? If you like numbers, then very!

[Andy] wrote Momentous in Typescript with React Native and Expo. Baked into the app is a computed list of fun number facts for every conceivable time from 00:00 to 23:59. All these timely numbers were processed through a “fact generation” algorithm to dig up mathly tidbits. Do they contain primes? Do the numbers show up in a famous irrational number sequence? Are they palindromic, or can some neat facts be gleaned from Wikipedia? Maybe the current time shows up in your best friend’s phone number! Momentous uses all these and more to make every minute of the day a little bit more interesting.

You can check out the clock for yourself in your web browser. Alternatively, you can install it on your iPhone if you so desire. We feature all kinds of fun clocks here, from the wordy to the absurdy. If you’re cooking up your own timely hacks, we always love to to hear about them on the tipsline!

[Yang-Hui He] Presents To The Royal Institution About AI And Mathematics

February 2, 2026 by John Elliot V 2 Comments

Over on YouTube you can see [Yang-Hui He] present to The Royal Institution about Mathematics: The rise of the machines.

In this one hour presentation [Yang-Hui He] explains how AI is driving progress in pure mathematics. He says that right now AI is poised to change the very nature of how mathematics is done. He is part of a community of hundreds of mathematicians pursuing the use of AI for research purposes.

[Yang-Hui He] traces the genesis of the term “artificial intelligence” to a research proposal from J. McCarthy, M.L. Minsky, N. Rochester, and C.E. Shannon dated August 31, 1955. He says that his mantra has become: connectivism leads to emergence, and goes on to explain what he means by that, then follows with universal approximation theorems.

He goes on to enumerate some of the key moments in AI: Descartes’s bête-machine, 1617; Lovelace’s speculation, 1842; Turing test, 1949; Dartmouth conference, 1956; Rosenblatt’s Perceptron, 1957; Hopfield’s network, 1982; Hinton’s Boltzmann machine, 1984; IBM’s Deep Blue, 1997; and DeepMind’s AlphaGo, 2012.

He continues with some navel-gazing about what is mathematics, and what is artificial intelligence. He considers how we do mathematics as bottom-up, top-down, or meta-mathematics. He mentions about one of his earliest papers on the subject Machine-learning the string landscape (PDF) and his books The Calabi–Yau Landscape: From Geometry, to Physics, to Machine Learning and Machine Learning in Pure Mathematics and Theoretical Physics.

He goes on to explain about Mathlib and the Xena Project. He discusses Machine-Assisted Proof by Terence Tao (PDF) and goes on to talk more about the history of mathematics and particularly experimental mathematics. All in all a very interesting talk, if you can find a spare hour!

In conclusion: Has AI solved any major open conjecture? No. Is AI beginning to help to advance mathematical discovery? Yes. Has AI changed the speaker’s day-to-day research routine? Yes and no.

If you’re interested in more fun math articles be sure to check out Digital Paint Mixing Has Been Greatly Improved With 1930s Math and Painted Over But Not Forgotten: Restoring Lost Paintings With Radiation And Mathematics.

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Math Breakthrough Helps Your Feng Shui

January 9, 2026 by Al Williams 34 Comments

In 1966, a mathematician named [Leo Moser] proposed what sounds like a simple problem: What’s the largest shape you can move through a 1-meter corridor with a right-angle corner? Now, Korean mathematics whiz [Baek Jin-eon] claims to have solved the problem, nearly 60 years later.

The trick is, apparently, the shape of the sofa. By 1968, [John Hammerley] introduced a shape that did better than a rectangle, and by 1992, [Joseph Gerver] proposed something shaped like a phone handset, which remains the largest anyone had found, at 2.2195 square meters.

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Meet The Shape That Cannot Pass Through Itself

November 17, 2025 by Donald Papp 21 Comments

Can a shape pass through itself? That is to say, if one had two identical solids, would it be possible to orient one such that a hole could be cut through it, allowing the other to pass through without breaking the first into separate pieces? It turns out that the answer is yes, at least for certain shapes. Recently, two friends, [Sergey Yurkevich] and [Jakob Steininger], found the first shape proven not to have this property.

A 3D-printed representation of a cube passing through itself [image: Wikipedia]

Back in the late 1600s, Prince Rupert of the Rhine proved it was possible to accomplish this feat with two identical cubes. One can tilt a cube just so, and the other cube can fit through a tunnel bored through it. A representation is shown here.

Later, researchers showed this was also true of more complex shapes. This ability to pass unbroken through a copy of oneself became known as Rupert’s Property. Sometimes it’s an amazingly tight fit, but it seems to always work.

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The 19th Century Quantum Mechanics

September 26, 2025 by Al Williams 18 Comments

While William Rowan Hamilton isn’t a household name like, say, Einstein or Hawking, he might have been. It turns out the Irish mathematician almost stumbled on quantum theory in the or around 1827. [Robyn Arianrhod] has the story in a post on The Conversation.

Famously, Newton worked out the rules for the motion of ordinary objects back in 1687. People like Euler and Lagrange kept improving on the ideas of what we call Newtonian physics. Hamilton produced an especially useful improvement by treating light rays and moving particles the same.

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Hackaday Links: August 24, 2025

August 24, 2025 by Dan Maloney 9 Comments

“Emergency Law Enforcement Officer Hologram program activated. Please state the nature of your criminal or civil emergency.” Taking a cue from Star Trek: Voyager, the Seoul Metropolitan Police Agency is testing a holographic police officer, with surprisingly — dare we say, suspiciously? — positive results. The virtual officer makes an appearance every two minutes in the evening hours in a public park, presumably one with a history of criminal activity. The projection is accompanied by a stern warning that the area is being monitored with cameras, and that should anything untoward transpire, meat-based officers, presumably wearing something other than the dapper but impractical full-dress uniform the hologram sports, will be dispatched to deal with the issue.

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