Dave Richeson

A boy has an exam with an F at the top. A tarot card reader has the cards "The Lecture," "The Homework," and "The Office Hours" laid before her. She says, "Let's see what the cards suggest..."

A comic I had AI create for me.

(Re: the question, "What can I do to improve my performance in this class?)

I heard that The Police's song "Every Breath You Take" is not a love song, but it is sung from the point of view of a stalker. I asked Google, and this was the AI reply.... in Indonesian. 🤷‍♂️😂

I wanted to try printing in two colors with my printer. So I designed and printed this thing.

AI solves Knuth's open problem:
"Shock! Shock! I learned yesterday that an open problem I’d been working on for several weeks had just been solved by Claude Opus 4.6... It seems that I’ll have to revise my opinions about 'generative AI' one of these days."
www-cs-faculty.stanford.edu/~knuth/paper...

I did just read it. I agree that it seems fine. But I didn't know if there was anything I should be concerned about. (I have no reason to doubt it other than past experience with various tech acquisitions!)

I just saw that MyMiniFactory purchased Thingiverse. I've been putting a lot of my models on Thingiverse, but I don't know anything about the pros or cons of this acquisition. I'm happy to not know, but if there's something I should know about this, let me know!

Archimedes's Sphere Slices by divbyzero Archimedes proved that if you slice a sphere of radius r with two planes a distance h apart, the surface area is 2πrh—the same as a cylinder of the same radius and height. So, the surface area doesn't...

I just put these files on Thingiverse for anyone to download and print. www.thingiverse.com/thing:7305536 cc @cardcolm.bsky.social

The Napkin Ring Problem by divbyzero Recall the "napkin ring problem": Take a sphere of radius r and drill a hole along a diameter so the resulting shape has height h. Then the volume, V = πh³/6, does not depend on r!These files consist ...

I just put these files on Thingiverse for anyone to download and print. www.thingiverse.com/thing:7305545 cc @cardcolm.bsky.social

Weight of one slice: 16 grams.

Weight of one slice: 16 grams.

Weight of one slice: 16 grams.

Weight of one slice: 16 grams.

Idea: Produce 3D-printed slices of a (hollow) sphere, all of the same height. Print with 100% fill. They should all weigh the same.

Bam!
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A 3D-printed sphere sliced into equal-height pieces.

Another 3D-printing suggestion from @cardcolm.bsky.social:

Archimedes proved that if you slice a sphere of radius r with two planes a distance h apart, the surface area is 2πrh—the same as a cylinder of the same radius and height. So, it doesn't depend on where the slicing occurs.
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One shape on the scale: weight = 44g

One shape on the scale: weight = 43g

One shape on the scale: weight = 43g

One shape on the scale: weight = 43g

if we print these shapes as solids (i.e., with 100% fill), they should all weigh the same.

Ta da!

(Equal ±ε)

Four napkin rings of various radii

The four napkin rings are the same height

At Gathering 4 Gardner, @cardcolm.bsky.social suggested I try the following 3D-printing project.

Recall the "napkin ring problem": Take a sphere of radius r and drill out a hole along a diameter so the remaining shape has height h. Then the volume, V = πh³/6, does not depend on R.

He thought that

The left-handed boy problem A few months ago Gary Foshee was scheduled to speak at the Gathering for Gardner. He got up and gave a presentation that was all of three sentences. He said: I have two children. One is a boy born …

Here's what I wrote about the problem when I first heard it in 2010: divisbyzero.com/2010/08/05/t...

The Counterintuitive Math Behind the Boy Born on Tuesday Problem YouTube video by polymathematic

Here was the top video I found online. He discusses the probability of BG rather than BB, so the answer to my question is 1-(his answer). www.youtube.com/shorts/khfqV...

Not 50/50!

Exactly! Or even at the extreme point, "One is a boy who is standing right here next to me."

At G4G, there was a slideshow of past attendees who passed away since the last conference. One was Gary Foshee, who in 2010 gave the shortest-ever talk. It was three sentences:

"I have two children. One is a boy born on a Tuesday. What is the probability that I have two boys?"

Great problem!

My students wanted to write the minimum of two values. I asked ChatGPT for the preferred notation. It gave a=min(b,c). I decided I wanted to ask a more general question. So, I opened a new chat, modified the question, and it gave a different answer: a=min{b,c}.

A photo of a sign saying topology [top-ol-uh-jee] noun 1. The study of adding tasty toppings.

Someone posted this photo on Twitter a few years ago (account now deleted). It still makes me laugh.

made more clearly apparent."
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"almost without realizing it—render the idea of the infinite familiar to themselves. Moreover, I have here resolved many problems by the methods of ordinary algebra, which are usually treated within the analysis of the infinite, so that the connection between the two methods may henceforth be
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"books will abundantly supply this deficiency. For I have taken care not only to set forth more fully and distinctly those matters which the analysis of the infinite strictly requires than is commonly done, but also to work through quite a number of problems by which readers may gradually—and
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"exist many questions whose development is capable of preparing the minds of learners for that higher science—yet these are either omitted from the usual elements of algebra, or are not treated with sufficient care. For this reason, I do not doubt that the material I have assembled in these
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"the threshold, but even form distorted notions of that infinite, whose understanding is here brought to their aid. Now, although the analysis of the infinite requires not only a thorough knowledge of algebra but also an acquaintance with all the methods thus far discovered, there nevertheless
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"hinder students of mathematics in approaching the analysis of the infinite arises from this source: although they scarcely grasp common algebra, they nevertheless attempt to apply their minds to that more sublime art. From this it comes about that they not only remain standing, as it were, at
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A screenshot of the first paragraph of Euler's work, in Latin.

A screenshot of the first paragraph of Euler's work, in Latin.

Here's the first paragraph of the preface to Euler's pre-calculus textbook (Introductio ad analysin infinitorum, 1748) as translated from Latin by ChatGPT. The more things change, the more they stay the same!

"I have very often observed that by far the greatest part of the difficulties which
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This afternoon was the "Hands-On Activities" portion of the conference. I brought the supplies (150 laser-cut pieces of wood, 1000 yards of yarn, wood glue, and 50 binder clips) to make a giant cardioid and a giant nephroid. It was fun, and I think they turned out great.

Well, that was a fun evening at G4G! Eating dinner and chatting with Donald Knuth, followed by a talk by Adam Savage speak and a Q&A with @standupmaths.bsky.social!

Donald Knuth gives a Q&A. “I’m like Gemini. I’ll answer anything, but my answers may contain errors.”

Thanks! You killed it today! Your talk was perfect for the conference, and got a lot of ooohs and aaahs and stunned expressions!