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Bill Shillito @solidangles.bsky.social · 31/08/2026

Which of these is named "Kiki", and which of these is named "Bouba"?

A summation sign, the Greek capital letter sigma.

An integration sign, an elongated letter S.

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Bill Shillito @solidangles.bsky.social · 25/06/2026

I’m going to start calling non-commutative groups “abelian’t.”

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Bill Shillito @solidangles.bsky.social · 05/06/2026

Not that there's anything inherently wrong with the arguments in the video, obviously! I just wish it were said more often that this sort of thing is taking place under the assumption that we're working in the real numbers, and that there are other equally valid number systems out there.

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Bill Shillito @solidangles.bsky.social · 05/06/2026

Besides, arguments (1) and (2) work just as well to show that ...9999 (with "infinitely many nines" to the left) equals -1. How weird is that?

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Bill Shillito @solidangles.bsky.social · 05/06/2026

I never liked the sleight-of-hand that turns 0.4999... into 0.5. The hidden assumption is that we're working with real numbers, so 0.4999... doesn't mean "infinitely many nines" but the real-number limit of 0.49, 0.499, 0.4999, ⋯. But what if I don't feel like working with real numbers? 🙃

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Matt Salomone @matthematics.com · 09/04/2026

#HoagieHomies : it's more than a hashtag, people

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Bill Shillito @solidangles.bsky.social · 25/03/2026

Giving students extra credit if they use \varepsilon instead of \epsilon on their LaTeX assignment

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Chanda Prescod-Weinstein 🌌 @chanda.blacksky.app · 25/02/2026

I think Harvard's plan to respond to the every-decade moral panic about grade inflation by capping A's is pedagogically obscene. Grades should be a measure of learning, not competition. Grade caps engender competition and anxiety where we should be teaching collaboration and a love of learning.

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Bill Shillito @solidangles.bsky.social · 24/02/2026

It especially hurts because even though I've bent over backwards trying to make my classroom a place where you can make mistakes, learn from them, revise your work, and improve without it tanking your grade, a significant number of students will just bypass that and outsource their learning to AI.

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Bill Shillito @solidangles.bsky.social · 24/02/2026

I feel this. I've had to return to handwritten exams, and I kind of hate it.

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Charlotte Lydia Riley @lottelydia.bsky.social · 23/02/2026

AI is going to trash every single way that we had modernised university teaching and send us back to handwritten exams and vivas for every assessment. Which will bring back every problem with those assessment models (and make us seem even more out-of-touch even as we just try to do meaningful work).

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Raj Raizada @rajraizada.bsky.social · 22/10/2025

Complex function domain-colouring of roots of unity, in @desmos.com Here's the graph: www.desmos.com/3d/hadt9rebbe They recently enabled colouring a surface using functions, so far only in 3D grapher. Side-effect: allows complex domain colouring, using 3D tool as a 2D one! #iTeachMath #MathSky

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Bill Shillito @solidangles.bsky.social · 13/02/2026

You didn’t! But I think I’ve solidly decided on CoV so this will come in handy! The thing that clinched it is that to derive E-L, you need to diff under the integral sign. How do you justify that? Fubini’s theorem! So even if there’s no literal double integral, it explains an important step!

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Bill Shillito @solidangles.bsky.social · 13/02/2026

I love this and might do it even if it isn't the capstone, but ... I've never done 3D printing! 😂 Any recommended resources for my students (and for me)?

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Bill Shillito @solidangles.bsky.social · 13/02/2026

Then again, tbh I'm okay with giving a high-level hand-wavy look at minimal surfaces if needed, at least if I can show the *principle* behind what's going on.

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Bill Shillito @solidangles.bsky.social · 13/02/2026

I'd been thinking about minimal surfaces, but actually SOLVING those? Oof.

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Bill Shillito @solidangles.bsky.social · 13/02/2026

I know right?!? It's like Generalization: The Course. The question is, would there be a good way to connect it to multiple integrals? I'm also writing my own book, and I want to put this capstone at the end of the multiple integrals chapter.

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Bill Shillito @solidangles.bsky.social · 13/02/2026

By the way, by "a future class" I just mean "a future calculus class in the I-IV sequence"!

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Bill Shillito @solidangles.bsky.social · 13/02/2026

For reference, my other capstones: * Calc I: Proving FTC (since they've seen it early, but we do limits at the end) * Calc II: Riemann hypothesis (uses SO many things related to series!) * Calc IV: Differential forms and exterior calculus (fundamental all the theorems!)

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Bill Shillito @solidangles.bsky.social · 13/02/2026

Calc IV contains: * Polar / cylindrical / triple integrals, Jacobians * Vector fields, curl / div * Line integrals, surface integrals * All the fundamental theorems (Gradient, Green, Divergence, Stokes) So I'm actually trying to avoid something that's going to show up in a future class.

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Bill Shillito @solidangles.bsky.social · 13/02/2026

This wouldn't be something I'd be testing students on, by the way — just a "wow that's cool" thing to do on the last day. So it's totally okay for it to be a little bit of a stretch. Any suggestions?

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Bill Shillito @solidangles.bsky.social · 13/02/2026

For reference, at my school, Calculus III covers: * Thinking in higher dimensions * Partial derivatives (+ optimization) * Vector-valued functions * Gradients (+ Lagrange multipliers) * Multiple integrals (Cartesian coordinates only) Vector calculus stuff is pushed to Calculus IV.

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Bill Shillito @solidangles.bsky.social · 13/02/2026

One thought I had was a peek into calculus of variations, since it stretches how we think of dimensions by optimizing over an infinite-dimensional space of functions. But the problem is, I really want something that somehow involves multiple integrals, and I'm not sure how I could work that in.

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Bill Shillito @solidangles.bsky.social · 13/02/2026

Question for anyone who's taught multivariable calculus (without line/surface integrals — just up through multiple integrals). If you were to choose a "capstone" topic that ties multiple topics together, what would you choose? Teaching the Calculus sequence again soon and trying to plan ahead.

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Bill Shillito @solidangles.bsky.social · 28/01/2026

Do you have any vivid examples? Would love to talk about this with my proofs class!

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Bill Shillito @solidangles.bsky.social · 28/01/2026

You asked why it would help didactically. I just gave my own observations from when I’ve taught Monty Hall. I would argue that convincing is a necessary but not sufficient component of effective explanation. The math seems to “stick” better if it aligns with experience.

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Bill Shillito @solidangles.bsky.social · 28/01/2026

I think one reason many struggle with Monty Hall is that they still feel like the probability “should be” 1/2 and so even a perfect explanation doesn’t convince them. I think a simulation like this can create a visceral cognitive dissonance that allows that gap to be bridged. They can SEE it now.

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Bill Shillito @solidangles.bsky.social · 23/01/2026

WOOHOO! Our sandwiches paper has been published! 🥳 ...in celebration, I'm going to claim that tonight's lasagna was a sandwich. 🥪

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Bill Shillito @solidangles.bsky.social · 21/01/2026

Teaching logic tomorrow ... with Clue!

Suppose you've made the following deductions:

* The murderer must be Miss Scarlett or Colonel Mustard.
S ∨ M

* If Miss Scarlett did it, it was in the kitchen with the lead pipe.
S → (K ∧ L)

If your friend shows you the kitchen card, what can you conclude?
¬K

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Bill Shillito @solidangles.bsky.social · 15/01/2026

It’s ironic that the people who seem to be able to benefit the most from AI tools are the ones who don’t actually need them.

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Bill Shillito @solidangles.bsky.social · 12/01/2026

If we want to destigmatize “guess-check-revise”, we need to also revise our assessments so we’re not expecting students to factor non-monic trinomials on a time crunch with a bajillion other skills. How can we accomplish that? Seriously, what would it take?

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Bill Shillito @solidangles.bsky.social · 12/01/2026

Unfortunately, “enjoying learning and understanding” isn’t part of the grade. 😭

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Bill Shillito @solidangles.bsky.social · 02/01/2026

The last step of subtracting from numbers with lots of zeros is done mentally. You can easily justify it using the "Same Distance, Same Difference" strategy in @howiehua.bsky.social's video. Although I first encountered it as a "Vedic Math" sutra — "All from nine and last from ten"!

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Bill Shillito @solidangles.bsky.social · 02/01/2026

As my contribution to sharing subtraction strategies, here's how I do subtraction nowadays, using negative numbers! Made this up on the fly way back when I first started tutoring because I couldn't remember how to do multiple borrowing anymore and I never liked the lie of "you can't take 3 from 2".

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Bill Shillito @solidangles.bsky.social · 01/01/2026

Deviled eggs for New Year's Eve!

Left: Everything bagel deviled eggs, with smoked salmon and chives.
Right: Dua Belibis deviled eggs, with green onion, cilantro, and chopped peanuts.

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Manim Community @manim.community · 26/12/2025

We are aware of an ongoing situation concerning our GitHub organization and Discord server (both of which have been deleted) and are working on resolving this as soon as possible. In the meantime we have setup discord.gg/fGG4TFSdKh as a new home on Discord for our community, come join us there!

discord.gg

Join the Manim Discord Server!

Check out the Manim community on Discord – hang out with 95 other members and enjoy free voice and text chat.

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Bill Shillito @solidangles.bsky.social · 23/12/2025

Had a dream last night… except the main thing of the dream was that I stayed in bed until like 4 PM. There were other things going on too, but I think someone is trying to tell me to get more sleep. 😂

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Matt Salomone @matthematics.com · 22/12/2025

🙂‍↔️🫸 Calculus II exam 😎👉 Series finale

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Bill Shillito @solidangles.bsky.social · 22/12/2025

Most underrated video game villain.

A blue tornado with wide white eyes named Mr. Glitch, who was the villain of the Mathman segment from the children's educational show Square One TV.

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Bill Shillito @solidangles.bsky.social · 18/12/2025

That means there are more questions like this? 👀

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Matt Enlow @unsolvedmre.bsky.social · 15/12/2025

For today’s Advanced Topics test I wrote my own @joeldavidhamkins.bsky.social -style question 😁 #iteachmath #MathSky

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Bill Shillito @solidangles.bsky.social · 11/12/2025

All great points! Full disclosure, this all came about because I wanted a quote for a calculus book I’m working on that isn’t just Ye Olde White Dude Newton or Leibniz again. Madhava and the Kerala school are some of my favorite examples of how much broader the history of calculus is. 🙂

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Bill Shillito @solidangles.bsky.social · 10/12/2025

Much appreciated! Are there any places where I could look at verified quotes from the work of the Kerala school in general that express a similar sentiment?

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Bill Shillito @solidangles.bsky.social · 10/12/2025

I'm a fan of James Tanton's treatment! He motivates the sine and cosine from the question of "how high up is the sun?" and builds everything very intuitively based on that. www.youtube.com/playlist?lis...

youtube.com

From Circle-ometry to Trigonometry: Select Videos from my website - YouTube

See section 7.7 of https://gdaymath.com/courses/gmp/ for now!

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Bill Shillito @solidangles.bsky.social · 09/12/2025

Honestly the best thing has been including the phonetic pronunciation wherever I can. 😂 Have not tried the anti-burrito method! What do you do?

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Bill Shillito @solidangles.bsky.social · 09/12/2025

That part was never the problem with the honorific and last name approach. You need to pronounce names correctly either way. (And I remember that lit teacher ALWAYS got my last name right. Which has always been pretty uncommon, even sometimes from people who've known me for years.)

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Bill Shillito @solidangles.bsky.social · 09/12/2025

My 9th grade literature teacher did this! At the time it made us feel very "grown up" and professional. That's why I also did so myself when I taught high school. I don't follow this practice anymore nowadays, though — I'm not a fan of the constant gender reinforcement.

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Bill Shillito @solidangles.bsky.social · 09/12/2025

Anyone have any idea where I can find a direct reference to the following quote? Especially in its original script? I want to verify the translation. "Anantam api sankhyaatmakam iti budhyate. / Through numbers, even the infinite can be understood." — Madhava of Sangamagrama

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