iiinova — where your digital self keeps evolving

Simon Rubinstein-Salzedo @complexzeta.bsky.social · 01/10/2026

I posted my notes on the pentagonal number theorem on Expositio: expositio.org/papers/exp-2.... Do you have any expository papers, lecture notes, etc., that you want to share? Please post them on Expositio!

expositio.org

The pentagonal number theorem

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 24/06/2026

If you have any high-quality expository papers you've written, and you'd like them to exist in a centralized repository, please submit them to Expositio! If you have any suggestions or find any bugs, please let me know.

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 24/06/2026

Expositio has support for optional peer review, which may be useful for students who want to get some experience with the peer review process. It also supports the creation of curated reading lists, saved papers, and overlay journal that any user can start.

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 24/06/2026

2) Professors and graduate students often post their expository notes on their own websites, so people will only be able to read these papers if they happen to stumble across their websites. If people post on Expositio, then these papers are easy to find in a single centralized repository.

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 24/06/2026

Expositio is intended to solve a few problems: 1) Students who write high-quality expository papers often have nowhere sensible to put them, so few other people are able to read their papers. Now there is a public repository where anyone can find them.

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 24/06/2026

I'm very excited to announce my new project: Expositio, which is what I've been spending most of my free time on for the last few months. This is an arXiv-like platform for expository papers, in all (or at least most) academic disciplines. expositio.org

expositio.org

Expositio

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 25/10/2025

A very positive review of my ergodic theory book has now appeared in the American Math Monthly. See simonrs.com/ETbookreview... to read it!

simonrs.com

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 25/09/2025

Another nice problem about dice that has a slick generating function argument: it is not possible to place weights on the sides of two dice (numbered 1--6) in such a way that every possible sum from 2 to 12 occurs with probability 1/11.

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 25/09/2025

So many good options here! But I'll just post one: There's a very beautiful and short generating function proof of the following result: There is no nontrivial partition of the nonnegative integers into arithmetic progressions with distinct moduli.

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 03/06/2025

Have you taught an introductory class on Lean? Would you be interested in teaching one at Euler Circle next summer? If so, let's chat!

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 07/05/2025

My copies of the ergodic theory book just arrived!

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 28/04/2025

I just learned a charming theorem, the Tait-Kneser Theorem, while editing my differential geometry notes for my summer class: If a smooth plane curve has strictly monotonic curvature, then the osculating circles are disjoint and nested.

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 20/04/2025

Our reward for accepting them is that they all come together so spectacularly into one formula, thus showing us that we were right to accept them.

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 20/04/2025

Many people find Euler's identity e^{iπ}=-1 or e^{iπ}+1=0 to be the most beautiful formula in mathematics. To me, this identity is a triumph of bravery: every ingredient in this formula was a controversial idea at one point: zero, negative numbers, irrational numbers, imaginary numbers.

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 20/04/2025

But there is a positive takeaway, which is that it encourages students to accept that their world can grow. If you don't have an object with properties that you want, then you can just make one. Of course it might not have good properties elsewhere, but the idea may be worth exploring.

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 20/04/2025

I believe that this is a harder pill for students to swallow than limits are, in that it requires a greater strain on their sense of reality.

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 20/04/2025

Should we teach calculus without limits? The obvious approach is using the dual numbers, i.e. introducing an ε such that ε is nonzero, but ε^2=0. Then you can define the derivative of f to be (f(x+ε)-f(x))/ε, at least for polynomials or power series, with no limits needed.

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 20/04/2025

I just learned that the Galois group of the nth truncation of the Taylor series for the exponential function is S_n if n is not a multiple of 4 and A_n if n is a multiple of 4. A very nice result of Schur.

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 19/04/2025

Also, every book title has to start with "An Introduction to" or "A First Course in" or "Elementary."

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 08/04/2025

Last month, I hosted two dinner parties to discuss logistics for gifted education. At the request of one of the attendees, I wrote a report, based in part on what we discussed there. I don't know what I should do with it, but I'll start by posting it here, and I'd love to hear your feedback on it.

docs.google.com

What Could Gifted Education Look Like?

What Could Gifted Education Look Like? Simon Rubinstein-Salzedo Introduction The purpose of this essay is to investigate what gifted education could look like, if we decided as a society that we car...

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 09/03/2025

This is one reason you should never use an indefinite integral. Instead, always use a definite integral, possibly with variable bounds.

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 25/01/2025

Applications to teach at Kaleidoscope are due in one week! Apply to teach physics, AI, CS, or something else to amazing high-school students who aim to become professionals in your chosen area. Ideal candidates will be able to teach in Palo Alto weekly and will have a PhD. www.kalcircles.com/hiring

kalcircles.com

Hiring — Kaleidoscope Circles

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 19/01/2025

Do you wish you could do my job? Do you want to teach physics, computer science, or artificial intelligence to outstanding kids? Apply to teach at Kaleidoscope Circles at www.kalcircles.com/hiring! Applications are due February 1.

kalcircles.com

Hiring — Kaleidoscope Circles

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 30/12/2024

New paper up by Euler Circle alum and TA Andrew Lin: arxiv.org/pdf/2412.19730

arxiv.org

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 28/12/2024

🎓 Seeking teacher to develop & lead college-level classes at Kaleidoscope! Focus areas: AI/AI safety, CS, physics (other fields possible). Teach the classes you've always dreamed of to talented high school students. Like Euler Circle, but for your field. Apply by Feb 1 at kalcircles.com.

kalcircles.com

Kaleidoscope Circles

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 25/12/2024

Recommend your favorite videos of math talks that you think I'll enjoy!

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 16/12/2024

New paper by Euler Circle student Anay Aggarwal: arxiv.org/pdf/2412.05857

arxiv.org

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 06/12/2024

The quote about standing on the shoulders of giants is most commonly attributed to Isaac Newton. But it goes back further, to Bernard of Chartres and William of Conches in the 12th century. en.wikipedia.org/wiki/Standin...

en.wikipedia.org

Standing on the shoulders of giants - Wikipedia

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 03/12/2024

My new institute, Kaleidoscope, is now up and running! This is an extension of Euler Circle to subjects other than mathematics. We're looking to hire a director of a new circle, likely AI/AI safety, CS, or physics. Please encourage people you know to apply! www.kalcircles.com

kalcircles.com

Kaleidoscope Circles

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Simon Rubinstein-Salzedo @complexzeta.bsky.social · 03/12/2024

New paper by Euler Circle alumna and TA Emma Cardwell: arxiv.org/pdf/2412.00895.

arxiv.org

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