A very positive review of my ergodic theory book has now appeared in the American Math Monthly. See simonrs.com/ETbookreview... to read it!
25.10.2025 18:31 ā š 1 š 0 š¬ 0 š 0@complexzeta.bsky.social
Mathematician. Founder and director of Euler Circle and Kaleidoscope Circles.
A very positive review of my ergodic theory book has now appeared in the American Math Monthly. See simonrs.com/ETbookreview... to read it!
25.10.2025 18:31 ā š 1 š 0 š¬ 0 š 0Another 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.
25.09.2025 04:23 ā š 3 š 0 š¬ 0 š 0So 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.
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!
03.06.2025 17:01 ā š 0 š 0 š¬ 0 š 0My copies of the ergodic theory book just arrived!
07.05.2025 19:44 ā š 1 š 0 š¬ 0 š 0I 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.
28.04.2025 17:42 ā š 1 š 0 š¬ 0 š 0Our 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.
20.04.2025 19:41 ā š 1 š 0 š¬ 0 š 0Many people find Euler's identity e^{iĻ}=-1 or e^{iĻ}+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.
20.04.2025 19:41 ā š 1 š 0 š¬ 1 š 0But 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.
20.04.2025 19:41 ā š 1 š 0 š¬ 1 š 0I 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.
20.04.2025 19:41 ā š 1 š 0 š¬ 1 š 0Should 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.
20.04.2025 19:41 ā š 2 š 0 š¬ 1 š 0I 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.
20.04.2025 19:17 ā š 1 š 0 š¬ 0 š 0Also, every book title has to start with "An Introduction to" or "A First Course in" or "Elementary."
19.04.2025 16:25 ā š 2 š 0 š¬ 0 š 0Last 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.
08.04.2025 19:42 ā š 2 š 0 š¬ 0 š 0This is one reason you should never use an indefinite integral. Instead, always use a definite integral, possibly with variable bounds.
09.03.2025 16:27 ā š 1 š 0 š¬ 0 š 0Coming soon! bookstore.ams.org/view?Product...
03.03.2025 00:18 ā š 9 š 1 š¬ 0 š 0Applications 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
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.
19.01.2025 22:52 ā š 1 š 0 š¬ 0 š 0Come back, both of you!
12.01.2025 00:10 ā š 2 š 0 š¬ 1 š 0New paper up by Euler Circle alum and TA Andrew Lin: arxiv.org/pdf/2412.19730
30.12.2024 16:46 ā š 4 š 1 š¬ 0 š 0š 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.
28.12.2024 16:14 ā š 1 š 0 š¬ 0 š 0Recommend your favorite videos of math talks that you think I'll enjoy!
25.12.2024 14:03 ā š 1 š 0 š¬ 0 š 0I just learned about a hilarious sorting algorithm: sleep sort.
www.geeksforgeeks.org/sleep-sort-i...
New paper by Euler Circle student Anay Aggarwal: arxiv.org/pdf/2412.05857
16.12.2024 01:26 ā š 3 š 0 š¬ 0 š 0The 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...
06.12.2024 16:22 ā š 2 š 0 š¬ 0 š 0My 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
New paper by Euler Circle alumna and TA Emma Cardwell: arxiv.org/pdf/2412.00895.
03.12.2024 16:48 ā š 1 š 0 š¬ 0 š 0