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Sridhar Ramesh Profile picture
Sridhar Ramesh
@RadishHarmers
Born Samuel Langhorne Clemens in rural Missouri. Adopted the pen name "Sridhar Ramesh" from riverboat slang.
Aug 7 • 14 tweets • 3 min read
Here we go. The compilation.
Jul 20 • 19 tweets • 4 min read
I've had a response sitting in my drafts since April 29, 2024, but for some reason I never posted it. Presumably because Twitter is the worst medium ever invented for discussing math. Still, here I go, clearing out my drafts: Image Before discussing the OP, I want to observe how I would prefer to think about this:
Feb 2 • 10 tweets • 6 min read
I've been playing with the new o3-mini-high model which came out this weekend, marketed as "Great at coding and logic". A surprising start to its chain of thought here.

(Some of you may enjoy thinking about this question yourself.) Image ChatGPT is not happy with me. How it started, how it ended. I unfortunately can no longer share a link to the full conversation but I'll share the salient points in posts below. Image
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Image
Oct 25, 2024 • 21 tweets • 5 min read
o1-mini (the latest OpenAI offering, ChatGPT with advanced reasoning skills) can be quite impressive, when you know the correct answers to accept and incorrect answers to reject. Here's a simple question, which some of you may enjoy figuring out. Image
Image Its answers in more detail. Can you figure out which is correct? Image
Image
Sep 15, 2024 • 64 tweets • 13 min read
Ok. Let's do this. Here's the full solution for the four people who care.

The previous discussion was here. You may want to read that first before this thread, but you don't need to. This new thread will be self-contained.

Mar 19, 2024 • 7 tweets • 2 min read
I find this clear now, like so (argument discovered by others such as @NoahJSnyder and @MtgJulian; I am only reframing or rewording it): Consider a random walk in which one takes equally likely steps of one unit up or one unit down, but with different distributions of speeds. (E.g., maybe up steps take one hour, while down steps have probability 1/2 of taking 2 hours, 1/4 of taking 3 hours, 1/8 of 4 hours, etc).
Mar 18, 2024 • 4 tweets • 1 min read
@llllvvuu @littmath @NoahJSnyder @MtgJulian Summarizing the proof you all devised:

A "tied" string has equally many HHs and HTs. A "flippy" string is tied of size > 1 starting and ending with H, with no such proper prefix. Reversal is a length-preserving involution exchanging flippy strings starting with HH vs. with HT. @llllvvuu @littmath @NoahJSnyder @MtgJulian Say S has base P if S is of the form PHQ, PH is tied, and HQ has no flippy prefix. As there are equally many Q of a given length starting with H vs. T, our above involution tells us there are equally many strings of a given length whose base is followed by HH vs. HT.
Oct 28, 2023 • 9 tweets • 1 min read
I condemn Hamas killing 1400 Israelis.

I condemn Israel killing 1400 Gazans.

I condemn Israel killing 1400 Gazans.

I condemn Israel killing 1400 Gazans.

I condemn Israel killing 1400 Gazans.

I condemn Israel killing 1400 Gazans. I condemn Israel killing 1400 Gazans.
Jul 13, 2020 • 11 tweets • 2 min read
One last desperate attempt to illustrate why unique prime factorization isn't just an obvious tautology:

Suppose you worked at a bank that only had quarters and dimes. There's lots of amounts of money you can pay out: You can make payments of a dollar, or $1.50, or $2.60, or 45¢, lots of things.
Jul 13, 2020 • 14 tweets • 3 min read
I gave one explanation but it's not my favorite. It's just the one that tied in with the discussion of fractions. I'll give another explanation I like much better: What are the last digits of the multiples of 4? Well, it goes like this: 0, 4, 8, 2, 6, 0, 4, 8, 2, 6, 0, 4, 8, 2, 6, ….
Sep 16, 2019 • 6 tweets • 1 min read
I often think there are two most basic, most ubiquitously applicable elementary mathematical insights that, for whatever reason, have not been included in standard curricula and which laypeople remain generally unaware of: 1. The greatest common factor of a collection of whole numbers is always obtainable by adding/subtracting multiples of those numbers (Bézout's theorem; Euclid's algorithm).