TotientQuotient
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totientquotient.bsky.social
TotientQuotient
@totientquotient.bsky.social
430 followers 410 following 350 posts
Survived tripos somehow. All effort, no skill. Still trying to become a mathematician. Probably suffering from some form of the Algernon-Gordon effect.

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totientquotient.bsky.social
My coauthor is absolutely cracked. She comes up with crazy ass combinatorial formulas like these. I dream to be just as good at this one day...

#MathSky
November 11, 2025 at 9:04 AM
totientquotient.bsky.social
my favorite player just won 2-0. good day to be watching chess :D
Wei Yi wins both games against Kacper Piorun in Round 2 of the FIDE World Cup. https://www.chess.com/events/2025-fide-world-cup/02-02/Piorun_Kacper-Wei_Yi
November 5, 2025 at 1:50 PM
totientquotient.bsky.social
This stupid meme is everywhere. Even my research couldn't escape the curse of gen alpha brainrot.

(For context, we proved that no such basis exists for n≥12, which is why our conjecture stops at n=11.)

#MathSky
It might seem that this pattern of choosing G and the H_λ's should easily generalize, but alas, no further bases with triangular transition matrices were found. Despite that, we found bases for n=6 and n=7, and we conjecture that we can find such a basis for n=8,9,10,11 as well.
November 5, 2025 at 1:12 PM
totientquotient.bsky.social
Best chess match I've watched in a hot minute.
The rollercoaster experience of spectating an unpredictable chess event is always something I look forward to after a long day, especially when Danya is commentating. Unfortunately he's no longer with us 💔
RIP Daniel Naroditsky 🙏
Fabiano beats Pragg 11-10 in Round 1 of the 2025 Speed Chess Championship
October 30, 2025 at 6:38 PM
totientquotient.bsky.social
You've heard of "proof by violent assertion" and "proof by authority", now get ready for "proof by wicked sorcery".
(Yes, this was a real excerpt from my submission to an undergrad assignment.)
#MathSky
to deduce that $\Sigma_{ij}=c^{|j-i|}\;\forall(i,j)\in\{1,2,...,n\}^2$. By some wicked sorcery, it follows that $\Sigma^{-1}$ is the tridiagonal matrix $$\Sigma^{-1}=\begin{pmatrix}s^{-2}&-cs^{-2}&0&0&\hdots&0&0&0\\-cs^{-2}&1+2c^2s^{-2}&-cs^{-2}&0&\hdots&0&0&0\\0&-cs^{-2}&1+2c^2s^{-2}&-cs^{-2}&\hdots&0&0&0\\0&0&-cs^{-2}&1+2c^2s^{-2}&\hdots&0&0&0\\\vdots&\vdots&\vdots&\vdots&\ddots&\vdots&\vdots&\vdots\\0&0&0&0&\hdots&1+2c^2s^{-2}&-cs^{-2}&0\\0&0&0&0&\hdots&-cs^{-2}&1+2c^2s^{-2}&-cs^{-2}\\0&0&0&0&\hdots&0&-cs^{-2}&s^{-2}\end{pmatrix}$$
September 26, 2025 at 3:40 PM
totientquotient.bsky.social
Just played my signature tactic once again, resulting in a 97% accuracy win in a 1+0 bullet game.
White to play. Find the top engine line for the next 6 moves (bonus challenge: the 3 moves thereafter) and refute every suboptimal black response.
#chess #chesspunks
FEN: rnbq1rk1/ppp1bppp/4p3/2np2P1/7P/1P1BP3/PBPP1P2/RN1QK1NR w KQ - 3 8
September 26, 2025 at 3:26 PM
totientquotient.bsky.social
Just published my first paper on arXiv and I'm already getting spam emails from predatory journals. "Dear Prof. Dr." when I'm neither a professor nor a PhD, lmao I can't 🤣🤣🤣

#AcademicSky #MathSky
Subject: [Q1 Journal | IF 2.5] Limited-Time APC Voucher for Selected Authors in Pure & Applied Mathematics Sender: gary@universalwiser.com Dear Prof. Dr., We are pleased to introduce Contemporary Mathematics, a peer-reviewed, Q1 journal with an Impact Factor of 2.5, publishing cutting-edge research across all areas of mathematics. The journal is indexed in ESCI (Web of Science), Scopus, and other major databases. You can learn more about the journal here: https://ojs.wiserpub.com/index.php/CM/ As part of our commitment to supporting high-quality mathematical research, we are delighted to offer you a limited-time APC voucher. This invitation is extended to a select group of authors recognized for their contributions in areas such as pure and applied mathematics. We warmly invite you to submit your next manuscript during the promotional period to enjoy both an APC discount and priority processing from review to publication.
September 23, 2025 at 8:35 AM
totientquotient.bsky.social
is this a good score for the graph isomorphism game (link in alt text)
https://github.ericmickelsen.com/graf/isomorphism.html
September 23, 2025 at 7:45 AM
totientquotient.bsky.social
Disquastung
September 15, 2025 at 2:40 PM
totientquotient.bsky.social
Nevermind, it's not over yet. Apparently the only move here is to sacrifice the knight and push a6, after which the best follow-up is to ignore the knight and play Ra4... And all of that just got played!
https://www.chess.com/events/2025-fide-grand-swiss-open/11/Bluebaum_Matthias-Firouzja_Alireza
September 15, 2025 at 12:48 PM
totientquotient.bsky.social
Ok ngl this looks over for Alireza. I don't see how black can keep pieces on the board without self-destructing. It looks like a dead draw, but then again what do I know about chess.
https://www.chess.com/events/2025-fide-grand-swiss-open/11/Bluebaum_Matthias-Firouzja_Alireza
September 15, 2025 at 12:23 PM
totientquotient.bsky.social
Arjun with the exchange sac 🔥🍿

#chess #chesspunks
https://www.chess.com/events/2025-fide-grand-swiss-open/11/Erigaisi_Arjun-Keymer_Vincent
September 15, 2025 at 12:03 PM
totientquotient.bsky.social
So this is how I found out that my institution affiliation expired on overleaf. Crazy how it took a whole year before overleaf figured out that I'm no longer at Cambridge lol
Your compile timed out Your project exceeded the compile timeout limit on our free plan. Upgrade to get more compile time (plus additional collaborators, document history, track changes, and more).
September 12, 2025 at 4:27 PM
totientquotient.bsky.social
I had 38 seconds on the clock when I got to this position in a bullet game. Can you find the forced checkmate within this time? (I didn't - chat, am I cooked?)

#chesspunks
r4rk1/1bpp2pp/1p2pnq1/8/2P5/P3PN1n/1B2BPPK/R2Q1R2 b - - 1 17
August 30, 2025 at 3:59 PM
totientquotient.bsky.social
Found an interesting MSE question (link in alt text)
#MathSky
https://math.stackexchange.com/questions/5089940/why-do-these-two-lines-have-the-same-probability-of-intersecting-the-circle
August 14, 2025 at 2:08 PM
totientquotient.bsky.social
How to say "thank you" in Spanish

#MathSky
grass c Papa Rudin
August 13, 2025 at 6:10 PM
totientquotient.bsky.social
I don't understand the intuition behind comultiplication in (co/bi)algebras. Yes I'm aware that it's the dual of multiplication, but categorical duality means nothing to me in terms of intuition. Is there a better explanation of how to find an expression for Δ(x) given μ?
#mathsky
Comultiplication in \mathbb{C}[x] is given by \Delta(x^n) = \sum_{i=1}^{n} x^i \otimes x^{n-i} which is what I don't get - this formula seems pulled out of a hat to me.
August 11, 2025 at 4:44 PM
totientquotient.bsky.social
I have a collection of roughly two dozen bullet games where I won using the exact same double bishop sacrifice. A certain GM might find this interesting or even disquastung, but it's all just opening prep.
August 9, 2025 at 4:18 PM
totientquotient.bsky.social
Board game: Chess
Card/party game: Avalon / One Night Ultimate Werewolf
Video game: Bloons Tower Defense (the entire series including BMC & Battles)
Favourite game(s)?
August 1, 2025 at 12:09 PM
totientquotient.bsky.social
This trend has been going viral on tw*tter so I'll cross-post my entry here as well.

Four math books that had a big influence on my mathematical thinking. Your turn.

#MathSky #AlgComb
July 30, 2025 at 8:50 AM
totientquotient.bsky.social
White to play.
Hint: eslw af fafw egnwk
#chess #chesspunks
r2n1k2/6p1/6Pp/8/5B2/3B4/2P3K1/r6R w
July 9, 2025 at 9:16 PM
totientquotient.bsky.social
Alright, since you asked, I composed a chess puzzle just for this occasion. See below:
Post more chess stuff
July 9, 2025 at 9:16 PM
totientquotient.bsky.social
I guess I should clarify. I haven't *confirmed* that I'm going into industry; I'm just saying that it's an extra option I've started considering in parallel to my attempts to get into grad school. As to what type of company/role(s) I'm setting my sights on, R&D in tech.
u said u were going into industry. what type of company/role ?
July 9, 2025 at 7:06 PM
totientquotient.bsky.social
that I know I can pass. Such as this one lol. I literally solved all 8 questions in my head in half an hour even though only 5 questions of our choice are marked. So it's just a matter of convincing others that there's more to my grades. Which can be a pretty tall task (as evidenced by my
(4/5)
sorry too lazy to alt text this so I'll just link the document: https://chrisj.math.gatech.edu/comps/25s/AlgebraCompSpring2025.pdf
July 9, 2025 at 6:56 PM
totientquotient.bsky.social
Yes I have considered other paths; in fact I'm currently applying for many careers in parallel, but at the same time I'm not giving up on math. Why? Because I like it (it's weird imagining myself doing something that isn't math), and it's not a sport where only the top few hundred players
(1/5)
Why do you insist on trying to stay in math academia after all your Cambridge setbacks? Have you considered letting it go and pursuing a different career? You're clearly an intelligent person who'd do well elsewhere, so I don't wanna see you suffer for a field that doesn't value you.
July 9, 2025 at 6:56 PM