@isomorphismes3

actual papers tweeted by @isomorphisms

isomorphismes.tumblr.com/tagged/mathematics
Joined November 2019
  • Tweets2.2K
  • Following50
  • Followers41
1Media
Notice how short the good old papers are?
1
5
Tait colorings, and an instanton homology for webs and foams P. B. Kronheimer T. S. Mrowka arxiv.org/abs/1508.07205 Cambridge, Mass. • 2015
Другая планета
@nihilunboundedOct 25
Thanks for the question! I don't think about the four color theorem; I try not to comment on things I don't understand (although a proof along the lines of Kronheimer-Mrowka would be awesome; see arxiv.org/abs/1508.07205) But in general I think (and of course, sinxe I am a nobody, you can vehemently disagree) a proof should be redefined to be something that brings insight and understanding, and not (just) a verifiable collection of symbols that lead to a certain truth value of the original statement. This may require overturning a century and a half of mathematician's conception of what constitutes a proof, but I think it is a worthwhile endeavour (and I also think the alternative is paperclip universe where LLM slop rules math and very few people understand wtf is going on). I think a computer assisted proof can do that (eg I have used SnapPy before). I think some nontrivial amount of rich mathematics is lost in this great project to pin down mathematics to the domain of dry formalism. This is most noxiously evident in LLM proofs with an autoformalized Lean certificate.

Tait colorings, and an instanton homology for webs and foams

We use SO(3) gauge theory to define a functor from a category of unoriented webs and foams to the category of finite-dimensional vector spaces over the field of two elements. We prove a...

arxiv.org
1
1
15
"We use SO(3) gauge theory to define a functor from a category of unoriented webs and foams to the category of finite-dimensional vector spaces over the field of two elements. … non-vanishing … for this SO(3) instanton homology of webs, using Gabai's sutured manifold theory."
1
8
Ray-marching Thurston geometries arxiv.org/html/2010.15801v2 Rémi Coulon / Rennes Elisabetta A. Matsumoto / Atlanta Henry Segerman / Stillwater, Oklahoma Steve J. Trettel / Stanford, Calif. Providence, Rhode Island • 2019–20
1
146
primary sources retweeted
5+ years of experience@isomorphedOct 13
After the JD: First Results of a National Study of Legal Careers NALP Foundation American Bar Foundation americanbarfoundation.org/wp… Chicago, IL Overland Park, Kansas • 2004
1
1
2
122
primary sources retweeted
5+ years of experience@isomorphedOct 13
Socioeconomic Diversity of the Matriculating US Medical Student Body by Race, Ethnicity, and Sex, 2017-2019 Arman A Shahriar Vikram V Puram Jonathan M Miller Varun Sagi Lorenzo Adolfo Castañón-Gonzalez Shailendra Prasad Renée Crichlow pmc.ncbi.nlm.nih.gov/article…

Socioeconomic Diversity of the Matriculating US Medical Student Body by Race, Ethnicity, and Sex,...

This survey study compares the socioeconomic composition of the 2017 to 2019 matriculating medical student body with that of the US population, by self-identified race and ethnicity and by sex.

pmc.ncbi.nlm.nih.gov
1
1
79
An algorithm for the machine calculation of complex Fourier series by James W. Cooley and John W. Tukey pubs.ams.org/MCOM/1965-19-09… IBM / Bell Labs / Princeton • New York / New Jersey • 1965
1
69
primary sources retweeted
Antoine Ducros@antoineducrosSep 27
Replying to @plumsirawit @littmath
I do not know if it will really answer your question but this text written by a prominent world-class expert of the topic is certainly worth reading. terrytao.wordpress.com/2026/…

The status of the Hodge conjecture

[This is a guest post by Claire Voisin. This blog post was initially written in a different file format and converted using AI. — T.] Hodge classes can be defined on any compact complex manif…

terrytao.wordpress.com
1
5
1
5
1,422
New monotile in 3d! arxiv.org/abs/2609.24779v1

Notes on a strongly aperiodic monotile in $E^3$

We provide a clearer presentation of the Chair44 monotile, a new strongly aperiodic monotile in three-dimensional Euclidean space $E^3$.

arxiv.org
2
1
4
356
A Memoir on the Theory of Matrices Arthur Cayley • 1858 jstor.org/stable/108649 Philosophical Transactions of the Royal Society of London, Vol. 148 (1858), pp. 17-37 (21 pages)

A Memoir on the Theory of Matrices | JSTOR

Arthur Cayley, A Memoir on the Theory of Matrices, Philosophical Transactions of the Royal Society of London, Vol. 148, 1858

jstor.org
1
42
Remarques sur la notation des fonctions algébriques. eudml.org/doc/147616 A. Cayley Journal für die reine und angewandte Mathematik (1855) Volume: 50, pages 282–285
1
1
49
The ubiquity of braids Tara Brendle youtu.be/qnmTcE5-HpI?is=tI8l… Oxford • 2024

The Ubiquity of Braids - Tara Brendle

What do maypole dancing, grocery delivery, and the quadratic formul...

youtube.com
1
1
171
primary sources retweeted
David Pfau@pfauSep 7
Replying to @ViewToATweet @spacefeudalist @isomorphisms
Well it turns out that it's extremely hard. arxiv.org/abs/1306.5709

Physical Principles for Scalable Neural Recording

Simultaneously measuring the activities of all neurons in a mammalian brain at millisecond resolution is a challenge beyond the limits of existing techniques in neuroscience. Entirely new...

arxiv.org
2
1
1
385
arXiv:2112.06186 (cs) [Submitted on 12 Dec 2021] Nalin: Learning from Runtime Behavior to Find Name-Value Inconsistencies in Jupyter Notebooks Jibesh Patra, Michael Pradel arxiv.org/abs/2112.06186

Nalin: Learning from Runtime Behavior to Find Name-Value...

Variable names are important to understand and maintain code. If a variable name and the value stored in the variable do not match, then the program suffers from a name-value inconsistency, which...

arxiv.org
1
33
primary sources retweeted
Rahul Saha@rah4927Aug 14
Our papers: Grothendieck bounds: arxiv.org/abs/2608.11158 AI for long-horizon mathematical research: arxiv.org/abs/2608.11195 Would love to hear any thoughts on the math or the research process; don’t hesitate to reach out.

New Lower and Upper Bounds for the Grothendieck Constant

We establish new bounds on the Grothendieck constant $K_G$: \[ \frac{6π}{11} \le K_G \le \fracπ{2\log(1+\sqrt2)} - 10^{-4}. \] Methodologically, our lower bound approach differs...

arxiv.org
4
20
1
143
7,950
primary sources retweeted
Rahul Saha@rah4927Aug 14
The Grothendieck constant is 1.7...! We are excited to share this breakthrough on a 70 year-old problem discovered through a year-long human-AI collaboration. We publish both the math and AI setup because academics should shape AI-assisted research to keep it fundamentally human.
39
222
31
1,845
163,873
masatohagiwara.net/recto.htm… "Recto is a 2D programming language that uses nested rectangles as its core syntax, encoding structure and recursion directly in space instead of a linear stream of text. Recto explores new ways to write, parse, and reason about code—and even natural language—spatially."

Recto — a truly 2D language

Recto is a 2D programming language that uses nested rectangles as its core syntax, encoding structure and recursion directly in space instead of a linear stream of text. Recto explores new ways to...

masatohagiwara.net
1
1
68
cs.cornell.edu/courses/cs612… CS 6120 is a PhD-level Cornell CS course by Adrian Sampson on programming language implementation. It covers universal compilers topics like intermediate representations, data flow, and “classic” optimizations as well as more research-flavored topics such as parallelization, just-in-time compilation, and garbage collection. The work consists of reading papers and open-source hacking tasks, which use LLVM and an educational IR invented just for this class.
1
1
1
102
primary sources retweeted
Antonio Lupetti
@antoniolupettiAug 2
"Understanding Transformers and Attention Mechanisms" is a very interesting paper that presents the Transformer architecture from the perspective of applied mathematics. It starts by representing text as vectors and explains mathematically how the attention mechanism processes these vectors to encode contextual information. It then develops Multi-Head Attention and shows how the main components of the Transformer architecture are constructed. The paper also discusses more recent methods designed to reduce the computational and memory costs of attention, including KV caching, Grouped Query Attention, and Latent Attention. I think it is a useful reference for anyone interested in understanding Transformers beyond their high-level architecture and in seeing the linear algebra behind modern language models. arxiv.org/pdf/2604.00965
22
429
15
2,695
232,592
primary sources retweeted
Greg Egan@gregeganSFJul 27
“The Burau representation of the braid group is faithful for n = 4” Vasudha Bharathram, Joan S. Birman, Tara E. Brendle arxiv.org/abs/2607.05283 I learned this from: scientificamerican.com/artic… See also: en.wikipedia.org/wiki/Braid_… en.wikipedia.org/wiki/Burau_…

The Burau representation of the braid group is faithful for n = 4

In this paper we use ideas introduced earlier by Moody, Long, Long-Paton, and Bigelow to prove the theorem of the title, that the Burau representation of the classical braid group is faithful for...

arxiv.org
1
7
1
180
18,506
primary sources retweeted
Andrew Conner
@connerdelightsJul 21
Terence Tao posted his ChatGPT session trying to understand the Jacobian conjecture counterexample. It's so lovely reading a slice of how his mind works, the connections he's making, etc. chatgpt.com/share/6a5fdc7a-d…
89
401
123
4,574
1,252,851
Load more