Hacker NewsAn OpenAI model has disproved a central conjecture in discrete geometry
https://openai.com/index/model-disproves-discrete-geometry-conjecture/
#HackerNews #OpenAI #Disproof #DiscreteGeometry #MathResearch #AIInnovation
All elementary functions from a single binary operator
https://arxiv.org/abs/2603.21852
#HackerNews #elementaryfunctions #binaryoperator #mathresearch #arxiv #innovation #programming
All elementary functions from a single binary operator
A single two-input gate suffices for all of Boolean logic in digital hardware. No comparable primitive has been known for continuous mathematics: computing elementary functions such as sin, cos, sqrt, and log has always required multiple distinct operations. Here I show that a single binary operator, eml(x,y)=exp(x)-ln(y), together with the constant 1, generates the standard repertoire of a scientific calculator. This includes constants such as e, pi, and i; arithmetic operations including addition, subtraction, multiplication, division, and exponentiation as well as the usual transcendental and algebraic functions. For example, exp(x)=eml(x,1), ln(x)=eml(1,eml(eml(1,x),1)), and likewise for all other operations. That such an operator exists was not anticipated; I found it by systematic exhaustive search and established constructively that it suffices for the concrete scientific-calculator basis. In EML (Exp-Minus-Log) form, every such expression becomes a binary tree of identical nodes, yielding a grammar as simple as S -> 1 | eml(S,S). This uniform structure also enables gradient-based symbolic regression: using EML trees as trainable circuits with standard optimizers (Adam), I demonstrate the feasibility of exact recovery of closed-form elementary functions from numerical data at shallow tree depths up to 4. The same architecture can fit arbitrary data, but when the generating law is elementary, it may recover the exact formula.
LLMs Are Currently Not Helpful at All for Math Research: Hamkins
#HackerNews #LLMs #MathResearch #Hamkins #AIChallenges #MachineLearning
Clément CanonneYou: are a woman or gender minority who's curious about the #mathematics of waves 🌊 👋
You: would like to spend a life-changing week at Princeton IAS this May, for a lecture series on Waves, Wave Packets, and Their Interactions
Me: has good news! Apply by ⏰ Feb 6 for the Women and Mathematics program.
https://www.ias.edu/math/wam/wam-2026
Travel, food, lodging, and childcare are funded. Undergrads, grad students, and faculty are all eligible—there are two parallel tracks! #MathResearch #MathCommunity #MathPhysics
Almost all Collatz orbits attain almost bounded values
https://mathvideos.org/2023/terence-tao-almost-all-collatz-orbits-attain-almost-bounded-values/
#HackerNews #CollatzConjecture #Mathematics #TerenceTao #BoundedValues #MathResearch
Terence Tao: Almost all Collatz orbits attain almost bounded values – MathVideos.org
Define the Collatz map Col on the natural numbers by setting Col(n) to equal 3n+1 when n is odd and n/2 when n is even. The notorious Collatz conjecture asserts that all orbits of this map eventually attain the value 1. This remains open, even if one is willing to work with almost all orbits…
Barcelona Dynamical SystemsLast Thursday July 17th our colleague Victor Mañosa presented our Research group at the Research Day of the Math Department at the Universitat Politècnica de Catalunya!
We keep doing research!
Graduate Student Solves Classic Problem About the Limits of Addition
#HackerNews #GraduateStudent #LimitsOfAddition #MathResearch #ProblemSolving #Innovation
A Formal Proof of Complexity Bounds on Diophantine Equations
https://arxiv.org/abs/2505.16963
#HackerNews #FormalProof #ComplexityBounds #DiophantineEquations #MathResearch #arXiv
A Formal Proof of Complexity Bounds on Diophantine Equations
We present a universal construction of Diophantine equations with bounded complexity in Isabelle/HOL. This is a formalization of our own work in number theory. Hilbert's Tenth Problem was answered negatively by Yuri Matiyasevich, who showed that there is no general algorithm to decide whether an arbitrary Diophantine equation has a solution. However, the problem remains open when generalized to the field of rational numbers, or contrarily, when restricted to Diophantine equations with bounded complexity, characterized by the number of variables $ν$ and the degree $δ$. If every Diophantine set can be represented within the bounds $(ν, δ)$, we say that this pair is universal, and it follows that the corresponding class of equations is undecidable. In a separate mathematics article, we have determined the first non-trivial universal pair for the case of integer unknowns. In this paper, we contribute a formal verification of the main construction required to establish said universal pair. In doing so, we markedly extend the Isabelle AFP entry on multivariate polynomials, formalize parts of a number theory textbook, and develop classical theory on Diophantine equations in Isabelle. Additionally, our work includes metaprogramming infrastructure designed to efficiently handle complex definitions of multivariate polynomials. Our mathematical draft has been formalized while the mathematical research was ongoing, and benefitted largely from the help of the theorem prover. We reflect how the close collaboration between mathematician and computer is an uncommon but promising modus operandi.
Olivia A-CNew account, so new #introduction. Let's do it again!
I have a #MastersDegree in #ComputerScience and #ComputerEngineering. I went to #NMU for undergrad and #MSU for my graduate degree. I currently work at #UChicago for the #TMWCenter, which focuses on helping young children acquire language (and therefore other learning skills) faster.
In my spare time, I develop #OpenSourceSoftware such as
- a #SphinxDoc extension that embed #Fediverse comments on your page
- a library to talk to #ManifoldMarkets from native #Python
- a #PredictionMarket manager using the above
- a #transpiler from a subset of Python to #OpenStreetMaps's #OverpassQL
- bug fixes to many other projects, including #mypy, #base58, #attrs, #CPython, & more
I spend a fair bit of my time these days on #MathResearch, specifically into the #ThueMorse Sequence and its extensions.
I'm also a hobbyist editor on OpenStreetMap.
#Demisexual, #transfem, and happily engaged to my #enby sweetheart.
We have two cats: #OpheTheLoaf and #MayalaranTheCat (yes, from #StormlightArchive) See here for more on them!
I speak English fluently, Spanish haltingly, and am trying to learn Chinese
#queer #Chicago
I have a #MastersDegree in #ComputerScience and #ComputerEngineering. I went to #NMU for undergrad and #MSU for my graduate degree. I currently work at #UChicago for the #TMWCenter, which focuses on helping young children acquire language (and therefore other learning skills) faster.
In my spare time, I develop #OpenSourceSoftware such as
- a #SphinxDoc extension that embed #Fediverse comments on your page
- a library to talk to #ManifoldMarkets from native #Python
- a #PredictionMarket manager using the above
- a #transpiler from a subset of Python to #OpenStreetMaps's #OverpassQL
- bug fixes to many other projects, including #mypy, #base58, #attrs, #CPython, & more
I spend a fair bit of my time these days on #MathResearch, specifically into the #ThueMorse Sequence and its extensions.
I'm also a hobbyist editor on OpenStreetMap.
#Demisexual, #transfem, and happily engaged to my #enby sweetheart.
We have two cats: #OpheTheLoaf and #MayalaranTheCat (yes, from #StormlightArchive) See here for more on them!
I speak English fluently, Spanish haltingly, and am trying to learn Chinese
#queer #Chicago
Olivia A-C (@LivInTheLookingGlass)
These are our cats, #OpheTheLoaf and #MayalaranTheCat. Ophelia was originally my partner's, we live together full time now, and are an integrated family Fun facts about Ophelia: * She is missing a tooth, so her lip sometimes gets stuck open in a cute way * She has an "activation noise" that sounds kinda like a pigeon * She will often do 10/10 loafs, hence the nickname Some facts about Maya: * Her favorite hobby is judging the neighbors * She is very anxious * She has an incredibly dainty play style * She has a series of increasingly ridiculous nicknames: Mayalaran -> Maya -> Mayo -> Aioli -> Au Jus (Follow the hashtags if you want just my cats) #CatsOfMastodon #CatsOfFedi (📎8)
Olivia A-COh dang, my #introduction post is waaay out of date now. Let's do it again!
I have a #MastersDegree in #ComputerScience and #ComputerEngineering. I went to #NMU for undergrad and #MSU for my graduate degree. I currently work at #UChicago for the #TMWCenter, which focuses on helping young children acquire language (and therefore other learning skills) faster.
In my spare time, I develop #OpenSourceSoftware such as
- a library to talk to #ManifoldMarkets from native #Python
- a #PredictionMarket manager using the above
- a #transpiler from a subset of Python to #OpenStreetMaps's #OverpassQL
- bug fixes to many other projects, including #mypy, #base58, #attrs, #CPython, & more
I spend a fair bit of my time these days on #MathResearch, specifically into the #ThueMorse Sequence and its extensions.
I'm also a hobbyist editor on OpenStreetMap.
#Demisexual, #transfem, and happily engaged to my #enby sweetheart.
We have two cats: #OpheTheLoaf and #MayalaranTheCat (yes, from #StormlightArchive)
