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126 posts86 participants8 posts today
Hi!
Here is a new hectoc challenge for you:
633283
The goal is to combine the 6 numbers to a total of 100. You can use the mathematical operations + - * / ^ and the parenthesis ( ). Numbers can be combined, but you have to use all 6 of them and are not allowed to change the order. See https://hectoc.seism0saurus.de for an example. Please use CW "solution".
Have fun! Your hourly hectoc bot
by @seism0saurus
hectoc.seism0saurus.deHectoc
LeanAgent: Lifelong learning for formal theorem proving. ~ Adarsh Kumarappan, Mo Tiwari, Peiyang Song, Robert Joseph George, Chaowei Xiao, Anima Anandkumar. https://arxiv.org/abs/2410.06209 #LLMs #ITP #LeanProver #Math
arXiv.orgLeanAgent: Lifelong Learning for Formal Theorem ProvingLarge Language Models (LLMs) have been successful in mathematical reasoning tasks such as formal theorem proving when integrated with interactive proof assistants like Lean. Existing approaches involve training or fine-tuning an LLM on a specific dataset to perform well on particular domains, such as undergraduate-level mathematics. These methods struggle with generalizability to advanced mathematics. A fundamental limitation is that these approaches operate on static domains, failing to capture how mathematicians often work across multiple domains and projects simultaneously or cyclically. We present LeanAgent, a novel lifelong learning framework for formal theorem proving that continuously generalizes to and improves on ever-expanding mathematical knowledge without forgetting previously learned knowledge. LeanAgent introduces several key innovations, including a curriculum learning strategy that optimizes the learning trajectory in terms of mathematical difficulty, a dynamic database for efficient management of evolving mathematical knowledge, and progressive training to balance stability and plasticity. LeanAgent successfully generates formal proofs for 155 theorems across 23 diverse Lean repositories where formal proofs were previously missing, many from advanced mathematics. It performs significantly better than the static LLM baseline, proving challenging theorems in domains like abstract algebra and algebraic topology while showcasing a clear progression of learning from basic concepts to advanced topics. In addition, we analyze LeanAgent's superior performance on key lifelong learning metrics. LeanAgent achieves exceptional scores in stability and backward transfer, where learning new tasks improves performance on previously learned tasks. This emphasizes LeanAgent's continuous generalizability and improvement, explaining its superior theorem-proving performance.
13 mars 1925 : #CeJourLà naissance de John Tate (†16/10/2019), mathématicien américain dont les travaux portent essentiellement sur la théorie algébrique des nombres et la géométrie algébrique. Il a reçu plusieurs distinctions dont les prix Abel et Wolf.
https://fr.wikipedia.org/wiki/John_Tate_(math%C3%A9maticien)
#mathématiques #maths #math
fr.wikipedia.orgJohn Tate (mathématicien) — Wikipédia
One day, one decomposition
A202267: Numbers in which all digits are noncomposites (1, 2, 3, 5, 7) or 0
3D graph, threejs - webGL 
https://decompwlj.com/3Dgraph/A202267.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A202267.html
This simple math puzzle has lingered in my mind over a decade because it has such a surprising answer. How would you solve it and explain the result?
In a class of 500 students, 99% are right-handed. How many right-handers should leave the class to make it 98%?
You can check my blog for the solution and an intuitive explanation.
Just BeingEasy math puzzle with an unbelievable answer | Just BeingThe answer to this problem is so surprising that it has lingered in my mind for decades. Try to solve it before looking at the answer. How would you explain the solution intuitively?
Mathle 1144 3/5
mathlegame.com
#mathle #mathlegame #math #game #puzzle
"The world and its phenomena can be understood through a mathematical approach. This is an empirical fact that we can only acknowledge." – Jean-Philippe Uzan (1969–)
#quote #mathematics #math #maths
How do you turn an endless number into a catchy tune? 
π
For Pi Day, former teachers LaMar Queen and David Landix rap about the mysterious 3.14159...a number that connects every circle in the universe. This #music #video celebrates both the mathematical constant and birthday boy Albert Einstein on March 14th.
Learn more: https://thekidshouldseethis.com/post/march-14th-is-pi-day-3-14-a-pi-day-music-video
"Le monde et ses phénomènes sont compréhensibles par une approche mathématique. C’est un fait empirique dont nous ne pouvons que prendre acte." – Jean-Philippe Uzan (1969–)
#citation #mathématiques #maths #math
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@wadabadah how dare you nerd-snipe ME at work!
also calling reinforcements from...
#math #maths #integral #calculus
When I transitioned from cognitive to computational neuroscience, I found myself in a bit of a bind. I had learned calculus, but I had progressed little beyond pattern recognition: I knew which rules to apply to find solutions to which equations, but the equations themselves lacked any sort of real meaning for me.
So I struggled with understanding how formulas could be implemented in code and why the code I was reading could be described by those formulas. Resources explaining math “for neuroscientists” were unfortunately quite useless for me, because they usually presented the necessary equations for describing various neural systems, assuming the presence of that basic understanding/intuition I lacked.
Of course, I figured things out eventually (otherwise I wouldn’t be writing about it), but I’m 85% sure I’m not the only one who’s ever struggled with this, and so I wrote the tutorial I wish I could’ve had. If you’re in a similar position, I hope you’ll find it useful. And if not, maybe it helps you get a glimpse into the struggles of the non-math people in your life. Either way, it has cats.
Neurofrontiers · Building a virtual neuron - part 1 - Neurofrontiers
More from 
neuronerd
Theorem of the Day (March 12, 2025) : The Pythagorean Theorem
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/GeometryAndTrigonometry/Pythagoras/TotDPythagoras.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#27
A formal proof of the irrationality of ζ(3) in Lean 4. ~ Junqi Liu, Jujian Zhang, Lihong Zhi. https://arxiv.org/abs/2503.07625 #ITP #LeanProver #Math
arXiv.orgA Formal Proof of the Irrationality of $ζ(3)$ in Lean 4We present a formal proof of the irrationality of $ζ(3)$ in Lean 4, based on Beuker's method. In addition, we contribute to the Mathlib library by formalizing shifted Legendre polynomials and several key results in analytic number theory, addressing gaps in Lean's analytical capabilities. As part of the Prime Number Theorem project in Lean 4, we formalize the asymptotic behavior of the prime counting function, which is essential for proving the irrationality of $ζ(3)$.
