My decomposition? (Reddit - r/math - new- 5 day ago)
My decomposition? (Reddit - r/math - new- 5 day ago)
Generation of four sequences decomposed into weight × level + jump (log(weight), log(level), log(jump)) - three.js animation:
1: The natural numbers (A000027) https://decompwlj.com/3DgraphGen/Natural_numbers.html
One day, one decomposition
A001494: Numbers k such that phi(k) = phi(k+2)
3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A001494.html
3D graph Gen, threejs animation https://decompwlj.com/3DgraphGen/A001494.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A001494.html
Generation of four sequences decomposed into weight × level + jump (log(weight), log(level), log(jump)) - three.js animation:
1: The natural numbers (A000027) https://decompwlj.com/3DgraphGen/Natural_numbers.html
One day, one decomposition
A001481: Numbers that are the sum of 2 squares
3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A001481.html
3D graph Gen, threejs animation https://decompwlj.com/3DgraphGen/A001481.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A001481.html
These are clever people: Quantum Scientists Building New Math of Cryptography
https://www.quantamagazine.org/quantum-scientists-have-built-a-new-math-of-cryptography-20250725/
One-way function
https://en.wikipedia.org/wiki/One-way_function
Quantum cryptography
https://en.wikipedia.org/wiki/Quantum_cryptography
Permanent (mathematics)
https://en.wikipedia.org/wiki/Permanent_(mathematics)
♯P-completeness of 01-permanent
https://en.wikipedia.org/wiki/%E2%99%AFP-completeness_of_01-permanent
Heute ist #Neumond, sagt mein mechanischer #Mondrechner "Meton". Und der muss es wissen.
https://www.thomasweibel.ch/?post=rechner-aus-dem-drucker
@paulfoerster #moon #fullmoon #history #antiquity #archaeology #astronomy #greece #babylon #mathematics #physics #astrophysics #mechanics #simulation #opendata #openglam #openeducation #3dprint #cad #digitalhumanities
Generation of four sequences decomposed into weight × level + jump (log(weight), log(level), log(jump)) - three.js animation:
1: The natural numbers (A000027) https://decompwlj.com/3DgraphGen/Natural_numbers.html
Theorem of the Day (July 25, 2025) : The Analyst’s Travelling Salesman Theorem
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/GeometryAndTrigonometry/ATST/TotDATST.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#108
One day, one decomposition
A001463: Partial sums of A001462; also a(n) is the last occurrence of n in A001462
3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A001463.html
3D graph Gen, threejs animation https://decompwlj.com/3DgraphGen/A001463.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A001463.html
One day, one decomposition
A001359: Lesser of twin primes
3D graph, threejs - webGL https://decompwlj.com/3Dgraph/Lesser_twin_primes.html
3D graph Gen, threejs animation https://decompwlj.com/3DgraphGen/Lesser_twin_primes.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/Lesser_twin_primes.html
A neat little trig relationship arose in class today.
In answering a question some students "panicked" and chucked it into "solve" in their TI Nspire graphics calculator (let's not get distracted by my hatred of such tech) and as part of the solution got:
π/2 - arctan(1/10)
Whereas if one did it (very simply) by hand, this term was:
arctan(10)
One hopes anyone marking this would understand they're the same, but it baffled the students... queue learning moment. 1/n
"In the hopes that these systems are someday released to outside review, here are some questions that we hope some day will be answered.
- How do these systems work and how were they trained? What allows them to do so much better than earlier systems? Do they come with a cost in solving other sorts of problems? In the case of OpenAI-IMO, do the "new techniques" employed at all explain the stylistic weirdness?
- What is the scope of these systems? Do they generalize to other kinds of mathematical problems, to scientific problems, to more general classes of problems? Or can they be extended to deal with these? Or would they be a useful component in a larger system that dealt with these?
- What was the cost per problem, both for inference time (clearly high) and any domain-specific expertise required for training/augmentation etc and what would the economics of using these models be when it is released?
- Are these system compatible with tools such as computational tools, coding, and web search?
- What did the two systems do with problem 6, the one they couldn’t correctly answer? Did they give up, did they produce a partial answer that was in the right direction, or did they hallucinate a nonsensical answer?
Overall, the new work certainly might be exciting. Until outside scientists get to dig for a serious review we won’t really know for sure what it all means."
https://garymarcus.substack.com/p/deepmind-and-openai-achieve-imo-gold
Google's AI models and OpenAI's models have reportedly achieved a significant milestone by winning gold medals at the International Mathematical Olympiad.
Generation of four sequences decomposed into weight × level + jump (log(weight), log(level), log(jump)) - three.js animation:
1: The natural numbers (A000027) https://decompwlj.com/3DgraphGen/Natural_numbers.html
Good for her!
She looks like she isn't Aryan. When will the Republican-American dictatorship send its goon squad to neutralize this threat?
Gemini Deep Think learns math, wins gold medal at International Math Olympiad
https://arstechnica.com/ai/2025/07/google-deepmind-earns-gold-in-international-math-olympiad-with-new-gemini-ai/
#AI #artificialintelligence #Google #DeepMind #DeepThink #mathematics #NLP
Now this animation is available for the 1000 sequences decomposed on my website.
Accessible from the 3Dgraph, 2Dgraph500terms and 2dgraphs pages https://decompwlj.com
A little more work on axis sizing and controls.