Mathematical Exploration and Discovery at Scale
https://terrytao.wordpress.com/2025/11/05/mathematical-exploration-and-discovery-at-scale/
#HackerNews #Mathematics #Exploration #Discovery #Scale #TerryTao
Chip Butty
and 2 others
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After decades of research, a seemingly unremarkable find retrieved from a Roman shipwreck proved to be a sensational scientific discovery, proving that the ancient Greeks were capable of making mechanical models of the cosmos. The Antikythera Mechanism is the world‘s first known analog computer.
https://blog.nationalmuseum.ch/en/2023/11/an-ancient-greek-computer/
My virtual replica:
https://www.thomasweibel.ch/anticythera2/
#history #sciencehistory #antiquity #archaeology #astronomy #digitalhumanities #mathematics #physics #astrophysics
[1/n] Continuing my work (see previous posts) about the geometric possibilities of the radiant number ρ (aka plastic ratio). Because it can serve as the base of a numeral system (just it and the golden ratio have this property among non-integers), every rectangle whose side ratio is a power of ρ can be decomposed into rectangles whose side ratio is a power of ρ. Particularly, if we take three consecutive powers of ρ we can make substitution tilings involving its corresponding rectangles. These properties are depicted in the first image. In the next images we see two possibilities regarding rectangles of ratios 1, ρ and ρ² (one just uses horizontal rectangles), and one for rectangles of ratios ρ, ρ² and ρ³. Of course any of these partitions, by rearranging/rotating/mirroring tiles, give many possible different tilings.
#Mathematics #geometry #tiling #mathart #radiantnumber
Substitutions for rectangles of side ratios ρ (purple colour), ρ² (green colour), and ρ³ (orange colour), .
Substitutions for rectangles of side ratios ρ⁰ = 1 (square, orange colour), ρ (purple colour) and ρ² (green colour), where rectangles are always put in horizontal position.
Substitutions for rectangles of side ratios ρ⁰ = 1 (square, orange colour), ρ (purple colour) and ρ² (green colour).
Seven colourful columns depict how each rectangle of ratio a power of the radiant number can be decomposed into rectangles of ratios in three consecutive powers of ρ.
After decades of research, a seemingly unremarkable find retrieved from a Roman shipwreck proved to be a sensational scientific discovery, proving that the ancient Greeks were capable of making mechanical models of the cosmos. The Antikythera Mechanism is the world‘s first known analog computer.
https://blog.nationalmuseum.ch/en/2023/11/an-ancient-greek-computer/
My virtual replica:
https://www.thomasweibel.ch/anticythera2/
#history #sciencehistory #antiquity #archaeology #astronomy #digitalhumanities #mathematics #physics #astrophysics
Beyond Smoothed Analysis: Analyzing the Simplex Method by the Book
https://arxiv.org/abs/2510.21613
#HackerNews #BeyondSmoothedAnalysis #SimplexMethod #AlgorithmResearch #Arxiv #Mathematics
The most accurate carotid artery model to date — the first to capture both the soft, low-pressure behavior and the stiff, high-pressure response of the vessel.
Built on the same principles as Fung’s law, but improved: our 2014 α–β framework fits strain energy first, then derives pressure — like how F = dE/dx gives the force in a spring. Here E is the strain energy — the quantity Fung’s law was originally built around. Strain energy is differentiated to give force, and in the fits below that force corresponds to pressure.
The 1987 plot below (Fung-type) fits well only at high pressures; the 2019 plot fits low pressures. Ours is the first to capture both perfectly.
#Biomechanics #MaterialScience #Physics #Mathematics #Modeling #Energy #Pressure #Research #Science #Innovation #london #askfedi
Emily Riehl is rewriting the foundations of higher category theory (2021)
#HackerNews #EmilyRiehl #HigherCategoryTheory #Mathematics #Innovation #Research
Charlie Stross
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Team claims to have Lean 4 proof that P≠NP
https://arxiv.org/abs/2510.17829
#HackerNews #PvsNP #Lean4 #Proof #Mathematics #ComputerScience #HackerNews
Team claims to have Lean 4 proof that P≠NP
https://arxiv.org/abs/2510.17829
#HackerNews #PvsNP #Lean4 #Proof #Mathematics #ComputerScience #HackerNews
Michał "rysiek" Woźniak · 🇺🇦
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Mathstodon.xyz is a Mastodon server for people who love mathematics. We have LaTeX rendering in the web interface!
This server has a post size of up to 1729 characters, and has been online since 2017.
You can find out more at https://mathstodon.xyz/about or contact the admin @christianp
#FeaturedServer #Mathematics #Maths #Math #Mastodon #Fediverse #FreeFediverse
Mathstodon.xyz is a Mastodon server for people who love mathematics. We have LaTeX rendering in the web interface!
This server has a post size of up to 1729 characters, and has been online since 2017.
You can find out more at https://mathstodon.xyz/about or contact the admin @christianp
#FeaturedServer #Mathematics #Maths #Math #Mastodon #Fediverse #FreeFediverse
OliverUv
boosted
The prompt for day 3 was 'Polyhedron'. In mathematics a 'convex polyhedron' is any subset of ℝ³ which can be obtained as the convex hull of finitely many noncoplanar points. However, when convexity is not required the definition of 'polyhedron' is in some dispute.
Certainly every convex polyhedron is a polyhedron, however there are multip-
On second thoughts, this post would be better expressed as an alignment chart meme.
The prompt for day 3 was 'Polyhedron'. In mathematics a 'convex polyhedron' is any subset of ℝ³ which can be obtained as the convex hull of finitely many noncoplanar points. However, when convexity is not required the definition of 'polyhedron' is in some dispute.
Certainly every convex polyhedron is a polyhedron, however there are multip-
On second thoughts, this post would be better expressed as an alignment chart meme.
STOP OCCUPATION 🍉 S. Costa
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I have a #science question. A major challenge in #climatology and climate models is reconstructing historical weather and climate data from incomplete and fragmentary data sets and many different sources. I know that there is a lot of thought put into these models, and that they largely do it well. But to outsiders, this process of reconstruction can often seem dubious and thus is frequently used to cased doubt against both these reconstructions and the field of climatology as a whole.
So what I could use for such discussions are other examples of mathematical reconstructions of historical datasets from fields _outside_ of climatology, to show that this is not a unique process but a widely used approach. Can anyone give me any suggestions?