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Quanta Magazine
Black Holes or Black Hole Stars? Astronomers Spar Over Webb Telescope’s ‘Little Red Dots.’
# Little Red Dots: A Cosmic Mystery
The James Webb Space Telescope has been capturing something unexpected across the early universe: tiny, faint red...
5h ago
Nautilus
Rope, Twine and Thread: Invisible Technologies of the Stone Age
# The Hidden Power of Ancient String
Long before metal tools or written language, early humans mastered one of the most transformative technologies i...
Sep 13
Quanta Magazine
Why Do These Fossil Shells Flip Their Spirals Every Few Millennia?
# The Flipping Shells Mystery
Foraminifera are tiny, ancient marine organisms that build spiral shells, and scientists have noticed something remarka...
Sep 12
Quanta Magazine
The Four-Color Theorem Gets a Rare New Proof
## A Classic Problem Gets Fresh Eyes
The Four-Color Theorem is one of mathematics' most famous results, stating that any map can be colored using jus...
Sep 11
Aperiodical
Double Maths First Thing: Issue 69
Here is a 3-paragraph summary of the article for mathopen.com:
Double Maths First Thing is a newsletter written by Colin, a mathematician dedicated t...
Sep 10
Quanta Magazine
What Is Math’s Mysterious Langlands Program Really About?
# The Langlands Program: Math's Grand Unified Theory
At the heart of modern mathematics lies a sweeping set of conjectures known as the Langlands Pro...
Sep 10
Does propagation of chaos hold for coloured epidemic models with heterogeneous infectivity when the infection kernel has long-range dependence, and if so, at what rate does the empirical measure converge to the mean-field limit?
The coloured epidemic paper establishes functional law of large numbers and propagation of chaos for structured epidemic models where individuals carry distinct types or colours affecting their susceptibility and infectivity. However, the results rely on kernels that decay fast enough to ensure well...
Probability
Open ProblemsView all →
Probability / Network Theory
Does the random walk mixing time on small-world networks in dimension d greater than or equal to 3 exhibit a sharp threshold as the rewiring probability crosses a critical value?
Small-world networks are constructed by taking a regular lattice in d dimensions and randomly rewiring or adding a small fraction of long-range edges. The rando...
Yesterday
Mathematical Logic / Proof Theory
What is the exact proof-theoretic strength of Fraisse's conjecture restricted to well-quasi-orders of finite width, and does it fall strictly between ATR0 and Pi11-CA0?
Fraisse's conjecture, now a theorem proved by Laver, states that the class of countable linear orders is well-quasi-ordered under embeddability. The reverse mat...
Yesterday
Constructive Mathematics and Logic
Does there exist a constructive proof that the arithmetic mean strictly exceeds the geometric mean for all distinct positive reals, without invoking the law of excluded middle or dependent choice?
The classical AM-GM inequality states that the arithmetic mean of distinct positive real numbers strictly exceeds their geometric mean, and this is provable in ...
Sep 13
Probability
Does propagation of chaos hold quantitatively for memory-dependent particle systems on the same timescales as their memoryless counterparts, and if so with what rate?
Consider a large system of interacting particles where each particle's future motion depends not only on its current position and interactions with others, but ...
Sep 12
Mathematical Logic and Quantum Foundations
Can every pair of compatible states on a quantum logic be simultaneously extended to a single state on the full algebra, and if not, what is the minimal algebraic obstruction?
This problem is open because the failure of distributivity in orthomodular lattices destroys the measure-theoretic machinery that resolves the analogous classic...
Sep 12