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MAA
The Importance of Community
Here is a 3-paragraph summary for mathopen.com:
Camille McKayle stepped into the role of Executive Director and CEO of the Mathematical Association o...
7h ago
Quanta Magazine
How Do You Take a Picture of a Black Hole?
# How Do You Take a Picture of a Black Hole?
Black holes are among the most mysterious objects in the universe, and for decades scientists believed p...
7h ago
Aperiodical
Double Maths First Thing: Issue 70
I don't have enough content from the article to write a complete and accurate summary. You've only shared the introduction/header section of the artic...
Yesterday
Quanta Magazine
How Spiders Spin ‘Silk Dope’ Into Nature’s Toughest Material
Here is a 3-paragraph summary of the article for mathopen.com:
Spider silk is one of the most remarkable materials in nature, combining incredible st...
Yesterday
Quanta Magazine
How Voting Is Like a Klein Bottle
# How Voting Is Like a Klein Bottle
Mathematicians have discovered a surprising connection between the way groups of people make collective decisions...
Oct 27
Nautilus
How Multiple Births Can Accelerate A Mother’s Biological Age
## How Pregnancy Affects a Mother's Biological Age
Pregnancy is one of the most physically demanding experiences a human body can go through. Growing...
Oct 24
For stochastic conservation laws with nonlocal interactions, does the rate of convergence in the nonlocal-to-local limit depend on the regularity of the initial data in a sharp and quantifiable way?
The nonlocal-to-local limit for stochastic conservation laws establishes that as the interaction kernel concentrates to a Dirac delta, solutions of nonlocal stochastic conservation laws converge to solutions of their local counterparts. However, the precise rate at which this convergence occurs, and...
Probability / Stochastic PDE
Open ProblemsView all →
Mathematical Logic and Set Theory
Does New Foundations set theory NF admit a natural well-ordering of its universe that is provably consistent without assuming large cardinal axioms?
New Foundations, the set theory invented by Quine in 1937, has a notoriously strange universe of sets governed by a stratification condition on formulas. While ...
7h ago
Mathematical Logic and Foundations
Does New Foundations set theory NF admit a natural hierarchy of proof-theoretic ordinals analogous to those of the Zermelo-Fraenkel subsystems, and if so how do they compare to the ordinals arising from iterated beta-model reflection?
New Foundations (NF), Quine's stratification-based alternative to ZF set theory, has resisted ordinal analysis for decades. While subsystems of second-order ari...
Yesterday
Probability / Stochastic PDEs
Does the non-local to local limit for stochastic conservation laws hold at the level of invariant measures when the noise is multiplicative and the kernel is not of convolution type?
The paper on non-local to local limits studies how solutions of stochastic conservation laws with non-local interaction kernels converge to solutions of local c...
Oct 28
Mathematical Logic and Set Theory
Does New Foundations set theory NF admit a natural well-ordering of its universe that is provable within NF itself, and if so what is the proof-theoretic ordinal of NF?
New Foundations, Quine's alternative set theory based on stratified comprehension, was proven consistent by Randall Holmes in a 2010 manuscript that is still un...
Oct 28
Probability
Does the product of random matrices satisfy a sharp cutoff phenomenon analogous to the coupon collector problem, and if so, what is the precise window of convergence to the limiting distribution?
The Berry-Esseen bounds for products of random matrices describe how quickly the distribution of a long matrix product converges to a Gaussian-type limit, but t...
Oct 27