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Without a Proof, Mathematicians Wonder How Much Evidence Is Enough
A new statistical model appears to undermine long-held assumptions in number theory. How much should it be trusted when all that really matters is proof?
Scientists Learn the Ropes on Tying Molecular Knots
As chemists tie the most complicated molecular knot yet, biophysicists create a “periodic table” that describes what kinds of knots are possible.
The (Imaginary) Numbers at the Edge of Reality
Odd enough to potentially model the strangeness of the physical world, complex numbers with “imaginary” components are rooted in the familiar.
A Proof About Where Symmetries Can’t Exist
In a major mathematical achievement, a small team of researchers has proven Zimmer’s conjecture.
How Equality and Inequality Shape the Birds and the Bees
Two dynamic, seemingly opposing forces likely played an important role in the evolution of reproduction and child rearing in social animals like bees and humans.
Graduate Student Solves Quantum Verification Problem
Urmila Mahadev spent eight years in graduate school solving one of the most basic questions in quantum computation: How do you know whether a quantum computer has done anything quantum at all?
Titans of Mathematics Clash Over Epic Proof of ABC Conjecture
Two mathematicians have found what they say is a hole at the heart of a proof that has convulsed the mathematics community for nearly six years.
Why Mathematicians Can’t Find the Hay in a Haystack
In math, sometimes the most common things are the hardest to find.
Solution: ‘Evolutionary Math and Just-So Stories’
How much stock should we put in mathematical models of evolution that have not been validated by rigorous empirical data?