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elliptic curves
cryptography
‘Post-Quantum’ Cryptography Scheme Is Cracked on a Laptop
Two researchers have broken an encryption protocol that many saw as a promising defense against the power of quantum computing.
number theory
Mathematicians Prove 30-Year-Old André-Oort Conjecture
A team of mathematicians has solved an important question about how solutions to polynomial equations relate to sophisticated geometric objects called Shimura varieties.
Quantized Academy
How to Find Rational Points Like Your Job Depends on It
Using high school algebra and geometry, and knowing just one rational point on a circle or elliptic curve, we can locate infinitely many others.
number theory
Mathematicians Set Numbers in Motion to Unlock Their Secrets
A new proof demonstrates the power of arithmetic dynamics, an emerging discipline that combines insights from number theory and dynamical systems.
Langlands program
‘Amazing’ Math Bridge Extended Beyond Fermat’s Last Theorem
Mathematicians have figured out how to expand the reach of a mysterious bridge connecting two distant continents in the mathematical world.
Multimedia
The Map of Mathematics
Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.
Quantized Academy
Where Proof, Evidence and Imagination Intersect
In mathematics, where proofs are everything, evidence is important too. But evidence is only as good as the model, and modeling can be dangerous business. So how much evidence is enough?
Abstractions blog
New Proof Shows Infinite Curves Come in Two Types
Alexander Smith’s work on the Goldfeld conjecture reveals fundamental characteristics of elliptic curves.
number theory
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?