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‘A-Team’ of Math Proves a Critical Link Between Addition and Sets
A team of four prominent mathematicians, including two Fields medalists, proved a conjecture described as a “holy grail of additive combinatorics.”
The Deep Link Equating Math Proofs and Computer Programs
Mathematical logic and the code of computer programs are, in an exact way, mirror images of each other.
Alan Turing and the Power of Negative Thinking
Mathematical proofs based on a technique called diagonalization can be relentlessly contrarian, but they help reveal the limits of algorithms.
Why Mathematical Proof Is a Social Compact
Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach.
Complexity Theory’s 50-Year Journey to the Limits of Knowledge
How hard is it to prove that problems are hard to solve? Meta-complexity theorists have been asking questions like this for decades. A string of recent results has started to deliver answers.
How Math Achieved Transcendence
Transcendental numbers include famous examples like e and π, but it took mathematicians centuries to understand them.
The Colorful Problem That Has Long Frustrated Mathematicians
The four-color problem is simple to explain, but its complex proof continues to be both celebrated and despised.
How Do You Prove a Secret?
Zero-knowledge proofs allow researchers to prove their knowledge without divulging the knowledge itself.
Computer Science Proof Unveils Unexpected Form of Entanglement
Three computer scientists have posted a proof of the NLTS conjecture, showing that systems of entangled particles can remain difficult to analyze even away from extremes.