Behold Modular Forms, the ‘Fifth Fundamental Operation’ of Math
Modular forms are one of the most beautiful and mysterious objects in mathematics. What are they?
Why Mathematical Proof Is a Social Compact
Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach.
How Quantum Physicists Explained Earth’s Oscillating Weather Patterns
By treating Earth as a topological insulator — a state of quantum matter — physicists found a powerful explanation for the movements of the planet’s air and seas.
The Lawlessness of Large Numbers
Mathematicians can often figure out what happens as quantities grow infinitely large. What about when they are just a little big?
Mathematicians Discover Novel Way to Predict Structure in Graphs
Mathematicians probe the limits of randomness in new work estimating quantities called Ramsey numbers.
In New Paradox, Black Holes Appear to Evade Heat Death
The puzzling behavior of black hole interiors has led researchers to propose a new physical law: the second law of quantum complexity.
The Physicist Who Glues Together Universes
Renate Loll has helped pioneer a radically new approach to quantum gravity. She assumes that the fabric of space-time is a blend of all possible fabrics, and she has developed the computational tools needed to calculate the far-reaching implications of that assumption.
Physicists Create Elusive Particles That Remember Their Pasts
In two landmark experiments, researchers used quantum processors to engineer exotic particles that have captivated physicists for decades. The work is a step toward crash-proof quantum computers.
A New Idea for How to Assemble Life
If we want to understand complex constructions, such as ourselves, assembly theory says we must account for the entire history of how such entities came to be.
Why Mathematicians Re-Prove What They Already Know
It’s been known for thousands of years that the primes go on forever, but new proofs give fresh insights into how theorems depend on one another.