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What Is Math’s Mysterious Langlands Program Really About?
Hidden correspondences hint at a deeper structure to the mathematical universe. Our columnist unpacks one of those connections and asks mathematicians what they might mean.
Graduate Student Proves a Quantum Uncertainty Principle for Fractals
The math, which combines chaos, quantum theory, and infinitely complex fractal structures, has been called a “foundational result.”
Living Fully in the Math World Means Threading the Needle
Focus, commitment, and insight resulted in a “once in a century” proof. Hong Wang is now just the third woman to win a Fields Medal.
Networks Hold the Key to a Decades-Old Problem About Waves
Mathematicians are still trying to understand fundamental properties of the Fourier transform, one of their most ubiquitous and powerful tools. A new result marks an exciting advance toward that goal.
What Is the Fourier Transform?
Amid the chaos of revolutionary France, one man’s mathematical obsession gave way to a calculation that now underpins much of mathematics and physics. The calculation, called the Fourier transform, decomposes any function into its parts.
At 17, Hannah Cairo Solved a Major Math Mystery
After finding the homeschooling life confining, the teen petitioned her way into a graduate class at Berkeley, where she ended up disproving a 40-year-old conjecture.
Graduate Student Solves Classic Problem About the Limits of Addition
A new proof illuminates the hidden patterns that emerge when addition becomes impossible.
‘Once in a Century’ Proof Settles Math’s Kakeya Conjecture
The deceptively simple Kakeya conjecture has bedeviled mathematicians for 50 years. A new proof of the conjecture in three dimensions illuminates a whole crop of related problems.
Monumental Proof Settles Geometric Langlands Conjecture
In work that has been 30 years in the making, mathematicians have proved a major part of a profound mathematical vision called the Langlands program.