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Harmonic analysis
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The Biggest Smallest Triangle Just Got Smaller
A new proof breaks a decades-long drought of progress on the problem of estimating the size of triangles created by cramming points into a square.
Mathematicians Solve Long-Standing Coloring Problem
A new result shows how much of the plane can be colored by points that are never exactly one unit apart.
New Proof Threads the Needle on a Sticky Geometry Problem
A new proof marks major progress toward solving the Kakeya conjecture, a deceptively simple question that underpins a tower of conjectures.
In Times of Scarcity, War and Peace, a Ukrainian Finds the Magic in Math
With her homeland mired in war, the sphere-packing number theorist Maryna Viazovska has become the second woman to win a Fields Medal in the award’s 86-year history.
In Music and Math, Lillian Pierce Builds Landscapes
Lillian Pierce wants to transform access to the world of mathematics, while making headway on problems that bridge the discrete and continuous.
Math’s ‘Oldest Problem Ever’ Gets a New Answer
A new proof significantly strengthens a decades-old result about the ubiquity of ways to represent whole numbers as sums of unit fractions.
How Wavelets Allow Researchers to Transform, and Understand, Data
Built upon the ubiquitous Fourier transform, the mathematical tools known as wavelets allow unprecedented analysis and understanding of continuous signals.
Out of a Magic Math Function, One Solution to Rule Them All
Mathematicians used “magic functions” to prove that two highly symmetric lattices solve a myriad of problems in eight- and 24-dimensional space.