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Mathematicians Attempt to Glimpse Past the Big Bang
By studying the geometry of model space-times, researchers offer alternative views of the universe’s first moments.
How Failure Has Made Mathematics Stronger
The topologist Danny Calegari discusses the inevitability of disappointment in math, and how to learn from it.
Strangely Curved Shapes Break 50-Year-Old Geometry Conjecture
Mathematicians have disproved a major conjecture about the relationship between curvature and shape.
A Rosetta Stone for Mathematics
In 1940 André Weil wrote a letter to his sister, Simone, outlining his vision for translating between three distinct areas of mathematics. Eighty years later, it still animates many of the most exciting developments in the field.
To Pack Spheres Tightly, Mathematicians Throw Them at Random
Four mathematicians broke a 75-year-old record by finding a denser way to pack high-dimensional spheres.
Mathematicians Marvel at ‘Crazy’ Cuts Through Four Dimensions
Topologists prove two new results that bring some order to the confoundingly difficult study of four-dimensional shapes.
Geometers Engineer New Tools to Wrangle Spacecraft Orbits
Mathematicians think abstract tools from a field called symplectic geometry might help with planning missions to far-off moons and planets.
Number of Distances Separating Points Has a New Bound
Mathematicians have struggled to prove Falconer’s Conjecture, a simple, but far-reaching, hypothesis about the distances between points. They’re finally getting close.
Merging Fields, Mathematicians Go the Distance on Old Problem
Mathematicians have illuminated what sets of points can look like if the distances between them are all whole numbers.