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Mathematics
Math Meets QFT
The Mystery at the Heart of Physics That Only Math Can Solve
The accelerating effort to understand the mathematics of quantum field theory will have profound consequences for both math and physics.
geometry
Mathematicians Identify Threshold at Which Shapes Give Way
A new proof establishes the boundary at which a shape becomes so corrugated, it can be crushed.
Insights puzzle
How a Simple Arithmetic Puzzle Can Guide Discovery
Playing with numbers can lead to deep mathematical and scientific insights.
Q&A
A Number Theorist Who Connects Math to Other Creative Pursuits
Jordan Ellenberg enjoys studying — and writing about — the mathematics underlying everyday phenomena.
polynomials
Mathematicians Find Long-Sought Building Blocks for Special Polynomials
Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them.
combinatorics
Mathematicians Answer Old Question About Odd Graphs
A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections.
mathematical physics
New Black Hole Math Closes Cosmic Blind Spot
A mathematical shortcut for analyzing black hole collisions works even in cases where it shouldn’t. As astronomers use it to search for new classes of hidden black holes, others wonder: Why?
topology
How Mathematicians Use Homology to Make Sense of Topology
Originally devised as a rigorous means of counting holes, homology provides a scaffolding for mathematical ideas, allowing for a new way to analyze the shapes within data.
Quantized Academy
How to Solve Equations That Are Stubborn as a Goat
Math teachers have stymied students for hundreds of years by sticking goats in strangely shaped fields. Learn why one grazing goat problem has stumped mathematicians for more than a century.