The Simple Math Behind the Mighty Roots of Unity

If you’ve ever taken an algebra or physics class, then you’ve met a parabola, the simple curve that can model how a ball flies through the air. The most important part of a parabola is the vertex — its highest or lowest point — and there are many mathematical techniques for finding it. You can try vertex form, or the axis of symmetry, or even calculus....

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Single Cells Evolve Large Multicellular Forms in Just Two Years

To human eyes, the dominant form of life on Earth is multicellular. These cathedrals of flesh, cellulose or chitin usually take shape by following a sophisticated, endlessly iterated program of development: A single microscopic cell divides, then divides again, and again and again, with each cell taking its place in the emerging tissues, until there...

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Mathematician Answers Chess Problem About Attacking Queens

If you have a few chess sets at home, try the following exercise: Arrange eight queens on a board so that none of them are attacking each other. If you succeed once, can you find a second arrangement? A third? How many are there? This challenge is over 150 years old. It is the earliest version of a mathematical question called the n-queens problem whose...

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Mathematical Analysis of Fruit Fly Wings Hints at Evolution’s Limits

Two years ago, to prepare for an unusual photo shoot, a team of scientists plucked the wings from thousands of fruit flies and pressed each flake of iridescent tissue between glass plates. As often as not, the wing tore or folded, or an air pocket or errant piece of dust got trapped along with it, ruining the sample. Fly wings are “not like Saran wrap,”...

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Biologists Rethink the Logic Behind Cells’ Molecular Signals

Back in 2000, when Michael Elowitz of the California Institute of Technology was still a grad student at Princeton University, he accomplished a remarkable feat in the young field of synthetic biology: He became one of the first to design and demonstrate a kind of functioning “circuit” in living cells. He and his mentor, Stanislas Leibler, inserted...

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A Massive Subterranean ‘Tree’ Is Moving Magma to Earth’s Surface

Réunion, a French island in the western Indian Ocean, is like a marshmallow hovering above the business end of a blowtorch. It sits above one of Earth’s mantle plumes — a tower of superheated rock that ascends from the deep mantle and flambés the bases of tectonic plates, the jigsaw pieces that make up the ever-changing face of the world. The plume’s...

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How Ancient War Trickery Is Alive In Math Today

Imagine you’re a general in ancient times and you want to keep your troop counts secret from your enemies. But you also need to know this information yourself. So you turn to a math trick that allows you to achieve both aims. In a morning drill you ask your soldiers to line up in rows of five. You note that you end up with three soldiers in the last...

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The Journey to Define Dimension

The notion of dimension at first seems intuitive. Glancing out the window we might see a crow sitting atop a cramped flagpole experiencing zero dimensions, a robin on a telephone wire constrained to one, a pigeon on the ground free to move in two and an eagle in the air enjoying three. But as we’ll see, finding an explicit definition for the concept...

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New Math Book Rescues Landmark Topology Proof

One of the most important pieces of mathematical knowledge was on the verge of being lost, maybe forever. Now, a new book hopes to save it. The Disc Embedding Theorem rewrites a proof completed in 1981 by Michael Freedman — about an infinite network of discs — after years of solitary toil on the California coast. Freedman’s proof answered a question...

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Karen Miga Fills In the Missing Pieces of Our Genome

In 1990, an international team of scientists began an ambitious attempt to sequence the human genome. By 2001 the Human Genome Project (HGP) had prepared a rough draft, and in April 2003, the draft sequence was declared finished. But Karen Miga, a geneticist now at the University of California, Santa Cruz and the associate director of the UCSC Genomics...

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