math
Why Some Animals Can Tell More From Less
Researchers find that densely packed neurons play an outsize role in quantitative skill—calling into question old assumptions about evolution.
Euler’s 243-Year-Old ‘Impossible’ Puzzle Gets a Quantum Solution
A surprising new solution to the famous “36 officers puzzle” offers a novel way of encoding quantum information.
At the Dawn of Life, Heat May Have Driven Cell Division
A mathematical model shows how a thermodynamic mechanism could have made protocells split in two.
The Algorithm That Lets Particle Physicists Count Higher Than 2
Through his encyclopedic study of the electron, an obscure figure named Stefano Laporta found a handle on the subatomic world’s fearsome complexity.
Cosmologists Close in on Logical Laws for the Big Bang
Physicists are translating commonsense principles into strict mathematical constraints for how our universe must have behaved at the beginning of time.
A New Theory for Systems That Defy Newton’s Third Law
In nonreciprocal systems, “exceptional points” are helping researchers understand phase transitions and possibly other phenomena.
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Mathematicians Finally Prove That Melting Ice Stays Smooth
They now have a complete understanding of the complicated equations that model the motion of free boundaries, like the one between ice and water.
How Wavelets Let Researchers Transform and Understand Data
Built upon the ubiquitous Fourier transform, these mathematical tools allow unprecedented analysis of continuous signals.
The Mathematics of Cancel Culture
To add fractions, you find the least common denominator—a term that has a certain resonance in our age of mass cancellation.
‘Impossible’ Particle Adds a Piece to the Strong Force Puzzle
The unexpected discovery of the double-charm tetraquark gives physicists fresh insight into the strongest of nature’s fundamental forces.
A Mathematician Answers a 150-Year-Old Chess Problem
The n-queens problem is about finding how many different ways queens can be placed on a chessboard so that none attack each other.
A Mathematician's Guided Tour Through Higher Dimensions
The concept of a dimension seems simple enough, but mathematicians struggled for centuries to precisely define and understand it.
Pigeons, Curves, and the Traveling Salesperson Problem
Mathematician Ian Stewart explains the twisty history of combinatorial optimization.
Computer Scientists Find a Key Research Algorithm's Limits
The most widely used technique for optimizing values of a math function turns out to be a fundamentally difficult computational problem.
How Big Data Carried Graph Theory Into New Dimensions
Researchers are turning to the mathematics of higher-order interactions to better model the complex connections within their data.
How to Ace Physics Class (Even if You Don’t Ace Physics)
It’s back-to-school season, so here are some tips on getting the most out of college science courses.
Animals Can Count. How Far Does Their Number Sense Go?
Crows recently demonstrated an understanding of the concept of zero. It’s only the latest evidence of animals’ talents for numerical abstraction.
Mathematicians Prove a 2D Version of Quantum Gravity Works
In three towering papers, a team of mathematicians has worked out the details of Liouville quantum field theory, forging a bridge between math and physics.
Ranked Choice Voting Reveals the Weird Math of Elections
The New York City mayoral race could show whether a new way of measuring voter desires can actually be an alternate timeline for democracy.
The Mystery at the Heart of Physics—That Only Math Can Solve
The full picture of quantum field theory has long eluded physicists. Calling in mathematicians will have profound consequences for both fields.
What Makes Quantum Computing So Hard to Explain?
Before we can even begin to talk about these computers' potential applications, we need to understand the fundamental physics behind them.
Wait, Vaccine Lotteries Actually Work?
Ooh, the behavioral economists are going to be so smug about this.
What If Gravity Is Actually a Double Copy of Other Forces?
An enigmatic connection between the forces of nature is allowing physicists to explore the quantum side of gravity.
Mathematicians Settle the Erdős Coloring Conjecture
Fifty years ago, three mathematicians came up with a graph theory problem that they thought they might solve on the spot. A team has finally settled it.