The Brain A Mathematical Model Unlocks the Secrets of VisionQuanta Magazine - Kevin Hartnett Mathematicians and neuroscientists have created the first anatomically accurate model that explains how vision is possible. This is the great mystery …

The Puzzling Search for Perfect RandomnessQuanta Magazine - Pradeep Mutalik Does objective, perfect randomness exist, or is randomness merely a product of our ignorance? Life is unpredictable, and random things happen to us …

New Proof Settles How to Approximate Numbers Like PiQuanta Magazine - Kevin Hartnett The ancient Greeks wondered when “irrational” numbers can be approximated by fractions. By proving the longstanding Duffin-Schaeffer conjecture, two …

Color Me PolynomialQuanta Magazine - Patrick Honner Polynomials aren’t just exercises in abstraction. They’re good at illuminating structure in surprising places. In 2015, the poet-turned-mathematician …

Software Development Decades-Old Computer Science Conjecture Solved in Two PagesQuanta Magazine - Erica Klarreich The “sensitivity” conjecture stumped many top computer scientists, yet the new proof is so simple that one researcher summed it up in a single …

How Randomness Can Make Math EasierQuanta Magazine - Kevin Hartnett Randomness would seem to make a mathematical statement harder to prove. In fact, it often does the opposite. Of all the tools available to the …

Mathematics Random Surfaces Hide an Intricate OrderQuanta Magazine - Kevin Hartnett Mathematicians have proved that a random process applied to a random surface will yield consistent patterns.

When Magic Is Seen in Twisted Graphene, That’s a MoiréQuanta Magazine - Pradeep Mutalik What do moiré patterns seen in optics, art, photography and color printing have to do with superconducting layers of graphene?

Mathematics A 53-Year-Old Network Coloring Conjecture Is DisprovedQuanta Magazine - Erica Klarreich In just three pages, a Russian mathematician has presented a better way to color certain types of networks than many experts thought possible. A paper …

Mathematics A Mathematician Whose Only Constant Is ChangeQuanta Magazine - Kevin Hartnett Amie Wilkinson searches for exotic examples of the mathematical structures that describe change.

Mathematics Why the Proof of Fermat’s Last Theorem Doesn’t Need to Be EnhancedQuanta Magazine - Michael Harris Decades after the landmark proof of Fermat’s Last Theorem, ideas abound for how to make it even more reliable. But such efforts reflect a deep …

Geometry How Geometry, Data and Neighbors Predict Your Favorite MoviesQuanta Magazine - Patrick Honner A little high school geometry can help you understand the basic math behind movie recommendation engines. Adrienne is a Marvel movie fanatic: Her …

Out of a Magic Math Function, One Solution to Rule Them AllQuanta Magazine - Erica Klarreich Mathematicians used “magic functions” to prove that two highly symmetric lattices solve a myriad of problems in eight- and 24-dimensional space. Three …

Quanta MagazineQuanta Magazine - Robbert Dijkgraaf It’s an educated guess, not a proof. But a good conjecture will guide math forward, pointing the way into the mathematical unknown. Mountain climbing …

Mathematicians Discover the Perfect Way to MultiplyQuanta Magazine - Kevin Hartnett By chopping up large numbers into smaller ones, researchers have rewritten a fundamental mathematical speed limit. Four thousand years ago, the …

Usain Bolt’s Split Times and the Power of CalculusQuanta Magazine - Steven Strogatz Just how fast can the fastest human run? This adapted book excerpt from Infinite Powers reveals how calculus helps us investigate the nature of …

Proof Finds That All Change Is a Mix of Order and RandomnessQuanta Magazine - Kevin Hartnett All descriptions of change are a unique blend of chance and determinism, according to the sweeping mathematical proof of the “weak Pinsker …

Science Sum-of-Three-Cubes Problem Solved for ‘Stubborn’ Number 33Quanta Magazine - John Pavlus A number theorist with programming prowess has found a solution to 33 = x³ + y³ + z³, a much-studied equation that went unsolved for 64 …

Maps Math Duo Maps the Infinite Terrain of Minimal SurfacesQuanta Magazine - Erica Klarreich A pair of mathematicians has built on an obscure, 30-year-old mathematical theory to show that soap-filmlike minimal surfaces appear abundantly in a …

Where Proof, Evidence and Imagination Intersect in Math | Quanta MagazineQuanta Magazine - Patrick Honner In mathematics, where proofs are everything, evidence is important too. But evidence is only as good as the model, and modeling can be dangerous …

Möbius Strips Defy a Link With InfinityQuanta Magazine - Evelyn Lamb A new proof shows why an uncountably infinite number of Möbius strips will never fit into a three-dimensional space. In math, three-dimensional space …

How to Find Simple Treasures in Complex NumbersQuanta Magazine - Pradeep Mutalik In spite of their name, “imaginary” numbers are as real as any other numbers, especially when it comes to hunting for lost treasure. For our first …

Smaller Is Better: Why Finite Number Systems Pack More Punch | Quanta MagazineQuanta Magazine - Kevin Hartnett Recent progress on the “sum product” problem recalls a celebrated mathematical result that revealed the power of miniature number systems. It’s one …

Mathematics How a Strange Grid Reveals Hidden Connections Between Simple NumbersQuanta Magazine - Kevin Hartnett A long-standing puzzle seems to constrain how addition and multiplication relate to each other. A graduate student has gone further than anyone else …

Equations The Trouble With TurbulenceQuanta Magazine - Michael Moyer Turbulence is everywhere, yet it is one of the most difficult concepts for physicists to understand. Fluids should be easy. They’re ordinary, …

A Movement to Close the Gender Gap in MathematicsQuanta Magazine - Siobhan Roberts The Brazilian mathematician Carolina Araujo, who calls herself “a bit of an anarchist,” is organizing meetings and building a support network to …

Unscrambling the Hidden Secrets of Superpermutations | Quanta MagazineQuanta Magazine - Patrick Honner A science fiction novelist and an internet commenter made breakthroughs on a longstanding problem about the number of ways you can arrange a set of …

Crossword Puzzles Quanta’s Science and Math Crossword Puzzle | Quanta MagazineQuanta Magazine - Pradeep Mutalik Celebrate a year’s worth of scientific and mathematical insights by solving this brain-teasing cryptic crossword from our puzzle columnist. Last …

Quanta’s Year in Math and Computer Science (2018) | Quanta MagazineQuanta Magazine - Michael Moyer Several mathematicians under the age of 30, and amateur problem-solvers of all ages, made significant contributions to some of the most difficult …