Quanta MagazineMathematics With Category Theory, Mathematics Escapes From EqualityQuanta Magazine - Kevin Hartnett Two monumental works have led many mathematicians to avoid the equal sign. Their goal: Rebuild the foundations of the discipline upon the looser …

Quanta MagazinePuzzles Solution: ‘Perfect Randomness’Quanta Magazine - Pradeep Mutalik Is nature inherently random or is perfect randomness just an illusion based on our ignorance? In last month’s Insights column, we explored randomness …

Quanta MagazineMathematics Big Question About Primes Proved in Small Number SystemsQuanta Magazine - Kevin Hartnett The twin primes conjecture is one of the most important and difficult questions in mathematics. Two mathematicians have solved a parallel version of …

Quanta MagazineMathematics On Your Mark, Get Set, MultiplyQuanta Magazine - Patrick Honner The way you learned to multiply works, but computers employ a faster algorithm. This summer, battle lines were drawn over a simple math problem: 8 ÷ …

Quanta Magazine 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 …

Quanta Magazine 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 …

Quanta Magazine 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 …

Quanta Magazine 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 …

Quanta MagazineSoftware 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 …

Quanta Magazine 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 …

Quanta Magazine 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.

Quanta Magazine 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?

Quanta MagazineMathematics 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 …

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

Quanta MagazineMathematics 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 …

Quanta Magazine 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 …

Quanta Magazine 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 Magazine 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 …

Quanta Magazine 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 …

Quanta Magazine 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 …

Quanta MagazineMathematical Modeling 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 …

Quanta Magazine 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 …

Quanta Magazine 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 …

Quanta Magazine 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 …

Quanta Magazine 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 …

Quanta Magazine 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 …

Quanta Magazine 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 …

Quanta MagazineMathematics 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 …

Quanta Magazine 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, …