number theory – Quanta Magazine

The Chinese remainder theorem is an ancient and powerful extension of the simple math of least common multiples. The post What Hot Dogs Can Teach Us About Number Theory first appeared on Quanta Magazine

Ana Caraiani seeks to unify mathematics through her work on the ambitious Langlands program. The post The Mathematician Who Delights in Building Bridges first appeared on Quanta Magazine

New work establishes a tighter connection between the rank of a polynomial and the extent to which it favors particular outputs. The post Mathematicians Find Structure in Biased Polynomials first appeared on Quanta Magazine

Legend says the Chinese military once used a mathematical ruse to conceal its troop numbers. The technique relates to many deep areas of modern math research. The post How Ancient War Trickery Is Alive in Math Today first appeared on Quanta Magazine

Using high school algebra and geometry, and knowing just one rational point on a circle or elliptic curve, we can locate infinitely many others. The post How to Find Rational Points Like Your Job Depends on It first appeared on Quanta Magazine

Laurent Fargues and Peter Scholze have found a new, more powerful way of connecting number theory and geometry as part of the sweeping Langlands program. The post New Shape Opens ‘Wormhole’ Between Numbers and Geometry first appeared on Quanta Magazine

Jordan Ellenberg enjoys studying — and writing about — the mathematics underlying everyday phenomena. The post A Number Theorist Who Connects Math to Other Creative Pursuits first appeared on Quanta Magazine

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. The post Mathematicians Find Long-Sought Building Blocks for Special Polynomials first appeared on Quanta Magazine

Despite finding no specific examples, researchers have proved the existence of a pervasive kind of prime number so delicate that changing any of its infinite digits renders it composite. The post Mathematicians Find a New Class of Digitally Delicate Primes first appeared on Quanta Magazine

Enter the world of perfect numbers and explore the mystery mathematicians have spent thousands of years trying to solve. The post The Mysterious Math of Perfection first appeared on Quanta Magazine

A new proof demonstrates the power of arithmetic dynamics, an emerging discipline that combines insights from number theory and dynamical systems. The post Mathematicians Set Numbers in Motion to Unlock Their Secrets first appeared on Quanta Magazine

A group of MIT undergraduates is searching for tetrahedra that tile space, the latest effort in a millennia-long inquiry. They’ve already made a new discovery. The post Undergraduates Hunt for Special Tetrahedra That Fit Together first appeared on Quanta Magazine

Four mathematicians have cataloged all the tetrahedra with rational angles, resolving a question about basic geometric shapes using techniques from number theory. The post Tetrahedron Solutions Finally Proved Decades After Computer Search first appeared on Quanta Magazine

A number theorist recalls his first encounter with the Riemann hypothesis and breaks down the math in a new Quanta video. The post How I Learned to Love and Fear the Riemann Hypothesis first appeared on Quanta Magazine

Even as mathematicians and computer scientists proved big results in computational complexity, number theory and geometry, computers proved themselves increasingly indispensable in mathematics. The post The Year in Math and Computer Science first appeared on Quanta Magazine

The p -adics form an infinite collection of number systems based on prime numbers. They’re at the heart of modern number theory. The post An Infinite Universe of Number Systems first appeared on Quanta Magazine

Despite recent progress on the notorious Collatz conjecture, we still don’t know whether a number can escape its infinite loop. The post The Simple Math Problem We Still Can’t Solve first appeared on Quanta Magazine

For millennia, mathematicians have wondered whether odd perfect numbers exist, establishing an extraordinary list of restrictions for the hypothetical objects in the process. Insight on this question could come from studying the next best things. The post Mathematicians Open a New Front on an Ancient Number Problem first appeared on Quanta Magazine

A powerful technique called SAT solving could work on the notorious Collatz conjecture. But it’s a long shot. The post Computer Scientists Attempt to Corner the Collatz Conjecture first appeared on Quanta Magazine

Two mathematicians have proved the first leg of Paul Erdős’ all-time favorite problem about number patterns. The post Landmark Math Proof Clears Hurdle in Top Erdős Conjecture first appeared on Quanta Magazine