Richard Dedekind was a 19th-century mathematical giant, responsible for reshaping the field right down to its foundations. He was the first to give a rigorous definition of infinity; he also came up with the definition of the real numbers that …
Six years ago, Afonso Bandeira and Shuyang Ling were attempting to come up with a better way to discern clusters in enormous data sets when they stumbled into a surreal world. Ling realized that the equations they’d come up with …
In math, as in life, small choices can have big consequences. This is especially true in graph theory, a field that studies networks of objects and the connections between them. Here’s a little puzzle to help you see why. Given …
For decades, a simple question has haunted Máté Matolcsi, a professor at the Budapest University of Technology and Economics. How much of an infinite plane can you color in while making sure that no two colored points are exactly one …
In 1917, the Japanese mathematician Sōichi Kakeya posed what at first seemed like nothing more than a fun exercise in geometry. Lay an infinitely thin, inch-long needle on a flat surface, then rotate it so that it points in every …
So far this year, Quanta has chronicled three major advances in Ramsey theory, the study of how to avoid creating mathematical patterns. The first result put a new cap on how big a set of integers can be without containing …
Many complicated advances in research mathematics are spurred by a desire to understand some of the simplest questions about numbers. How are prime numbers distributed in the integers? Are there perfect cubes (like 8 = 23 or 27 = 33) …
In 1886 the mathematician Leopold Kronecker famously said, “God Himself made the whole numbers — everything else is the work of men.” Indeed, mathematicians have introduced new sets of numbers besides the ones used to count, and they have labored …
It has been an exhilarating year in combinatorics research. In early 2023, mathematicians were stunned when two of the biggest problems in the field were solved in as many months. Now, a third major question has fallen with a 14-page …
How will advances in computing transform human society?
MIT students contemplated this impending question as part of the Envisioning the Future of Computing Prize — an essay contest in which they were challenged to imagine ways that computing technologies could …
As with so much in mathematics, the proof started with coffee. In September 2019, Kathryn Mann of Cornell University visited Kingston, Ontario, to give a guest lecture at Queen’s University. Afterward, she sat down with her host, Thomas Barthelmé, for …
There has been a remarkable surge in the use of algorithms and artificial intelligence to address a wide range of problems and challenges. While their adoption, particularly with the rise of AI, is reshaping nearly every industry sector, discipline, and …
Huge libraries of drug compounds may hold potential treatments for a variety of diseases, such as cancer or heart disease. Ideally, scientists would like to experimentally test each of these compounds against all possible targets, but doing that kind of …
Mathematicians rejoice when they prove that seemingly impossible things exist. Such is the case with a new proof posted online in March by Cédric Pilatte, a first-year graduate student at the University of Oxford. Pilatte proved that it is possible …
Until recently, gerrymandered districts tended to stick out, identifiable by their contorted tendrils. This is no longer the case. “With modern technology, you can gerrymander pretty effectively without making your shapes very weird,” said Beth Malmskog, a mathematician at Colorado …
Have you ever admired how the slats of a hardwood floor fit together so cleanly, or how the hexagons underneath your bathroom rug perfectly meet up? These are examples of geometric tilings, arrangements of shapes that fit snugly together while …
A three-year recipient of MIT’s Emerson Classical Vocal Scholarships, senior Ananya Gurumurthy recalls getting ready to step onto the Carnegie Hall stage to sing a Mozart opera that she once sang with the New York All-State Choir. The choir conductor …
To study ocean currents, scientists release GPS-tagged buoys in the ocean and record their velocities to reconstruct the currents that transport them. These buoy data are also used to identify “divergences,” which are areas where water rises up from below …
In 2009, a pair of astronomers at the Paris Observatory announced a startling discovery. After building a detailed computational model of our solar system, they ran thousands of numerical simulations, projecting the motions of the planets billions of years into …
Minhyong Kim rejects being called an optimist, but he sounds an awful lot like one. “If we take reality exactly as it is, I don’t think we have any real grounds for pessimism,” he said in a recent conversation. That …