3+ mon, 3+ week ago (398+ words) Some Mathematicians Don't Believe in Infinity Can "finitism" possibly describe the real world? By Manon Bischoff edited by Daisy Yuhas That concept doesn't sound particularly surprising. Even small children can grasp the basic principle. But Cantor realized that infinitely large quantities can be compared in this way. Using set theory, he came to the conclusion that there are infinities of different sizes. Infinity is not always the same as infinity; some infinities are larger than others. Mathematicians Ernst Zermelo and Abraham Fraenkel used set theory to give mathematics a foundation at the beginning of the 20th century. Before then subfields such as geometry, analysis, algebra and stochastics were largely in isolation from each other. Fraenkel and Zermelo formulated nine basic rules, known as axioms, on which the entire subject of mathematics is now based. One such axiom, for example, is the…...

2+ week, 6+ day ago (116+ words) Researchers spot the "tipping point" before mathematicians" moments of discovery By Matthew Hutson edited by Sarah Lewin Frasier If you want to know when mathematicians are about to have a breakthrough, you don"t need to look inside their heads. Just watch their movements at a chalkboard. Georgetown University psychologist Shadab Tabatabaeian, the paper"s lead author, imagines a "cool application" of their method: someday computer interfaces that track mouse or eye movements might know when not to disturb someone on the brink of a breakthrough or when to toss a new idea their way. Matthew Hutson is a freelance science writer based in New York City and author of The 7 Laws of Magical Thinking....

7+ mon, 3+ week ago (419+ words) Scientific American is the essential guide to the most awe-inspiring advances in science and technology, explaining how they change our understanding of the world and shape our lives. For a long time, the Kakeya conjecture, which involves rotating an infinitely narrow needle, kept mathematicians guessing'until now By Manon Bischoff edited by Daisy Yuhas Suppose there is an infinitely narrow needle on a table. Now you want to rotate it 360 degrees so that the tip of the needle points once in each direction of the plane. To do this, you can hold the needle in the middle and rotate it. As it rotates, the needle then covers the surface of a circle. Years later, mathematician Abram Besicovitch made an unexpected discovery. If you keep moving the needle back and forth like a complex parallel parking maneuver, the surface that the infinitely…...

2+ week, 4+ day ago (673+ words) How to Identify a Prime Number without a Computer For years, a French mathematician searched for a proof that a gigantic number is prime. His method is still used 150 years later By Manon Bischoff edited by Daisy Yuhas Is 170,141,183,460,469,231,731,687,303,715,884,105,727 prime? Before you ask the Internet for an answer, can you consider how you might answer that question without a computer or even a digital calculator? In the 1800s French mathematician "douard Lucas spent years proving that this 39-digit number was indeed prime. How did he do it? Lucas, who incidentally also designed the entertaining game Tower of Hanoi, developed a method that's still useful today, more than a century later. And math enthusiasts are constantly seeking new prime numbers. The current record (as of October 2025) for the largest prime is 2136,279,841 " 1, a number with 41,024,320 digits. Simply reading this number aloud would take…...

3+ mon, 1+ week ago (531+ words) Math Breakthroughs from Behind Bars People in prisons and jails have contributed to some of the greatest ideas in mathematics By Manon Bischoff edited by Daisy Yuhas In 2014 Mura Yakerson, a college student at the time, decided to practice driving in a quiet area in the countryside near Saint Petersburg, Russia. Then something went wrong. While she was pulling out of a parking space, Yakerson accidentally damaged another car. This incident turned out to be the beginning of a nightmare. Yakerson is not alone. Several renowned mathematicians gained invaluable experience despite the challenges of incarceration. As the ancient Greek philosopher and historian Plutarch noted while describing the accomplishments of the scholar Anaxagoras, "There is no place that can take away the happiness of man, nor yet his virtue or wisdom." In the fifth century B.C.E., Greek philosopher Anaxagoras refused to recognize…...

8+ mon, 4+ day ago (673+ words) Kashiwara introduced proven methods from algebra into analysis'the theory underlying calculus that explores functions, limits and other concepts'and, together with his colleagues, founded an entirely ... Abel Prize Goes to Pioneer Whose "Math Toolbox" Can Be Used to Describe the Natural World Masaki Kashiwara, this year's Abel Prize winner, co-founded a new field of mathematics called algebraic analysis By Manon Bischoff edited by Gary Stix Masaki Kashiwara'Abel Prize Laureate 2025. Peter Badge/Typos1/The Abel Prize One of the landmarks of Kyoto, the home of mathematician Masaki Kashiwara, is the Kamo River. At certain points, there are stepping stones that allow residents to cross the river away from the bridges. If you take a closer look at these stones, you can see how the water forms swirls and small eddies around them. Describing this flow of a liquid is not easy. You have…...

9+ mon, 3+ week ago (321+ words) The Wild and Contentious History of Mathematical Symbols A mathematician has uncovered the stories behind the symbols used in math By Max Springer edited by Clara Moskowitz Scientific American spoke to Rojas about this history, the deeply engaging humanity of mathematics and the egos at play in defining the mathematical language we take for granted today. [An edited transcript of the interview follows.] What inspired you to write this book about the stories behind these symbols? Throughout the book, you discuss symbols that ultimately failed to become the standard en route to the notation we know today. How were these things decided? Is there a particular symbol in the history of mathematics that significantly influenced how we think about abstract concepts? There is one symbol, which has an incredibly long history that has not yet been fully written: "0." How did…...

11+ mon, 1+ week ago (807+ words) Mysterious Constant that Makes Mathematicians Despair The proof that the Ap'ry constant is irrational remains one of the most bizarre events in the history of mathematics By Manon Bischoff edited by Daisy Yuhas Mathematicians attended Roger Ap'ry's lecture at a French National Center for Scientific Research conference in June 1978 with a great deal of skepticism. The presentation was entitled "On the Irrationality of "(3)," which caused quite a stir among experts. The value of the zeta function "(3) had been an open question for more than 200 years. The brilliant Swiss mathematician Leonhard Euler had cut his teeth on it and failed to solve it. Now Ap'ry, a French mathematician who was relatively unknown and in his 60s at the time, had claimed to have solved this centuries-old riddle. Many in the audience had doubts. But someone in attendance had an electronic calculator'an uncommon…...

6+ mon, 3+ week ago (761+ words) Scientific American is the essential guide to the most awe-inspiring advances in science and technology, explaining how they change our understanding of the world and shape our lives. Zero Is Foundational to Modern Mathematics. But It Was Rejected for Centuries Conceptual problems, ideology clashes and xenophobia prevented the concept of zero from catching on for a long time. Today all mathematics is based on it By Manon Bischoff edited by Daisy Yuhas I'm a zero at mental arithmetic. It's true'I struggle with this skill'but I want to focus on the phrase itself. In our language, we often equate zero with something negative. But zero is the only real number that is neither positive nor negative. It is neutral. Why the negative association? Humankind has long harbored strong feelings toward zero; it was even banned in some places at one point....

1+ day, 22+ hour ago (239+ words) Math Puzzle: The Ancient City The mathematician, who liked to annoy friends with improvised brainteasers, thought for a moment or two, then raised a glass and recited: A rose-red city half as old as Time.One billion years ago the city's ageWas just two fifths of what Time's age will beA billion years from now. Can you computeHow old the crimson city is today? The English professor had long ago forgotten algebra and quickly shifted the conversation to another topic, but readers of this department should have no difficulty with the problem. The rose-red city's age is seven billion years. Let x be the city's present age and y be the present age of Time. A billion years ago the city would have been x " 1 billion years old, and a billion years from now Time's age will be y + 1. The…...