Artificial intelligence is increasingly being used to solve the mathematical equations that describe the physical world, not only to recognize images or generate text. One promising approach, developed over the last decade, is the physics-informed neural network, or PINN: a type of neural network trained not on labeled examples but on the governing equations of […]
Authors: Sergi Muria Maldonado, Professor de Didàctica de les Matemàtiques, Universitat de Barcelona; Anton Aubanell Pou, Professor de l’Institut de Formació Continuada i professor jubilat de Didàctica de les Matemàtiques, Universitat de Barcelona, and Jordi Font González, Professor de Didàctica de les Matemàtiques, Universitat de Barcelona 2026 marks 100 years since the death of Antoni […]
Author: Melissa Lee, Senior Lecturer, School of Mathematics, Monash University Last week, OpenAI shocked the mathematical community by revealing that one of its internal artificial intelligence (AI) models had found a counterexample to a famous conjecture made by legendary Hungarian mathematician Paul Erdős in 1946. The planar unit distance problem, or Erdős problem 90, has […]
Authors: Kevin Burke, Associate Professor in Statistics, University of Limerick and David O’Sullivan, Associate Professor of Mathematics and Statistics, University of Limerick Recently, a cheerful 100-year-old message in a bottle was found on the south-west coast of Australia. In it, a world war one soldier proclaimed to be “as happy as Larry”. If you’re a […]
The simulation hypothesis—the idea that our universe might be an artificial construct running on some advanced alien computer—has long captured the public imagination. Yet most arguments about it rest on intuition rather than clear definitions, and few attempts have been made to formally spell out what “simulation” even means. A new mathematical framework emerges A […]
If you’ve ever fallen down a Wikipedia rabbit hole—clicking link after link until you’re far from where you started—you’ve explored a network, much like physicists map connections in systems like the internet or ecosystems. Each Wikipedia article is a dot, each hyperlink a line connecting ideas. This vast web, built by millions of contributors, mirrors […]
Deep inside caves, water dripping from the ceiling creates one of nature’s most iconic formations: stalagmites. These pillars of calcite, ranging from centimetres to many meters in height, rise from the cave floor as drip after drip of mineral-rich water deposits a tiny layer of stone. Beyond their beauty—echoed in fanciful nicknames like the “Minaret” […]
If you’re reading this, you’ve probably taken a calculus course before. How was it? Chances are you found it frustrating or, at least, complicated. You may remember one of the most feared parts of calculus courses: the computation of derivatives and integrals. For most students, this is the first time they face a mathematical problem […]
Author: Jeremiah Bartz, Associate Professor of Mathematics, University of North Dakota A shard of smooth bone etched with irregular marks dating back 20,000 years puzzled archaeologists until they noticed something unique – the etchings, lines like tally marks, may have represented prime numbers. Similarly, a clay tablet from 1800 B.C.E. inscribed with Babylonian numbers describes […]
I finished my last entry expressing my perplexity by the ‘solution’ mathematicians offered six decades ago to the problem of the continuum : Cohen’s theorem according to which both the assumption that there is some set (say, C) larger than the set of natural numbers but smaller than the set of real numbers, and the […]