Caltech’s own copy of the first edition of the Principia is part of the Institute’s Archives and Special Collections. In the 18th century, it belonged to French mathematician and natural philosopher Jean-Jacques d’Ortous de Mairan, whose signature can be seen in the left margin of the title page. More recently, […]

The goal of the “busy beaver” game is to find the longest-running computer program. Its pursuit has surprising connections to profound questions in math. A visualization of the longest-running five-rule Turing machine currently known. Each column of pixels represents one step in the computation, moving from left to right. Black […]

ANIMATION A team of mathematicians from RUDN University added new symbolic integration functionality to the Sage computerized algebra system. The team implemented ideas and methods suggested by the German mathematician Karl Weierstrass in the 1870s. The results were published in the Journal of Symbolic Computation. The first computer program capable of […]

Majorana constellations of some of the most quantum states in various dimensions. Credit: Luis L. Sánchez Soto Investigators develop a method to determine how quantum the state of a system is. Large objects, such as baseballs, vehicles, and planets, behave in accordance with the classical laws of mechanics formulated by […]

WPI mathematical physicist Mayer Humi has been studying the solar system for decades. Credit: Worcester Polytechnic Institute/Matthew Burgos Using a limited set of mathematical equations, Worcester Polytechnic Institute mathematical sciences professor Mayer Humi said he has confirmed a 224-year-old math conjecture about the origins of our solar system, providing insights […]

Example of a cross-section of K3 surface in 3-space, similar to a model Utah State University and University of Missouri-St. Louis mathematicians used to examine string dualities between F-theory and heterotic theory in eight dimensions. Credit: USU Thomas Hill and Andreas Malmendier of Utah State University explore a string duality […]

The ancient philosopher Plato conjectured that the universe was composed of particular geometric shapes; the earth, of cubes. Findings from a multidisciplinary research team found truth in Plato’s belief. The ancient Greek philosopher was on to something, researchers found. Plato, the Greek philosopher who lived in the 5th century B.C.E., […]