Forbes contributors publish independent expert analyses and insights. The Universe is out there, waiting for you to discover it. If all you had at your mathematical disposal was the idea of real ...

Define the Standard Model gauge group to be S ( U ( 2) × U ( 3)), the subgroup of SU ( 5) consisting of block diagonal matrices with a 2 × 2 block and then a 3 × 3 block. (This is isomorphic to the ...

New findings are fueling an old suspicion that fundamental particles and forces spring from strange eight-part numbers called “octonions.” In 2014, a graduate student at the University of Waterloo, ...

On this day in 1843, the great Irish mathematician William Rowan Hamilton discovered a new kind of numbers called quaternions. Each quaternion has four parts, like the co-ordinates of a point in ...

WORDS can be slippery. That is perhaps even more true in physics than it is in the rest of life. Think of a “particle”, for instance, and we might conjure an image of a tiny sphere. In truth, ...

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2025 marked a historic year in mathematics. Researchers solved a major case of Hilbert’s ambitious sixth problem, proved a sweeping new theorem about hyperbolic surfaces, and settled the longstanding ...

A forgotten number system invented in the 19th century may provide the simplest explanation for why our universe could have 10 dimensions As children, we all learn about numbers. We start with ...

The suspicion, harbored by many physicists and mathematicians over the decades but rarely actively pursued, is that the peculiar panoply of forces and particles that comprise reality spring logically ...