Like physics, math has its own set of “fundamental particles”—the prime numbers, which can’t be broken down into smaller ...

“If I have seen further than others, it is by standing upon the shoulders of giants.” This famous quote by Isaac Newton points to an axiom that lies at the heart of The Sciences — knowledge precedes ...

On Monday, I looked at the possibility of artificial intelligence through the perspective of history: the history of the field and of expert conjecture. That analysis revealed that, up until now, ...

Envision energy trajectories that curve and cross each other. Now envision energy trajectories that are straight lines and do not cross. Now see an explosion of energy at the points where the curved ...

Before it became the province of futurists, the word singularity had significance in both mathematics and the physical sciences. A mathematical singularity is a point at which a function is not “well ...

Watching this soap film stretch, rupture and reform in slow motion is mesmerising – but mathematicians see more than a trippy image. The point where the bubble breaks explosively is a mathematical ...