“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, ...

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 ...

With his telescope, Galileo gathered a vast trove of observations on celestial objects. With his mind, he found patterns in that universe of data, creating theories on motion and mechanics that paved ...

Partial Differential Equations (PDEs) are central to both pure and applied mathematics. Any quantity which changes in space and time will satisfy certain partial differential equations because the ...

Black holes and wormholes are the ultimate fodder for science fiction. Need to travel through time? No problem! Build a wormhole. Want to see a different universe? Dive into a black hole! Though these ...

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 ...

The original version of this story appeared in Quanta Magazine. Two blind spots torture physicists: the birth of the universe and the center of a black hole. The former may feel like a moment in time ...

How do things break? The fracture of materials is part of our everyday experience, and yet the process is not well understood. A study of crack propagation at microscopic scales shows the devil in the ...

Partial Differential Equations (PDEs) are central to both pure and applied mathematics. Any quantity which changes in space and time will satisfy certain partial differential equations because the ...