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, ...

“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 ...

“Our universe isn’t just described by math, but it is math in the sense that we’re all parts of a giant mathematical object.” – Max Tegmark I knew virtual reality was going to make mathematical ...

A painless, non-invasive brain stimulation technique can significantly improve how young adults learn math, my colleagues and I found in a recent study. In a paper in PLOS Biology, we describe how ...

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 ...

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 Economic Singularity is a term I coined a decade ago to denote the moment when there are no longer any jobs for the vast majority of humans. In mathematics, the word “singularity” means a point ...

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 ...