The mathematician Alex Kontorovich speaks with host Steven Strogatz about regaining his creative freedom in an intimidating collaboration and about the pleasures of spherical geometry.

Olena Shmahalo/Quanta Magazine

New research finds that the subjective experience of time is linked to learning, thwarted expectations and neural fatigue.

It was an old idea of Stephen Hawking’s: Unseen “primordial” black holes might be the hidden dark matter. A new series of studies has shown how the theory can work.

Despite recent progress on the notorious Collatz conjecture, we still don’t know whether a number can escape its infinite loop.

Computer scientists are trying to build an AI system that can win a gold medal at the world’s premier math competition.

Renormalization has become perhaps the single most important advance in theoretical physics in 50 years.

Two computer scientists found — in the unlikeliest of places — just the idea they needed to make a big leap in graph theory.

A novel form of immunological memory that was mostly ignored for a century extends the benefits of vaccines. It could be of help in ending the COVID-19 pandemic.

Mathematicians have long grappled with the reality that some problems just don’t have solutions.

The mathematician Alex Kontorovich speaks with host Steven Strogatz about regaining his creative freedom in an intimidating collaboration and about the pleasures of spherical geometry.

In our mind’s eye, the universe seems to go on forever. But using geometry we can explore a variety of three-dimensional shapes that offer alternatives to “ordinary” infinite space.

*Quanta Magazine* is committed to in-depth, accurate journalism that serves the public interest. Each article braids the complexities of science with the malleable art of storytelling and is meticulously reported, edited and fact-checked. Launched and funded by the Simons Foundation, *Quanta* is editorially independent — our articles do not reflect or represent the views of the foundation.