Terence Tao gives mathematics six shelves

Numbers. Algebra. Geometry. Probability. Analysis. Dynamics.

In a long-form Big Think conversation, Fields medallist Terence Tao uses those six ideas as shelves for an intimidatingly large subject. The pleasure lies in watching the familiar become strange again: algebra is not just letters replacing numbers, and geometry is not merely triangles patiently waiting for an exam.

Watch the complete Terence Tao interview. It loads only when selected; there is no autoplay here.

Three possible viewing routes:

• Creators: begin with geometry and ask how representation changes what becomes visible.
• Builders: begin with algebra, where reusable structures let ideas travel between problems.
• Everyone living through uncertain weather, markets or headlines: begin with probability—and retain Tao’s warning that rare events are difficult precisely because evidence is scarce.

The later discussion moves into mathematical discovery and AI. Tao’s useful corrective is that acceleration is not identical to understanding: mathematics also needs judgment about which problem matters and which result explains anything.

Big Think provides the full chaptered transcript and accompanying article.