Terence Tao

A digestion of the proof of Sendov’s conjecture

This post concerns the following conjecture of Sendov, as well as its strengthening by Phelps–Rodriguez: Conjecture 1 (Sendov’s conjecture) Let $latex {n \geq 2}&fg=000000$, and…

A partial digestion of the HRT counterexample

A function $latex {f(t) \in L^2({\bf R})}&fg=000000$ of one variable can be translated in space by a spatial shift $latex {x}&fg=000000$ to obtain a new function $latex \displaystyle…

Terence Tao on AI in mathematics (and beyond)

A digestion of the Jacobian conjecture counterexample

The notorious Jacobian conjecture can be formulated concretely over the complex numbers as follows.

Two more apps: visualizing the zeta process and the motions of the heavens

I believe that the creation of visualization apps to illustrate mathematical or scientific concepts is a particularly favorable use case for modern coding agents, as many of the downside risks…

Call for long programs, workshops, and summer schools at IPAM

(I am writing here in my capacity as Director of Special Projects at IPAM.) IPAM seeks program proposals from the mathematical, statistical, and scientific communities for long programs…

Visualizing the Gilbreath expectation sequence

One byproduct of learning how to use coding agents to create visualization apps is that it now becomes straightforward to convert any figure in one’s papers that had already been generated…

A paper diagram visualizer

I am finding the newly revealed capability to code old applet ideas into reality to be very tempting to sink more time into, though I am certainly encountering the common “vibe coding”…

A random variable visualizer

With the advent of modern coding agents, many visualization projects that I had proposed in the past, but dropped due to the time and complexity of the coding portion of the task, have now become…

Old and new apps, via modern coding agents

I have been interested in machine-assisted ways to do and teach mathematics from as far back as 1999, when I started coding several applets in Java 1.0, both for my complex analysis and linear…