Terry Tao on Coding Agents: A Fields Medalist's Take on Vibe Coding

Terry Tao - the mathematician who won a Fields Medal at 31 and is widely considered the greatest living mathematician - wrote a blog post about using AI coding agents. Not for math research (he's done that too), but for building software: porting legacy Java applets and creating new visualization tools.

The post is a practical account of what works, what doesn't, and how he thinks about risk when the code isn't mission-critical. It's generating a lot of discussion on Hacker News.

The Migration Project

Back in 1999, Tao created Java applets for his complex analysis and linear algebra courses at UCLA. These visualized mathematical objects like honeycombs and Besicovitch sets - useful teaching tools that became obsolete as browsers dropped Java support.

Working with an AI coding agent, Tao converted about two dozen of these legacy applets to JavaScript in a few hours. The results surprised him:

• Only one minor bug was discovered (a drag event issue)
• The agent found two previously unknown bugs in the original Java code
• Several graphical improvements were added, like colorization of the Besicovitch set visualization
• A complex 1999 honeycomb applet (co-authored with Allen Knutson) was successfully restored

The code quality was acceptable for the use case. These are supplementary teaching materials, not production systems, so the standard is different.

New Applications Built From Scratch

With the migration complete, Tao moved to building new tools he'd always wanted but never had time for.

Spacetime Diagram Applet: He describes this as "Inkscape, but in Minkowski space" - a special relativity visualization tool he'd envisioned in 1999 but abandoned because the complexity wasn't worth the development time. With AI assistance, he built a functional version in hours, complete with documentation of the development process.

Gilbreath Conjecture Visualization: Following a blog post on the mathematical conjecture, Tao created an interactive visualization tool to accompany the paper.

This is the pattern that keeps emerging with coding agents: projects that were technically possible but economically impractical suddenly become feasible when development time drops by an order of magnitude.

What HN is Saying

The HN discussion is split between people reading this as validation of AI coding and people reading it as a cautionary tale.

The "balanced perspective" camp highlights Tao's framing that this is acceptable "because such supplements are not mission-critical to the core of the paper." The top comment thread emphasizes: "It's a tool. Good for some things but not others and generally not to be trusted."

The "domain expert advantage" observation came up multiple times. One commenter noted the pattern: "When it comes to a field I'm not an expert in, AI is a great tool." Tao knows the math deeply, so he can verify the visualizations are correct. The quality bar is lower for supplementary materials than for production code.

Skepticism about conflicts of interest appeared in one subthread, noting Tao's previous appearances in OpenAI promotional content. This seems like overreach - a mathematician writing about porting old Java applets isn't exactly a high-stakes endorsement.

The "infinite demand" perspective is compelling. As one commenter put it:

There is infinite latent demand for software, most especially outside the traditionally software-focused spaces. If LLMs stopped improving today it would take us 10 years to catch up to the new software-writing abilities that have become available.

Tao represents a whole class of domain experts who have ideas for software tools but lack the time to learn JavaScript frameworks. Coding agents change that equation.

The Trust Framework

Tao's approach to trust is pragmatic. These visualizations are secondary aids rather than core components of mathematical arguments. If a bug slips through, the consequences are limited - a student might see an incorrect diagram, but the theorem doesn't become false.

This risk assessment is explicit in the post:

Since these visualizations serve as secondary aids rather than core components of mathematical arguments, potential bugs pose manageable risks.

Compare this to using AI for the proofs themselves, where an undetected error would be much more serious. Tao has written separately about using AI for mathematical reasoning, but that's a different level of verification.

Language Irrelevance

One observation worth highlighting: Tao notes that precise programming languages matter less when translation friction approaches zero. He's not a JavaScript expert, but the agent handles the implementation details. As long as sufficient context exists, agents convert between languages effectively.

This matches what we're seeing across the industry. The "one true language" debates feel increasingly academic when you can describe what you want and get working code in whatever stack the project uses.

Implications for Teaching

Several comments noted the broader impact on education. One CS professor mentioned using LLMs to build visualizations for courses:

Building visualizations with LLMs has been a major boost for my CS classes. Many visualizations that I have always wanted but just didn't have the time to build, I now have.

The pattern is the same: domain expertise plus AI coding tools equals dramatically expanded capacity for supplementary materials.

For math education specifically, interactive visualizations have always been valuable but expensive to produce. If domain experts can build them directly without learning web development, the supply of quality educational tools should increase significantly.

The Balanced Take

Tao isn't claiming AI will replace programmers or that vibe coding is appropriate for everything. His position is narrower: for non-critical supplementary materials where the author has deep domain expertise, AI coding agents offer an acceptable tradeoff between development speed and code quality.

That's a useful calibration point. Not "AI can code everything" and not "AI code is always unreliable" - but a specific claim about specific use cases where the risk/reward calculation works out.

For developers watching this space, the lesson isn't about math or Java migrations. It's about identifying your own domains where you have deep expertise and where the quality bar is lower than production systems. Those are the places to experiment first.

Sources

• Terry Tao's blog post: "Old and new apps, via modern coding agents"
• HN discussion with 260+ points and 70+ comments
• Terry Tao's archived AI-related blog posts