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# Headlines and inside stories: understanding and trust in AI for mathematics, science, and engineering

Tapio Schneider (guest post on Terence Tao's blog), Blog, 2026-09-23.
Source: https://terrytao.wordpress.com/2026/09/23/headlines-and-inside-stories-understanding-and-trust-in-ai-for-mathematics-science-and-engineering/

## Why it matters

A climate scientist's argument, on Tao's blog, that AI predictions in science must sit inside auditable scaffolds, as proofs do in mathematics.

## Summary

Guest post by Tapio Schneider (Caltech, CliMA). Starting from OpenAI's Sept 8 forced Navier–Stokes blow-up result, he argues that "theorems are the headlines, proofs are the inside story": proofs carry understanding, not only truth. In science and engineering, predictions such as climate projections or aircraft designs must often be trusted before they can be checked, so "an auditable causal chain from assumptions and input data to the predicted outcomes is what makes predictions trustworthy". He proposes keeping AI inside auditable scaffolds (e.g. conservation laws), with learned components such as turbulence closures tested against verifiers, and says humans remain essential for understanding and trust. Few comments (4 when checked).

## Archived text

Short quotes only (see Summary). Full text at the URL.

## Cited in

- 2026-09-08: [OpenAI claims a Millennium Prize problem](https://postcutoff.com/e/2026-09-08-openai-navier-stokes-blowup/)

## People in this post

- [Terence Tao](https://postcutoff.com/person/terence-tao/), Professor of mathematics, UCLA