Radiologist answers Strogatz: AI in medicine and math both raise the question of understanding

A practicing radiologist published a Forbes column on Oct. 30 replying to mathematician Steven Strogatz's essay on AI and mathematics. Paul Hsieh argues that radiologists, like mathematicians, want to understand how AI reaches its answers.

The exchange matters because mathematics is in the middle of a dispute over AI-generated proofs. The same question now runs through medicine: is a correct answer enough, or does understanding still count?

What the Forbes column says

Hsieh, a Forbes contributor, writes that he has practiced radiology for more than 30 years and holds an undergraduate mathematics degree from MIT. He was responding to Strogatz's recent essay in The Atlantic.

Strogatz quoted Harvard mathematician and Fields Medalist Curtis McMullen. McMullen said: "Mathematics is not radiology." Strogatz added that radiologists often cannot say how an AI model reaches its conclusion, yet physicians act on it anyway.

Hsieh disagrees with the contrast. He says radiologists may not yet know how an AI diagnoses certain diseases, but they keep seeking to understand the link between the AI result and the underlying biology.

He makes four main points:

• Radiologists rely on anatomy, physiology and pathophysiology when they read scans, he writes.
• The journal Radiology: Artificial Intelligence regularly covers how reliable AI tools are, and when they should or should not be trusted.
• Medicine has long used correlations without a known cause. His example is fingernail clubbing, which doctors have linked to heart and lung disease since Hippocrates.
• Researchers are working on "Explainable AI", which can mark a suspicious region on a chest X-ray with a heat map and a written description.

Hsieh also cites an FDA-approved tool that predicts breast cancer risk from mammograms five years ahead. He says it estimates likelihood and does not diagnose existing cancer. He also points to a newer system that appears to detect prostate cancer on MRI about as accurately as a good radiologist, according to AuntMinnie.

This is an opinion column. It is not a study, and it does not test any of the tools it mentions.

What changed in mathematics

Strogatz's essay, as excerpted in a newsletter, opens with the line "My field is in crisis." We could not open the Atlantic essay directly. Our account of it relies on the Forbes quotes and that excerpt.

The trigger was OpenAI's announcement in early September. The company said an internal system had produced a solution showing that the Navier-Stokes equations can develop a singularity in finite time. OpenAI says this settles the Millennium Prize problem by establishing statement "C" and also "D" in the official formulation. The company says it does not intend to claim the prize.

The claim is not settled. Mathematicians at King's College London and the University of Cambridge reported in a preprint that OpenAI's Lean version of the proof does not fully match the proof written for human readers. The paper has not been peer reviewed. The researchers say they have not shown that the original proof is wrong.

Commentators also differ on how much the result proves. DataCamp reports that the Clay Mathematics Institute has not certified it and independent peer review has not taken place. At the Heidelberg Laureate Forum, IEEE Spectrum reported that Fields Medalist Jacob Tsimerman said solving Navier-Stokes "feels pretty definitive". He added that he did not know the details.

Who it affects

Working mathematicians are the most exposed. IEEE Spectrum quoted Sydney mathematician Geordie Williamson on the problem of measuring progress. He said of OpenAI: "I think that OpenAI behaved extremely poorly." He also said the field's goal of understanding is becoming uncorrelated with the solving of problems. As a result, he said, the community must rethink how it assesses people, who gets jobs and how it educates students.

Early-career researchers described pressure of a different kind. Mita Ramabulana of the University of Cape Town said two of OpenAI's August announcements overlapped with his own work. Ailsa Robertson of the University of Amsterdam said colleagues feel they must use language models heavily to keep pace with peers.

Radiologists and their patients are affected in a different way. Strogatz's question is whether a patient should care that a risk prediction cannot be explained. Hsieh's answer is that validated tools are worth using, but explanation remains a professional duty. He says many physicians and patients would prefer AI that supports understanding over a "black box".

Sources disagree on one point

OpenAI describes its result as resolving the problem. Quartz reported that rivals contested OpenAI's account of events before the proof was published. The independent checks so far do not confirm the result. They also do not refute it.

What happens next

The KCL and Cambridge preprint still needs peer review. The Clay Mathematics Institute has not certified OpenAI's result, according to DataCamp. Mathematicians are still working out how to judge AI-produced proofs.

In medicine, the open question is how far explainable AI can close the gap between an accurate prediction and a clear reason. Hsieh's column does not offer new data on that. It is a argument that the two fields face a similar choice.