Steven Strogatz Says AI Math Answers May Need Accuracy Testing

Cornell applied mathematician Steven Strogatz argues that researchers may need to judge some AI-generated mathematical results by their accuracy when systems cannot offer reasoning people can understand.

Strogatz describes computing’s role in mathematics through three stages: servant, scout and oracle. A servant follows instructions, while a scout searches problems for results that people can later explain. An oracle offers answers that may be useful even when people cannot understand how the system reached them.

He traces the scout role to computer simulations in the 1950s. Enrico Fermi and colleagues modeled vibrations between atoms and expected energy to spread out over time. Instead, about 98% of the energy returned to its original vibrational mode, an unexpected result that helped lead to soliton theory. In this stage, computers could reveal a result first, while researchers could still develop an explanation afterward.

Strogatz says some AI now fits the oracle role. He points to Google Translate and AlphaFold as tools that produce useful results without revealing the principles behind them. In his view, Google Translate has not established new linguistic principles, while AlphaFold identifies patterns to predict protein structures without explaining its method in terms people can follow.

To judge results that users cannot inspect, Strogatz proposes measuring how often an AI system gives correct answers. He compares that process with controlled, randomized trials in medicine, which can test whether a treatment is safe even when its mechanism is not fully understood. Repeated tests would offer evidence about reliability without providing a proof of why each answer works.

That shift would change mathematics’ standard of confidence. Pure mathematics has traditionally prized certainty through proof, while science and engineering also assess claims through observation and performance. Strogatz contrasts those methods with Euclid’s Elements, compiled around 300 B.C., whose proofs remain accepted today. Using empirical checks for mathematics, he argues, would mean giving up some of the certainty that proofs are meant to provide.

Strogatz treats possible future developments separately. He says AI might become a good teacher. He speculates that people may understand some currently opaque AI systems within 10 years. He also expects some systems could remain beyond human comprehension because of human limits in speed, intelligence or memory.

Strogatz says AI is currently poor at asking good research questions, but he believes systems can be trained to ask them.