Not since Socrates complained that the written word might make people lazy about remembering things has there been such an outpouring of angst against a new technology in the world of academia. In an open letter published on September 11th 24 Fields Medal winners—akin to Nobel laureates in the field of mathematics—issued a stark warning. They say AI could ruin the foundations of maths.
The letter is in response to AI apparently making a spate of breakthroughs at the frontier
Not since Socrates complained that the written word might make people lazy about remembering things has there been such an outpouring of angst against a new technology in the world of academia. In an open letter published on September 11th 24 Fields Medal winners—akin to Nobel laureates in the field of mathematics—issued a stark warning. They say AI could ruin the foundations of maths.
The letter is in response to AI apparently making a spate of breakthroughs at the frontier of the subject. On September 8th OpenAI said it had solved the Navier-Stokes problem, one of the seven “Millennium Problems” chosen in 2000 by the Clay Mathematics Institute as the hardest and most important going. OpenAI appears to have gazumped Tristan Buckmaster (pictured) and Levent Alpöge, a duo of mathematicians labouring on the task. The firm released a 166-page paper detailing the work, which was done using internal models that are not yet available to the public. Despite its length, the paper contains little of the explanation that mathematicians typically provide when sharing a new discovery.
The group argues that AI companies are solving mathematical problems to benchmark the strength of their models. Doing so, they say, is “detrimental to the science of mathematics, and to the mathematical community”. And while it has impressed scholars everywhere, “solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight.” Proving things without comprehending them is, they argue, a threat to intellectual work in general.
Mathematicians’ fears resemble those that accompanied the invention of the ball-point in a world of fountain pens, or even the advent of electronic calculators. Intellectuals have often worried about so-called technological determinism. Will a new tool control humans? Will it lead to mental decay? Such fears have typically turned out to be unfounded. People still wrote with ball-point (despite worries about the decline of the fountain pen and the lack of sensory impact on the brain)—only faster. Mathematicians still did maths—only with quicker calculations. Socrates’ worries didn’t quite play out: people read books to learn and they now have yet more to read.
Today the scholars fear the loss of the ancillary benefits of discovery. The academy has long lauded those who were first to discover a proof or demystify a conjecture. But those final answers to problems are only one aspect of the academic process, the letter argues. Working on problems has usually led to the asking of yet more questions and the creation of new areas of study. If AI just churns out proofs, that might not happen. “We’ve gotten too good at optimising,” says Terence Tao, one of the letter’s signatories. Another, Hugo Duminil-Copin, draws a comparison: airdropping someone on the summit of Mount Everest is very different from climbing it.
Are mathematicians talking their own book out of fear? It is hard to argue that humanity is worse off with the extra knowledge ai is producing. Yet technological advance has certainly affected how humans think. One consequence is “cognitive offloading”, where tools reduce the load on human memory, which causes the mind’s skills to atrophy. A study published in 2011 by Betsy Sparrow of Columbia University and her co-authors showed that the proliferation of search engines, such as Google, had “become a primary form of external or transactive memory where information is stored collectively outside ourselves.” People turned to Google-searching answers when faced with tough questions, instead of attempting to recall what they knew (maybe Socrates was right, after all). All that can affect how humans process information. A more recent study by Michael Gerlich of the SBS Swiss Business School found “a negative correlation between the frequent use of AI tools and critical thinking abilities”.
If AI starts curing cancers or improving energy supplies, few will care how the advances came about. Yet some abstract mathematics has little practical application; its primary purpose is human understanding. If abstract proofs come to be done by machines and incomprehensible to humans, it might become hard to see the purpose of the endeavour.
One Subscription.
Get 360° coverage—from daily headlines
to 100 year archives.
Archives
HT App & Website