The below is written by my friend and colleague, Filipe Campante. I’ll have more (together with a co-author) to say on related topics soon.
If the Navier-Stokes Conjecture has been proved, but no human can understand the proof, has it actually been proved? This is not just a philosophical parlor game, akin to trees falling in the middle of the forest. What the AI revolution means for mathematicians – and to human expertise more broadly – hinges on that question.
Recent advances by AI models in tackling dozens and dozens of fiendishly hard math problems have shaken mathematicians to the core. A piece published in the New York Times describes the shock, felt by luminaries such as Terry Tao and by PhD students alike, and everyone in between. It seems obvious that mathematicians could well become irrelevant in a world where AI can solve problems much faster than humans possibly could.
But is it? I cannot help but sense that this seemingly unavoidable conclusion misses something crucial: what use is knowledge if humans can’t understand it to put it to use? And if humans need to understand, the value of human experts who can figure out what the AI has done can actually increase – even as their expertise also gets degraded by the rapid advancement of AI.
To understand the point, let’s get to a very different context: news media. It’s long been speculated that the spread of generative AI content that is very hard to distinguish from real content – think deepfakes – would lead to a collapse in trust in the media. If I can’t tell apart what’s high-quality news, why would I pay to consume any news?
There’s certainly logic to that, of course. But as an economist, I think it also misses an important nuance: in a world where something (say, trustworthiness) becomes very scarce, it also becomes very valuable. If it’s very hard for me to figure out if a picture or video or audio recording is real or not, then I really value a reliable source that can tell me that at least some of the time.
I decided to test that proposition, along with my coauthors Ruben Durante, Felix Hagemeister, and Ananya Sen, in a research paper. In partnership with Süddeutsche Zeitung, a major German newspaper, we set up an experiment where a group of SZ readers were asked to figure out whether a set of pictures was real or AI-generated. This succeeded in raising their concerns over AI-generated misinformation, relative to a control group that were only asked to look at real pictures and tell where they were from, with no reference to AI or deepfakes.
What happened afterwards was the really interesting part. First, those readers exposed to AI photos reported lower trust in the news content of many different platforms – including their trusted SZ itself. Yet, in spite of that, their demand for SZ went up: they visited the platform more, and were more likely to remain subscribers. In short, confronted with the challenge posed by AI, news consumers respond by lowering their assessment of the quality of available content, but also increase their demand for a trustworthy source.
A mathematical model in the paper elucidates the logic, and shows its broader generality. If a consumer is interested in learning whether something is true or not, and a technological change makes that harder to distinguish, two things happen. First, the consumer realizes that now all content poses a bigger challenge for them, and gets degraded from their perspective. But second, and very importantly, any source that mitigates that problem – even while still suffering from it – becomes more valuable, not less. Yes, they are worse in absolute terms, but the important thing for the consumer is that they are less worse, so to speak, than the alternative of not having them.
Which brings us back to Navier-Stokes. In the NYT piece, Terry Tao himself observes how hard it is to actually understand the proof that OpenAI claims their agents produced. “Claims” here is important, because math is not about saying you proved something: it’s about others being able to verify that your proof is indeed correct.
Well, if Terry Tao has a hard time figuring that out, what hope do the rest of us have? It is remarkable how he and his students long for a human author with whom they could engage in human terms, to arrive at a humanly intelligible explanation.
What our research shows is that the age of AI can actually increase the value of human expertise, even as it makes them seem expendable on a superficial look. AI is very good at producing what we may call “expert-looking” content: something that looks correct and authoritative, but that it’s very hard for a non-expert to tell if it is or not. In that situation, a human can really use a human expert to check it out.
But you may say: that rests on the assumption that we need human understanding. What if something just works, and we can tell it does? Do we really need to understand whether a proof is correct? Well, true. But that only shifts the role of expertise towards experimental validation: knowing that something works means subjecting it to tests and seeing if it passes – that’s how we do it, from experimental physics to drug trials to consumer products.
As long as the demand for knowledge comes from humans who want to figure out if stuff is true (or that it really “works”), AI that makes advances in more and more rarefied domains will make it more and more valuable to have humans who can follow them along. Far from making Terry Tao and his colleagues and students expendable, AI is more likely to make us realize how much we need all of them and more.