Last week OpenAI dropped more than 300 mathematical results produced by its machines. Last month the company announced that its machines had solved a long unsolved mathematical problem related to equations governing fluid behavior. Both events made headlines with some people claiming it’s evidence that Super-intelligence is just around the corner. Soon, they say, AI will “solve physics” and cure cancer. Today I want to unpack these claims just a bit so you can get a better view of what’s going on.

This post is part of a broader series I am going to be taking on here about AI, life and society. I am, indeed, deeply worried about what’s happening but not for the reasons the tech-bros want you to believe. We are entering a transformative era and understanding how to maintain our humanity in its midst may be the defining challenge of our age.

So, what exactly is going on with AI and Math? The events of this week and last month involve machines being directed to solve long-standing problems in mathematical science. This means AIs were given (by humans) both the problems and the history of work on that problem (done over the years by humans). The AIs were then able to either work out proofs or use other means of establishing the required result. This is without a doubt an achievement, full stop. And it absolutely demonstrates the power of cutting edge AI technology.

But does it mean we are at the dawn of Super-intelligence, Skynet and the age of Robot Overlords (including their AI-driven human extinction)?

No. Not even close.

Mathematics is a formal “science”. That means it exists entirely within a domain governed by the formal rules of logic. This is very similar to how chess is governed by the formal rules of which pieces can make which kinds of moves. That means mathematics was always going to be susceptible to machines that are good at the application of formal rules in a step-by-step algorithmic fashion.

There is a reason why, historically, AI began with an emphasis on games like Chess and Go. Conquering those games was a matter of computational power and innovative machine design in applying formal algorithmic methods to the games’ formal rules. Lots of mathematics is exactly that. In fact, it was exactly those kinds of mathematical problems that the AIs were directed to by their human programmers.

So, while it’s really impressive that we’ve built machines with this kind of algorithmic power, its implications for the rest of science are limited. Why? Because the rest of science lives in the very real, very messy physical world.

Progress in science begins by pushing on our actual lived, embodied experience via experiments - not by thinking alone in a dark room. Even Einstein’s great theoretical advances required years of people before him poking and prodding chunks of metal and glass connected by wires and sealing wax, trying to get these contraptions to behave in a stable way so that some reasonable data could be extracted. While AI can help with experimental design it can’t anticipate what will come from new and clever experiments.

Even more important, most of the stuff we explore in science requires seeing it, knowing it exists, before we try and explain it. Indeed, the majority of what we’re trying explain - mountains, planets, life, societies - constitute what are called “complex systems”. You can’t derive their existence from a set of axioms like you can in mathematics. Instead, you actually have to exist in the real physical, biological and social world to even know what they are or what they mean as problems science can explore. That kind of contextual understanding is something AI (at least the kind that has been built now) sucks at.

I could also go on about how pissed off mathematicians are at what OpenAI is doing with its large-scale harvesting of old mathematical problems. Dumping a proof of an old conjecture is very different from understanding the nature of whatever it was the conjecture was about (the nature of numbers or shapes etc). The world’s greatest mathematicians recently wrote an open letter criticizing AI companies, saying:

“solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight… Indeed, the mass production at faster and faster pace of "true/false" statements could destroy fertile ground instead of breathing life into new ideas.”

So, what we are seeing here is a general trend that will demand a lot of attention from all of us. AI has indeed become powerful but in not in terms of producing sentient super-intelligences. That super-intelligence narrative is distraction that keeps us from seeing the real dangers of the technology (job loss, societal disruption, unsafe programs) and the misbehavior of companies whose actions are often deeply self-serving and troubling.

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PS If you have specific questions or issues you want me to address leave a comment on the website or email me at [email protected]

PPS I could not get this proof-read so please excuse typos etc.

— Adam Frank 🚀