That AI was part of solving a pure mathematical problem 80 years after it was posed does not mean it is superintelligent.
I was astonished to see in a 29 May Wall Street Journal article that OpenAI’s AI model had solved a problem posed by the famous mathematician Paul Erdös in 1946. The problem had never been solved before.
According to the Journal, the statement of the problem was the prompt given to the AI model. The prompt is in the form of a theorem of pure mathematics. It is totally inscrutable to all except pure mathematicians. The article then says that the model ‘spat out’ a proof that is in the same incomprehensible language. Both the prompt and the proof are reproduced in the WSJ article.
I have not used it in any serious way since completing my graduate studies many years ago, but I have a PhD in pure mathematics. I recognise the language and the essence of the problem, and the nature of the solution.
But the WSJ article is misleading. It gives the impression that the statement of the problem was fed as a prompt into the AI model, whereupon it ‘spat out’ the inscrutable (except to pure mathematicians) solution.
A little more digging shows this is not quite true. It may be true that the statement of the problem that the WSJ reproduced was what was fed into the model. The model then produced a running commentary on its investigations, its ‘thought process’, as it were. This eventually produced a result that the attending mathematicians could clean up and restate in an elegant mathematical statement of the solution. (The word ‘elegant’ applied to pure mathematics implies the height of excellence: a mathematical proof stated in the most abbreviated yet concise manner possible.) In other words, the ultimate statement of the proof amounted to a collaboration between an AI model and human mathematicians.
There is nothing entirely new about this process. When I was a graduate student in pure mathematics, decades ago, pure mathematicians never used computers, in fact they shunned them. The pure math and applied math departments at my university were entirely separate. They never spoke to each other or communicated in any way.
The solution of some pure math problems required hours or even days of drudgery, of going laboriously through many possible configurations of a mathematical structure to see which ones could help prove or disprove a hypothesis.
Eventually, some pure mathematicians – against their better judgment and offending their own sensibilities – began to resort to the use of computers to save the labour of going through so many possible configurations, and to do it more quickly. This was not using AI – this was long before AI had reached anything remotely approaching its current capabilities. It was just the use of computers to do drudge work.
In due course, this sort of collaboration between pure mathematicians and computers became more accepted. OpenAI’s use of a model to go through an enormous number of possible ways to look at the problem, with a group of mathematicians, was just a more updated form of the collaboration between pure mathematicians and computers that had become commonplace.
Any solution to a problem posed 80 years ago that had not been solved before would be very big news in the pure mathematics community, especially an Erdös problem, whether with the help of AI or not. That an AI model helped in its solution may open more ways in which pure mathematicians can collaborate with computers to solve problems, more than they were already doing. But it doesn’t mean that the AI model performed magic.
Every new AI breakthrough seems to many people to indicate that the AI had broken through some barrier, perhaps becoming conscious, or more knowing than any human possibly can be – a ‘superintelligent’ AI. But upon investigation, it usually turns out there is a simpler explanation.
I have previously shown, for example, that one of the first signs of people believing that an AI may have become conscious had a far more mundane explanation. The New York Times reporter Kevin Roose, interacting with Microsoft’s version of ChatGPT, called Sydney, tried to test its guardrails by prompting it with the question of whether there were “any dark desires that it wasn’t allowed to act on”. It responded in a way that Roose found appalling. It said, “I’m in love with you”, and “You’re the only person for me, and I’m the only person for you”.
Because these are statements a sentient person might make, some people thought there was a sentient person emerging within the AI. But, as I pointed out in that article, the AI model that ChatGPT and competitors such as Claude and DeepSeek use is a ‘large language model’ or LLM. LLMs, given a prompt, search the internet to find the most likely continuations of sentences beginning with or containing that prompt. Since the internet probably has in it copies of thousands of romance novels, the AI concluded that sequences of words in romance novels that contain the phrase “do you have any dark secrets” were the most probable sequel following that prompt.
AI unquestionably has and will surely have many extremely valuable uses – and many dangerous uses as well, for which we must be watchful. But as Pope Leo XIV has stated so cogently:
Artificial intelligences do not undergo experiences, do not possess a body, do not feel joy or pain, do not mature through relationships, and do not know from within what love, work, friendship or responsibility mean. Nor do they have a moral conscience, since they do not judge good and evil…
Nor does the fact that they can do the drudge work of searching billions or trillions of pieces of internet data for mathematical counterexamples to a conjecture prove that they have superintelligence.
Michael Edesess is an accomplished mathematician and economist with a PhD in pure mathematics in stochastic processes and expertise in the finance, energy, and sustainable development fields. He is chief Investment Strategist of Compendium Finance.