Digital Economy

Is AI ready for mathematics? Gemini put to the test with 700 unsolved problems

For the past few months, an online collection of mathematical problems has become the test bed for testing the abstract capabilities of artificial intelligence.

by Enrico Schlitzer

19 February 2026

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4' min read

Translated by AI

Versione italiana

4' min read

Translated by AI

Versione italiana

For the past few months, an online collection of mathematical problems has become the testing ground for the abstract capabilities of artificial intelligence. In the most recent attempt, made public at the end of January, Gemini managed to solve thirteen of them. The aim of the experiment was also to understand to what extent a language model can be useful in frontier research.

The database collects the legacy of Paul Erdős, one of the most prolific mathematicians ever, who at his death in 1996 had amassed hundreds of outstanding problems. In order to catalogue them and track their progress, thethe erdosproblems.com website was created, which currently includes 1,179 problems, of which about 60% are unsolved.

In October 2025, OpenAI announced that ChatGPT-5 had succeeded in solving ten Erdős problems, but the claim was soon downgraded: the proposed solutions were already known in the scientific literature. The episode helped to turn the spotlight on the collection, which in recent months has become a testing ground for many language models. Google's GPT-5.2, AlphaProof and AlphaEvolve, DeepSeek and Claude Opus 4.5 have measured themselves against it, with varying results: many partial advances, but few complete and original answers. One of these came from Google's recent DeepMind experiment, in collaboration with nine international universities, thanks to Aletheia, an AI agent specialising in mathematics and based on Gemini Deep Think.

The Google DeepMind experiment

The process took place in two stages. First, Aletheia proposed an answer for each of Erdős' 700 remaining open problems; then it applied an automatic checking mechanism to discard the clearly incorrect ones and drastically reduce the number of results to be examined. Only then did a team of mathematicians intervene to analyse the remaining 200 cases, eliminating the incorrect ones and checking that the results had not already been discovered by others.

There were 63 technically correct solutions, but in many cases Aletheia had not interpreted the question correctly. Only thirteen answers, about 7% of the total, were considered significant. Of these, two were complete and another two only partial. The remaining nine, which were checked later, turned out to be already solved without the database having been updated, but the agent still managed to identify existing solutions or propose new ones.

What worked (and what didn't)

The interest of the experiment also lies in understanding the capabilities of a language model when faced with an abstract problem. In the simplest cases, he was able to apply established techniques and produce correct, though not particularly original, answers. But the most interesting aspect is another. Although he discarded hundreds of problems in the initial phase, Aletheia focused the researchers' attention on a small number of cases, making in-depth human verification easier. It demonstrated its ability to navigate through a vast and fragmented literature, finding hidden information in works that had gone unnoticed. For example, the solution to question 1089 was found in an observation in the margins of a paper published in 1981 by two Japanese mathematicians, who probably had not even realised that they had solved an Erdős problem.

Several limitations also emerged, such as the tendency to misunderstand the real intent of the questions by interpreting them in an overly literal way. Moreover, the model is still far from being fully autonomous and, although it has reduced the number of cases to be directly reviewed, it still requires significant human supervision. The risk is to create a bottleneck in the review phase: depending on the problem and its difficulty, the number of experts capable of evaluating the output of an AI agent specialised in research may be very small, and even for them the review is not necessarily quick. Especially since, as the authors of the experiment note, the most challenging part was to make sure that the results obtained were original. Without this check, there is a risk of unknowingly plagiarising discoveries already made by others and assimilated in the training phase.

How far is the autonomous search?

Google's experiment suggests that AI, rather than an 'artificial mathematician', could in the near future become an assistant capable of assisting researchers and accelerating certain phases of their work. It is no coincidence that mathematics remains a particularly challenging field for artificial intelligence. Unlike other fields, there are often no large experimental datasets on which to train deep learning models. Many questions require demonstrations consisting of rigorous logical steps, where even a single hallucination can invalidate the entire procedure.

The situation changes if a problem can be formulated in the appropriate language for an AI system. When there is a well-defined set of possible solutions to be evaluated, a trained search agent is able to explore them and identify the correct ones. Terence Tao, one of the most famous living mathematicians, tested Google's AlphaEvolve on 67 such problems in November: in most cases it matched the already known results and in a significant proportion, around 20 per cent, it managed to improve on them.

In the same days, Tao stated in a post on Mastodon that he believed that "in the short term, the most productive uses of AI in mathematics will come not so much from applying the most powerful models to the most difficult problems (...) but rather from using mid-power tools to accelerate and scale up more ordinary and time-consuming, but nonetheless essential, research tasks".