Terence Tao on the Enduring Relevance of Erdős Problems and the Importance of Collaborative Mathematics
A new entry reporting on lively mathematical discussions surrounding problems posed by the highly esteemed Paul Erdős has recently appeared. In a fresh post on his personal blog, Fields Medallist and University of California, Los Angeles (USLA) professor Terence Tao refers to the website erdosproblems.com, created last year. In his view, the site has become an active, “hotbed” of mathematical thinking in recent months, after AI systems solved several Erdős problems that Tao describes as “easier” and less complex. Tao has repeatedly emphasized that, beyond personal reasons, he is professionally connected to Erdős Pál, as much of his own research, particularly in combinatorics, builds on the work of the brilliant Hungarian mathematician.
Tao has also visited Hungary: in 2020, the Hungarian Academy of Sciences (MTA) awarded him the János Bolyai International Mathematical Prize for his book Nonlinear Dispersive Equations and for his influential contributions to mathematical outreach.
Erdős’s work remains a defining source of inspiration for contemporary research -not only for Tao. In recent interviews on online platforms aimed not exclusively at mathematicians, Tao has spoken about changes in mathematics as a discipline and the growing prominence of what is often called collaborative mathematics. He contrasts this with what he describes as the earlier, more “romantic” and individualistic era of the field. The former child prodigy believes that the next major mathematical breakthrough will not come from a solitary genius, but from thinkers working closely together. An interesting interview with Tao about the aforementioned can be watched HERE. The Atlantic also interviewed Tao, you can read the article HERE.
According to the erdosproblems.com database, 488 out of 1,179 Erdős problems (41%) have been solved so far.
Another noteworthy point Tao raises in his interviews concerns the concept of failure in mathematics, which he sees as fundamentally different from its interpretation in some other disciplines. “We have to teach our students that it is acceptable to fail here, but then they should try again. In mathematics, we often test ideas that may seem stupid, and sometimes we reach dead ends. That is part of mathematical thinking.”
Tao has also frequently articulated his views and concerns about artificial intelligence. He argues that if AI takes over many cognitive tasks from humans, human cognitive abilities may inevitably decline: “In the twentieth century, developed countries had an abundance of food. People gained weight and now have to exercise regularly. Artificial intelligence may create a similar situation. If it takes over some of our cognitive tasks, we may find ourselves needing deliberate mental exercises to keep our brains sharp.”
Researchers at the HUN-REN Rényi Alfréd Institute of Mathematics who work on artificial intelligence are likewise aware that the proper use of AI is becoming an unavoidable part of mathematics, says academician Balázs Szegedy, head of the Institute’s Artificial Intelligence Department. At the same time, he warns that if AI begins to replace human labor at a pace for which society is unprepared, it could pose unprecedented challenges to humanity and fundamentally reshape the world as we know it.
Terence Tao increasingly advocates for the collaborative nature of mathematics, adding that he devotes extra energy to ensuring his students understand that there are beneficial and less beneficial, even harmful ways to use artificial intelligence, and that it is crucial to grasp the difference. As a teacher, he often finds the prompts written by his students at least as interesting as what the AI ultimately generates from them.
Main page portrait: UCLA