AI prompts mathematicians to rethink the value of finished results — The Japan Times
Artificial intelligence is becoming increasingly involved in the search for mathematical proofs, prompting the field to reconsider whether the value of mathematics lies only in the finished result or also in the lengthy human process of discovery. This was discussed in a column by Parmy Olson for Bloomberg, published by The Japan Times.
The author notes that AI is helping work on long-standing problems, including the so-called Jacobian conjecture. Kirwin Hampshire, a graduate student in pure mathematics, wrote in a post that spread online about a spiritual crisis caused by the risk that mathematicians could become mere observers while bots create new proofs.
From a shortage to an abundance of proofs
Fields Medal laureate Terence Tao believes that AI could move mathematics from a shortage of proofs to an abundance of them. In such a scenario, finished mathematical results could lose value, much like texts, images, or analytical materials that algorithms generate on a mass scale.
Retired University of Cambridge mathematician Keith Carne explained that computers have an advantage due to their ability to compare many possible connections and approaches to a single problem. At the same time, according to Olson's account, the most important mathematical breakthroughs are not limited to proving a particular theorem: they open new ways of thinking and create a foundation for further research and practical applications.
More current news is available on the UA.News Telegram channel Telegram.
The problem of human understanding
Kyoto University mathematics researcher Benjamin Collas called collective knowledge the true result of mathematical work, while published theorems and proofs are its residue. In his view, the risk is that software will generate increasingly more mathematical knowledge that people understand increasingly less.
Olson writes that creating a proof with the help of AI can take several hours, whereas making sense of the result and incorporating it into human knowledge takes years. In her view, this raises questions for universities about supporting teaching, explaining others' results, and creating shared databases and mathematical libraries, rather than focusing only on the number of scientific publications.
A similar dilemma, the column notes, also arises in writing and law: when AI makes the creation of texts and documents cheaper, human judgment, the ability to identify important questions, and the selection of arguments gain greater importance.
