By: Leo Shao
Mathematics has a massive history that goes very far back. Galileo, Euclid, Newton, and other great men have poured hours into developing modern math. Millions have followed in their footsteps, studying math, and developing more theorems and proofs to further expand mathematical knowledge (Timeline of Mathematics | Mathigon). However, can AI ruin mathematics for many?
For more than 2000 years, Euclid’s ways of reasoning were the basis of mathematical argumentation. “He built the mathematics of the time … proving things in such a way that each successive step ‘clearly follows’ from previous ones,” explains Jeremy Avigad, a logician at Carnegie Mellon University. However, by the 20th century, mathematicians were no longer willing to develop proofs in this intuitive foundation. Instead, they developed systems that used symbols, and mechanical rules. This formalization allowed mathematics to be translated into computer code. Proving the four-color theorem showed that computational brute force is hugely effective.
Now mathematicians are facing the latest force: artificial intelligence. In 2019, the findings of computer scientist Christian Szegedy predicted that computers would match and even exceed the problem-solving abilities of the best human mathematicians within 10 years.
Terence Tao, the youngest ever winner of the International Mathematical Olympiad (imo-official.org) when he was 13, agrees with the growing threat of AI. Dr. Tao also notes that mathematicians only began seeing AI as a threat in the recent couple of years.
These days, there are lots of technological advancements that aid in optimizing humans’ daily lives, including dieting, sleep, and exercising. Jordan Ellenberg, a mathematician of Wisconsin-Madison University, points out that AI gadgets will expand to mathematics. One math gadget that has been developed is called Proof Assistant. A mathematician translates his proof into code, and the program checks the reasoning.
However, the assistant also has its drawbacks. It often complains that it doesn’t understand the reasoning steps entered by the mathematician. All that “whining” can make research extremely annoying.
Another automated tool with issues is what computer scientist Marijn Heule calls “brute reasoning.” This supercomputer network searches through a large space to determine whether the theorem is true or false. However, the finalized solutions take up many terabytes in size. This raises questions of whether automated proofs are truly counted as math, and challenges whether artificial intelligence is truly qualified to replace humans in mathematics.
As artificial intelligence continues to grow and improve, mathematicians may see how math will be forever changed. On the other hand, evidence also shows that artificial intelligence also has its lacking areas, including an inflexibility to understand mathematical proofs. However, it will be interesting to witness the birth of an era of artificial intelligence.
Source:
A.I. Is Coming for Mathematics, Too – The New York Times (nytimes.com)
Timeline of Mathematics | Mathigon