If math is more than proof, we need to better celebrate the rest of it (terrytao.wordpress.com)

Article summary

The article discusses the need to redefine the value of mathematical work beyond generating proofs, as machines can now perform this task. It proposes the concept of a 'motivated explanation' as a new measure of mathematical understanding. The author argues that this shift is necessary to correct misconceptions about the role of mathematicians and to better celebrate the contributions of mathematicians. The article also provides examples of motivated explanations and suggests ways to elevate their status in the mathematical community.

Main themes

• mathematical understanding
• AI-generated proofs
• motivated explanations
• funding and utility
• human vs AI capabilities
• redefinition of mathematical work
• Goodhart's Law
• falsification and proof

What commenters say

• Mathematics is suffering from Goodhart's Law, where the measure of generating proofs has become the target, rather than a means to an end.
• The rise of AI-generated proofs may render human mathematicians obsolete, but some argue that human understanding and explanation are still essential.
• The concept of proof is not opposed to falsification, but rather, positive proofs advise against wasting effort on searching for counterexamples.
• The funding and utility of mathematical research are being reevaluated in the face of AI advancements, with some arguing that the field must adapt to remain relevant.
• The idea that the purpose of math is to produce machine-checkable proofs is a modern concept, and understanding has always been the true point of mathematics.
• Some argue that AI will never be able to perform intellectually at the same level as humans, while others believe that AI will surpass human capabilities, making human research obsolete.
• The shift towards motivated explanations may require a redefinition of what constitutes meaningful mathematical work and how it is valued and rewarded.
• The relationship between human mathematicians and AI is complex, with some seeing AI as a tool to enhance human understanding, while others view it as a threat to human relevance.