Communications of the ACM
The niverse or the Brain: Where Does Math Originate?
Credit: The Kavli Foundation
Math describes and predicts the world all around us — from the helical structure of DNA to the spirals of galaxies. But does this mean our world is inherently mathematical?
The question has become a hot topic of debate as neuroscientists continue to uncover mathematical abilities we seem to be born with, and have pinpointed regions in the brain responsible for mathematical thinking. "[N]umbers are not properties of the universe, but rather they reflect the biological grounding for how people make sense of the world," says Rafael Núñez, professor of cognitive science at the University of California, San Diego and member of UCSD's Kavli Institute for Brain and Mind.
Says Brian Butterworth, emeritus professor of cognitive neuropsychology at the Institute of Cognitive Neuroscience at University College London, "Numbers are not necessarily a property of the universe, but rather a very powerful way of describing some aspects of the universe."
Núñez and Butterworth are among four scientists who recently grappled with this question at the invitation of The Kavli Foundation. Offering a different perspective: physicists Simeon Hellerman and Max Tegmark. "I think many physicists, including myself, agree that there should be some complete description of the universe and the laws of nature," says Hellerman, associate professor at the Kavli Institute for Physics and Mathematics of the Universe at the University of Tokyo, Japan. "Implicit in that assumption is the universe is intrinsically mathematical."
"[N]ature is clearly giving us hints that the universe is mathematical," says Tegmark, professor of physics at the Massachusetts Institute of Technology, and member of MIT's Kavli Institute for Astrophysics and Space Research. According to Tegmark, many mathematicians even feel that they don't invent mathematical structures, "they just discover them — that these mathematical structures exist independently of humans."
Tegmark also points out this isn't just interesting as an academic idea; if correct, then mathematics has a special role for advancing human knowledge.
"If math is inherent out in the universe, then mathematics can give us hints for solving future problems in physics," Tegmark says. "If we really believe that nature is fundamentally mathematical, then we should look for mathematical patterns and regularities when we come across phenomena that we don't understand. This problem-solving approach has been at the heart of physics' success for the past 500 years."
An edited transcript of the scientists' discussion is online at http://www.kavlifoundation.org/science-spotlights/kavli-origins-of-math.
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