When mathematicians describe equations as beautiful, they are not lying. Brain scans show that their minds respond to beautiful equations in the same way other people respond to great paintings or masterful music. The finding could bring neuroscientists closer to understanding the neural basis of beauty, a concept that is surprisingly hard to define.
In the study, researchers led by Semir Zeki of University College London asked 16 mathematicians to rate 60 equations on a scale ranging from "ugly" to "beautiful." Two weeks later, the mathematicians viewed the same equations and rated them again while lying inside a functional magnetic resonance imaging (fMRI) scanner. The scientists found that the more beautiful an equation was to the mathematician, the more activity his or her brain showed in an area called the A1 field of the medial orbitofrontal cortex. (...)
Mathematicians say they are unsurprised by the findings. "When I see a beautiful mathematical construction, or an unexpected and wonderfully intricate argument with precise logical interlocking pieces in a proof, I do feel the same way as when I see some art that amazes me," says mathematician Colin Adams of Williams College in Williamstown, Mass. Daina Taimina, a mathematician at Cornell University in Ithaca, N.Y., says beautiful math results "sound like a melody. For me equations are beautiful if they have elegant solution or lead to unexpected, surprising results."
Understanding just what beauty is, not to mention what makes a thing beautiful, is not easy. Beauty is not simply something pleasing that brings happiness. Sad things, after all, can be beautiful. "There is the experience of beauty in pain," Zeki says. Take Michelangelo's Pietà, a statue of the Virgin Mary holding the dead Jesus Christ in her arms. "It's not a joyful thing, but it's very beautiful." (...)
Zeki and his colleagues admit that beauty is not perfectly defined, but say their studies could lead toward a deeper understanding of the idea. "The question we address is what neural mechanisms allow us to experience beauty," Zeki says. "The central issue that emerges from this work for the future is, why is it that an equation is beautiful?"
The study found, for example, that the beauty of equations is not entirely subjective. Most of the mathematicians agreed on which equations were beautiful and which were ugly, with Euler's identity, 1+eiπ=0, consistently rated the most attractive equation in the lot. "Here are these three fundamental numbers, e, pi and i," Adams says, "all defined independently and all critically important in their own way, and suddenly you have this relationship between them encompassed in this equation that has a grand total of seven symbols in it? It is dumbfounding."
by Clara Moskowitz, Scientific American | Read more:
Image:Quinn Dombrowski/Wikimedia Commons
In the study, researchers led by Semir Zeki of University College London asked 16 mathematicians to rate 60 equations on a scale ranging from "ugly" to "beautiful." Two weeks later, the mathematicians viewed the same equations and rated them again while lying inside a functional magnetic resonance imaging (fMRI) scanner. The scientists found that the more beautiful an equation was to the mathematician, the more activity his or her brain showed in an area called the A1 field of the medial orbitofrontal cortex. (...)Mathematicians say they are unsurprised by the findings. "When I see a beautiful mathematical construction, or an unexpected and wonderfully intricate argument with precise logical interlocking pieces in a proof, I do feel the same way as when I see some art that amazes me," says mathematician Colin Adams of Williams College in Williamstown, Mass. Daina Taimina, a mathematician at Cornell University in Ithaca, N.Y., says beautiful math results "sound like a melody. For me equations are beautiful if they have elegant solution or lead to unexpected, surprising results."
Understanding just what beauty is, not to mention what makes a thing beautiful, is not easy. Beauty is not simply something pleasing that brings happiness. Sad things, after all, can be beautiful. "There is the experience of beauty in pain," Zeki says. Take Michelangelo's Pietà, a statue of the Virgin Mary holding the dead Jesus Christ in her arms. "It's not a joyful thing, but it's very beautiful." (...)
Zeki and his colleagues admit that beauty is not perfectly defined, but say their studies could lead toward a deeper understanding of the idea. "The question we address is what neural mechanisms allow us to experience beauty," Zeki says. "The central issue that emerges from this work for the future is, why is it that an equation is beautiful?"
The study found, for example, that the beauty of equations is not entirely subjective. Most of the mathematicians agreed on which equations were beautiful and which were ugly, with Euler's identity, 1+eiπ=0, consistently rated the most attractive equation in the lot. "Here are these three fundamental numbers, e, pi and i," Adams says, "all defined independently and all critically important in their own way, and suddenly you have this relationship between them encompassed in this equation that has a grand total of seven symbols in it? It is dumbfounding."
by Clara Moskowitz, Scientific American | Read more:
Image:Quinn Dombrowski/Wikimedia Commons
