Kung, Caruthers, and Goldman performed the canon, with Caruthers gamely assuming responsibility for the bottom two parts.īefore the final musical offering of the evening-the last movement of the Vivaldi trio-Kung reiterated the reciprocity that exists between math and music: 'Math helps us understand music, and music helps us understand math,' he said. This time, though, it was Bach who anticipated the future of mathematics-through the use of transformations in the composition of his fugues and canons.Īlthough the mathematical study of transformations falls under the umbrella of group theory-pioneered by Gauss and Galois as recently as the early 1800s-Kung noted that 'composers were using similar ideas long before.'Ĭonsider, for example, Canon 14 from Bach’s 'Fourteen Canons on the First Eight Notes of the Goldberg Ground.' It comprises a single line of music, along with a cryptic subtitle: 'a canon in four parts with augmentation and diminution.' Each of the second through fourth parts, it turns out, is derived from the written one via a combination of augmentation, transposition, and inversion. The third and final movement, 'Bach’s Mathematical Foresight,' hearkened back to the earlier prediction theme. He corrected a common misconception-it was aeroelastic flutter that took down the Tacoma Narrows Bridge, not wind-speed resonance-and, with a demonstration of Tuvan throat singing, showed that his musical talents extend beyond his prowess on the violin. In the second movement, titled 'Bridges, Wineglasses, and the Bay of Fundy,' Kung used the wooden boxes that form the bodies of stringed instruments as an entrée into the topic of resonance. The same math helpful in understanding musical overtones also describes the energy levels of an electron, Kung said.

'Once you know the sort of abstract idea of addition, you can apply it in all of these different places.' 'You can add fish, you can add cinnamon rolls, you can add spark plugs,' Kung riffed. Although you first learn to add two piles of, say, apples, you soon discover that you can add other things. Kung also emphasized that the abstractness of mathematics gives it the power of broad application. the goal was more like to get through chapter four.' 'It seems to me that when I was taking a lot of my math classes the goal wasn’t something so grand. 'I think we missed that in a lot of our math classes,' Kung said. He explained that, often, the goal of mathematics is to predict the future. He asked the audience to use mathematical reasoning to determine whether covering the end of a tube would make it sound a higher, lower, or unchanged note when struck. (It’s not just a sine wave.) The discussion of overtones-which touched on differential equations and Newton’s laws of motion, summation notation, and boundary conditions-afforded Kung the opportunity to make two pet points about mathematics. The first movement bore the title 'Symphony in a Single Note,' an allusion to the complexity of the vibration that coaxes music from a string on a violin or the column of air inside a flute.

Musical interludes from a Vivaldi trio punctuated the evening. The three of them presented a program in three movements, one focusing on each of overtones, resonance, and transformations. Math-savvy members of the audience chuckled at this remark, but the MAA Distinguished Lecture 'Symphonic Equations: A Mathematical Exploration of Music' also offered music enthusiasts plenty to engage with and mull over.Īn amateur violinist himself, Kung had two of the 'Closer Than You Think' musicians on stage with him: cellist Yvonne Caruthers and flutist Aaron Goldman, both members of the National Symphony Orchestra. The seminar was called 'Math and Music-Closer Than You Think,' but, as Kung told a packed auditorium at the Carnegie Institution for Science on February 26, he already regarded the two disciplines as ' epsilon apart.' Mary’s College of Maryland mathematics professor David Kung heard a public radio story about a presentation devoted to math and music, he took issue with the presentation’s title. Goldman, Caruthers, and Kung at the Carnegie Institution for Science

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