Topology is the only major branch of modern mathematics that wasn't anticipated by the ancient mathematicians. Throughout most of its history, topology has been regarded as strictly abstract mathematics, without applications. However, illustrating Wigner's principle of "the unreasonable effectiveness of mathematics in the natural sciences", topology is now beginning to come up in our understanding of many different real world phenomena. In this minisymposium, Robert MacPherson ...
For more than eighty years, scholars at the Institute for Advanced Study have sought to understand the complexities of the physical world and of humanity, prompting advances in science and society. Access a listing of the Institute’s community of scholars from our founding to today and learn more about some noted figures in IAS history.
How a lone theorist’s pursuit of symmetry shaped music history
On the second Sunday after Trinity in 1724, the congregation at the Thomaskirche in Leipzig heard Johann Sebastian Bach’s new cantata that began with the words Ach Gott. Bach set the word Gott to the most dissonant triad known at the time: the augmented triad.
The augmented triad has long been a headache for music theorists, only partially on the basis of its harsh sound.