“If mathematicians really understood, that would lead to profound advances in mathematics.” Fields Forever “We won’t know until we get there, but it’s certainly my expectation that we’re just seeing the tip of the iceberg,” said Greg Moore, a physicist at Rutgers University. In recent years, they’ve finally begun to understand some of the basic objects in QFT itself - abstracting them from the world of particle physics and turning them into mathematical objects in their own right. It’s just a better way to organize them,” said David Ben-Zvi, a mathematician at the University of Texas, Austin.įor 40 years at least, QFT has tempted mathematicians with ideas to pursue. “Physics itself, as a structure, is extremely deep and often a better way to think about mathematical things we’re already interested in. The rewards are likely to be great: Mathematics grows when it finds new objects to explore and new structures that capture some of the most important relationships - between numbers, equations and shapes. This means defining the basic traits of QFT so that future mathematicians won’t have to think about the physical context in which the theory first arose. Now mathematicians want to do the same for QFT, taking the ideas, objects and techniques that physicists have developed to study fundamental particles and incorporating them into the main body of mathematics. This impulse (along with revelations from Gottfried Leibniz) birthed the field of calculus, which mathematics appropriated and improved - and today could hardly exist without.
Almost 2,000 years later, Isaac Newton wanted to understand Kepler’s laws of planetary motion and attempted to find a rigorous way of thinking about infinitesimal change. Mathematics turned it into a discipline with definitions and rules that students now learn without any reference to the topic’s celestial origins. The ancient Greeks invented trigonometry to study the motion of the stars. For millennia, the physical world has been mathematics’ greatest muse.
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