Visualizing the Riemann zeta function and analytic continuation
This function is famously confusing outside its "domain of convergence", but a certain visualization sheds light on how it extends. There are posters for this ...
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The Riemann zeta function. This is one of those objects in modern math that a lot of you might have heard of, but which can be really difficult to understand. Don't worry, I'll explain that animation that you just saw in a few minutes. A lot of people know about this function because there's a one-million-dollar prize out for anyone who can figure out when it equals 0. An open problem known as the Riemann hypothesis. Some of you may have heard of it in the context of the divergent sum 1 + 2 + 3 + 4... on and on up to infinity. You see there's a sense in which the sum equals -1/12, which seems nonsensical if not obviously wrong. But a common way to define what this equation is actually saying uses the Riemann zeta function. But as any casual Math enthusiast who ...
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The Riemann zeta function. This is one of those objects in modern math that a lot of you might have heard of, but which can be really difficult to understand. Don't worry, I'll explain that animation that you just saw in a few minutes. A lot of people know about this function because there's a one-million-dollar prize out for anyone who can figure out when it equals 0. An open problem known as the Riemann hypothesis. Some of you may have heard of it in the context of the divergent sum 1 + 2 + 3 + 4... on and on up to infinity. You see there's a sense in which the sum equals -1/12, which seems nonsensical if not obviously wrong. But a common way to define what this equation is actually saying uses the Riemann zeta function. But as any casual Math enthusiast who ...
