Analytic continuation Lucille says, “I’m going to stick an equals sign between the value of the analytic continuation of a function at a point and the infinite series that defines the function elsewhere.” Video from Fox, gif from fanpop.com.
I’m usually a fan of the Numberphile crew, who do a great job making mathematics exciting and accessible, but this video disappointed me. There is a meaningful way to associate the number -1/12 to the series 1+2+3+4…, but in my opinion, it is misleading to call it the sum of the series. Furthermore, the way it is presented contributes to a misconception I often come across as a math educator that mathematicians are arbitrarily changing the rules for no apparent reason, and students have no hope of knowing what is and isn’t allowed in a given situation. In a post about this video, physicist Dr. Skyskull says, “a depressingly large portion of the population automatically assumes that mathematics is some nonintuitive, bizarre wizardry that only the super-intelligent can possibly fathom. Showing such a crazy result without qualification only reinforces that view, and in my opinion does a disservice to mathematics.”
Read the full post at Roots of Unity.
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