the sum of the positive real integers equals -1/12?
That intuitively, and actually, incorrect result appeared to be used in a book on string theory:
If they used that bad summation then what other bad math is in that book? Well, they used an analytic continuation method to rescue their results. Numberphile used standard summation, not super summation, to obtain their result, which is wrong because the sum is divergent.
Burkard Polster, prof of maths at Monarch University in Australia, hits the meat of the response at the 23 minute mark, including analytic continuation, but the whole video is worth the watch:
That intuitively, and actually, incorrect result appeared to be used in a book on string theory:
If they used that bad summation then what other bad math is in that book? Well, they used an analytic continuation method to rescue their results. Numberphile used standard summation, not super summation, to obtain their result, which is wrong because the sum is divergent.
Burkard Polster, prof of maths at Monarch University in Australia, hits the meat of the response at the 23 minute mark, including analytic continuation, but the whole video is worth the watch: