Oh, good. There’s this claim going around that the sum of all natural numbers (1+2+3+4+5…) converges on the value -1/12. I saw that and said to myself that it’s obviously wrong, but saw the smooth patter and rapid-fire use of mathematical jargon and infinities, and no mathematician myself, couldn’t see where the error slithered in. Mathematician to the rescue: Mark Chu-Carroll explains why the story doesn’t work. Short answer: they falsely equated a summation with a converging series.
Inconsistency is death in mathematics: any time you allow inconsistencies in a mathematical system, you get garbage: any statement becomes mathematically provable. Using the equality of an infinite series with its Cesaro sum, I can prove that 0=1, that the square root of 2 is a natural number, or that the moon is made of green cheese.
What makes this worse is that it’s obvious. There is no mechanism in real numbers by which addition of positive numbers can roll over into negative. It doesn’t matter that infinity is involved: you can’t following a monotonically increasing trend, and wind up with something smaller than your starting point.
I could see the point he makes in the second paragraph, but it takes much deeper knowledge to pick out the flaw in the argument.
(Dang — I don’t even have a category for math here. Should I start one? Not that I can talk about math very often.)