"1/2 = infinity, great is the glory.... "

[nomadreid]

I am looking for the details of when a famous mathematician in history (Gauss? Euler?) tried to find an infinite sum (integrate?) in two different ways, and got two different answers, one of them one-half and the other one infinity (where maybe a negative was attached to one of them). When he couldn't find his error, he penned (in Latin) some sarcastic remark like "One half equals infinity. Great is the glory of God!" at the end of the calculations.
When I try to google it, I get the usual huge number of sites about the misapplication of the Riemann zeta function that "proves" that infinity equals a negative 1/12. As I remember hearing the story many years ago from multiple sources, it was not apocryphal.

 

[fresh_42]

This is not much information for a qualified search. My second approach was to search for Kronecker, because he really was, other than Gauß or Euler, a sarcastic person. But "God"+"Kronecker" inevitably yields the integer quotation and answers to it.

 

[nomadreid]

Thanks for trying, fresh_42. As you say, this isn't enough for a decent Internet search, which is why I was hoping that someone in the forum may have heard (and remembered) this story.

 

[fresh_42]

I have found a "proof" for $\infty =1/2$ but it is certainly nothing a mathematician would have written, except for joking. And I didn't encounter the anecdote, and I love anecdotes like this, anywhere else, not even during my research about Ramanujan sums when I wrote the insight article on the Riemann hypothesis.

 

[nomadreid]

OK, if I am able to find a reliable and more detailed account from another source than this forum, I will post it here.

 

[Rive]

I recall something vaguely resembling regarding Grandi's series, but that was not sarcasm at all, but some serious, religious addition...

 

[pinball1970]

I am looking for the details of when a famous mathematician in history (Gauss? Euler?) tried to find an infinite sum (integrate?) in two different ways, and got two different answers, one of them one-half and the other one infinity (where maybe a negative was attached to one of them). When he couldn't find his error, he penned (in Latin) some sarcastic remark like "One half equals infinity. Great is the glory of God!" at the end of the calculations.
When I try to google it, I get the usual huge number of sites about the misapplication of the Riemann zeta function that "proves" that infinity equals a negative 1/12. As I remember hearing the story many years ago from multiple sources, it was not apocryphal.

Numberphile? They like the querky stuff.
My infinite series = -1/12 post, crashed and burned though. They got that one wrong apparently.

Always have in mind that Mathematicians like to mess with humans so it is probably just an in joke they have.

 

[nomadreid]

I recall something vaguely resembling regarding Grandi's series, but that was not sarcasm at all, but some serious, religious addition...

There were a couple of religious (or pseudo-religious) connections; Grandi was a Jesuit priest, and thought that getting 0 on one hand and 1/2 on the other meant that God could create something out of nothing. Then Leibniz thought Grandi's series was a good addition to his list of interesting things that might help a missionary friend of his convince the Chinese into seeing that mathematics was just God's manifestation, and thus help convert them to Christianity. But, as you say, this was not the sarcastic instance I was looking for. Thanks for the mention, though.

 

[nomadreid]

so it is probably just an in joke they have.

When I first came across it, it was not stated as either apocryphal or an invented joke, but perhaps my source was mistaken. If I do not find it after more digging, I will assume that it was one of those things that had entered (and exited) the mathematics folklore.