I have a different approach when I see a suspicious-looking claim from an authoritative-seeming source. The first thing I do is rephrase the claim so that instead of a yes/no question it’s an open-ended question. (In this case: “What is the sum of 1+2+3+4+...”) Then I go to Google (or PubMed or wherever) and try to it, without using any references or other clues from the original source. If the first answer I find matches, this is evidence that the original source is trustworthy; if it doesn’t match, and the claim was presented as though it were uncontroversial, then I give the original source a big credibility hit.
The idea is to escape the original source’s framing, because if it isn’t trustworthy, then any thinking you do on its terms will also be suspect. I find this works much better than trying to engage with suspicious claims on their author’s terms.
That’s a good approach for things where there’s a ‘real answer’ out there somewhere. I think it’s often the case that there’s no good answer. There might be a group of people saying they found a solution, and since there no other solutions they think you should fully buy into theirs and accept whatever nonsensities come packaged with it (for instance, consider how you’d approach the 1+2+3+4+5..=-1/12 proof if you were doing math before calculus existed). I think it’s very important to reject seemingly good answers on their own merits even if there isn’t a better answer around. indeed, this is one of the processes that can lead to finding a better answer.
I have a different approach when I see a suspicious-looking claim from an authoritative-seeming source. The first thing I do is rephrase the claim so that instead of a yes/no question it’s an open-ended question. (In this case: “What is the sum of 1+2+3+4+...”) Then I go to Google (or PubMed or wherever) and try to it, without using any references or other clues from the original source. If the first answer I find matches, this is evidence that the original source is trustworthy; if it doesn’t match, and the claim was presented as though it were uncontroversial, then I give the original source a big credibility hit.
The idea is to escape the original source’s framing, because if it isn’t trustworthy, then any thinking you do on its terms will also be suspect. I find this works much better than trying to engage with suspicious claims on their author’s terms.
That’s a good approach for things where there’s a ‘real answer’ out there somewhere. I think it’s often the case that there’s no good answer. There might be a group of people saying they found a solution, and since there no other solutions they think you should fully buy into theirs and accept whatever nonsensities come packaged with it (for instance, consider how you’d approach the 1+2+3+4+5..=-1/12 proof if you were doing math before calculus existed). I think it’s very important to reject seemingly good answers on their own merits even if there isn’t a better answer around. indeed, this is one of the processes that can lead to finding a better answer.