What are appropriate historical questions?

Recently, I heard a lecture about education in which the speaker went on for a few minutes about what he described as an historical mathematical controversy, involving (among others) Einstein and Newton.

The entire thing didn't sound right to me, but I like to learn and so I tried to research it. I couldn't find anything on the topic, and since "History and development of mathematics" is one of the topics of discussion here at math.stackexchange.org, I decided to ask here.

Within minutes of asking the question it was downvoted and closed, and the best I can gather is because the speaker's assertion, that I originally thought "sounded wrong," was indeed wrong.

However, I'm at a loss as to why simply asking if such a controversy existed or not was a bad question. If I knew ahead of time that it was an invalid historical claim about math, I would not have asked. When we hear a lecture about something, we're only allowed to ask about if it we already know it's correct? That's the message I'm getting here.

I genuinely don't understand why my question was not a valid historical question ("is this something in math history?"). How could I have written my question to be on-topic?

When composing my question I thought about saying something like "this seems highly dubious" or "this doesn't make sense to me," but I went out of my way to try and sound as neutral as possible, and just see what more knowledgeable people than me had to say about the topic. It wouldn't be the first time that I just wasn't aware of something, or didn't understand something on the first explanation.

• Mr. DeMille has, all from an unaccredited school, a BA in Biblical Studies; an MA in Christian Political Science, and a PhD in Religious Education; additionally, a BA in International Relations from BYU. Your question was arguably downvoted for wackiness. – gnometorule Jul 22 '14 at 1:22
• If someone is sincerely trying to discern whether or not a particular assertion is true, is that wacky? Again, if I was knew the answer to my question ahead of time, I wouldn't have asked it. It seems like this is a catch-22: don't ask wacky questions--and you'll know your question is wacky if you ask it and are told so. But how are you to know ahead of time? – Josh Jul 22 '14 at 1:35
• it's wacky to "want to learn about math" using someone with above's credentials as a guide. Someone had to tell you, and a site of mostly US members supporting "independent exploration and thirst for knowledge of special children" wasn't going to tell you. – gnometorule Jul 22 '14 at 1:39
• I'm not sure what I said that made you think I wanted to use DeMille as a "guide" to learning more about math. I did, however, want to know whether or not an assertion he made had any truth to it. I take it from your response that I should have known the answer to my question; in essence, you feel it was a dumb question, and as such was unwelcome here. I'll try not to make such a mistake here again. – Josh Jul 22 '14 at 1:50
• The referenced question seems to have been deleted, so there is no way for some of us to know what the rest of you are talking about. – DanielV Jul 31 '14 at 3:17
• @DanielV: The person with the amazing credentials I summarize above (who OP felt strongly enough about to link to, and underline how great he is) claimed in one of his "lectures" that Newton had proved "1+1=2"...but Einstein later showed him wrong/cast doubt on it!!! Question: is that true? That's how I remember it. – gnometorule Jul 31 '14 at 21:02
• I never said anything intended to "underline how great he is." Everything I said about DeMille was merely to provide context for the question. Not knowing what aspects of the context might be important (because DeMille's claim seemed so outrageous as to make me think there may be a major misunderstanding on my part), I erred on the side of providing as more rather than less context. I'm sorry if that offended you somehow. – Josh Jul 31 '14 at 22:11
• @DanielV, gnometorule's summary is more or less correct. DeMille asserted that mathematicians have debated whether or not you can formally prove 1+1=2, Newton provided a formal proof for 1+1=2, and Einstein demonstrated an error in his proof. I had never heard these assertions, was highly skeptical (1+1=2 seemed axiomatic to me) but still curious if there was any truth to his claim. I researched and couldn't find any controversy, and so I posted here asking if there really was any such historical "controversy" regarding the equation 1+1=2. Apparently, it's not ok to ask that question here. – Josh Jul 31 '14 at 22:18
• @Josh Let me expand on user72694's answer below. In 1910 Russell and Whitehead published [ en.wikipedia.org/wiki/Principia_Mathematica ](Principia Mathematica) which contained a proof in Volume I page 379 (see link) that 1+1=2. Russell is also famous for publishing a foundational paradox in the set theory of the time. This is probably what the author is quite terribly confusing. Foundational questions like "can we prove 1+1=2" weren't even really studied in Newton's time, probably would have been answered "no it's an assumption", and during Einstein's time it was only just starting. – DanielV Aug 1 '14 at 0:45

To address the title question, I think that historical questions are appropriate

if they are likely to have a definitive answer supported by facts.

I fished through some questions with the math-history tag and found these as roughly fitting that description:

How did Hermite calculate $e^{\pi\sqrt{163}}$ in 1859?

Why are rings called rings?

Can you provide me historical examples of pure mathematics becoming "useful"?

Examples of mathematical results discovered "late"

In contrast,

historical questions which are a challenge to debate would be considered off-topic.

Sometimes such questions are asked in good-faith without realizing the question is not a good fit. Very occasionally, such posts are intentionally disruptive: anyone on the internet for very long is sure to have met one of those personality types. (And I'd prefer not to give examples of this type because I don't want to single anyone out, and because the worst offenders are already deleted and hard-to-find, and also because it would be bad to once again feed attention to them.)

Actually, this last grey box is a very mild way of describing what I mean. One litmus test that should probably be applied to each historical question (or maybe all questions) is: "does this have potential to generate backlash?" For the worst offenders, this is exactly the goal. What generates backlash? The main thing that comes to mind for me is when fringy posters go on about work that runs largely counter to the main body of mathematics.$^\ast$ We don't like to see such folks manipulating our forum to gain attention. Fortunately this is rare and will hopefully remain that way.

$^\ast$ Unorthodox mathematics has its place, but it's just not often on-topic here :)

• very good summary – David Holden Aug 2 '14 at 14:27

Your question would be received better without the copy-pasted passage, which dominates the text. You could have simply asked whether there is any historical evidence of Newton proving $1+1=2$ and Einstein disproving that. Copy-pasting a large amount of rambling text does not improve the presentation. And mentioning that the book is for sale (with a link to the seller) makes the question look more like spam than a scientific inquiry.

Not every question that could conceivably be asked about mathematics is a question worth keeping on a Stack Exchange site. This particular question is of no use, and should be deleted. Closing it is the first step toward that.

• Because I was so confounded by the author's assertion, I wanted to transcribe what he said; I was concerned that if I simply asked the "short version" there would be a nuance I was missing in the author's assertion. I posted a link to the lecture on his website because I didn't know of simpler way to source it and be very particular about the source in question. I certainly stand nothing to gain from somebody purchasing it, or downloading it, or doing anything else with it. – Josh Jul 21 '14 at 20:33
• Thank you for taking the time to respond and offering some suggestions on how I could have asked the question differently. If I have a question the future I will take your advice into account. – Josh Jul 21 '14 at 20:34

There may soon be a History of Mathematics and Science site on SE (now getting commitments in Area 51). If it comes to pass, you might ask those questions there. For now, questions on the history of mathematics that actually employ mathematics are on topic here.

• – Martin Sleziak Jul 22 '14 at 15:41
• that is good news. i have many questions about the history of mathematics, but have not felt it appropriate to post them on MSE – David Holden Aug 2 '14 at 14:29

I disagree with and would not have voted for closure.

The problem with your question is that DeMille is, in my opinion, a crank, and the passage you posted about "$1+1 = \infty$" is mathematical crankery. This does not reflect negatively on you, and I happen to think that far worse things could come about through this site than debunking this kind of nonsense and teaching people the correct history of mathematical ideas like the axiomization of arithmetic, but people probably reacted negatively to the crankery.

That said, linking to the book for sale was inappropriate, and may have made some user's trigger fingers itchier than usual.

• Teaching people the correct history of mathematical ideas is a noble goal. But teachers won't go about it by reading a passage of DeMille and then building classroom discussion around it. To get good answers, one needs a sensible question to begin with. – user147263 Jul 31 '14 at 21:12
• @900sit-upsaday I don't follow. Nobody is suggesting (I don't think!) that one should read DeMille to learn about mathematics. Rather, I'm saying it's a noble goal to clarify misconceptions like "Newton first proved $1+1=2$, and Einstein later disproved it" when they arise on this site, rather than closing and downvoting to -4. – user7530 Aug 1 '14 at 15:43
• "Clarify rather than closing" is false dichotomy. The misconception should be clarified -- and it was; and the question should be closed and deleted -- as it was. There is no permanent place for cranks' theories on this site. The downvotes were unnecessary, but they were deleted together with the question, and do not affect the asker's reputation. – user147263 Aug 1 '14 at 17:08
• @900sit-upsaday Well, I certainly agree we shouldn't turn math.se into a vehicle or self-publishing crank theories. But I don't see the harm in debunking said theories should a non-expert encounter them and ask about them, as occurred here, or leaving our clarification undeleted so that others searching for said theories can encounter the real mathematics. – user7530 Aug 1 '14 at 18:17
• I'm sure I'm not the first or the last person to hear DeMille make this claim, and by deleting this question and the clarification that DeMille is way off base, any who hear him and try to find out if this claim has any basis in reality will not be able to find that clarification. RE: the link to an MP3 for sale, which I provided for context, not because I thought anyone would buy it (and I certainly wouldn't get anything if they did): it could have simply been edited out of the question if it violates the TOS. I viewed it as no different than providing a reference to the original source. – Josh Aug 2 '14 at 15:32

I suspect that DeMille got Newton and Russell confused. They both wrote Principia Mathematica. DeMille's claims do seem whacky but I second Josh's sentiment that there is too much intolerance here for historical questions. Several of my own questions that ended up being quite popular were initially closed and much effort was wasted in having them reopened.

• Really? "much effort was wasted"? this was closed and it looked like that when it was reopened. It's sad to see a member of the site with 10k saying that extending a short and arguably not serious question into a proper question is a wasted effort. – Asaf Karagila Jul 31 '14 at 19:22
• (Your other popular question that has been closed also underwent improvements including the explanation of what sort of answer you are looking for, when the original question was strange and unclear (and therefore it got closed). So again, I don't see how improving a question into reasonable form is a wasted effort.) – Asaf Karagila Jul 31 '14 at 19:24
• @AsafKaragila, certainly questions should be improved, but why close it on the same day it was asked? That seems intolerant. – Mikhail Katz Aug 3 '14 at 7:51
• So when a student fails the first exam, you give him a passing grade and fail him after the resit, if he hasn't come to improve the grade? – Asaf Karagila Aug 3 '14 at 9:55
• Why close on the same day? Because it's an efficient thing to do. When I see a question that fits a close criterion, I press the close button. I'm not going to pull out my calendar and mark on the next day's agenda "go look at that question again". – user147263 Aug 3 '14 at 15:21