# Discussion about “motivation of concept” kind of questions

Very often in mathematics and related sciences the motivation of a concept is helpful or even fundamental for its understanding. Obviously, this motivation has two origins: a historical one, and a technical one. For this reason, a question asking about the origin or motivation of a concept could fit, more or less, either into hsm.se and math.se, physics.se, etc. What should we do about this?

This question came to mind because of this question: Why is the Dirac delta "function" often presented as the limit of a Gaussian with a fraction in the exponent? which in my opinion doesn't belong in hsm, but in math.

I'd like to discuss what to do about the general case, and also what should be done about the particular example.

In my opinion, these fit in hsm. There are two main reasons for my answer.

• Often, the answer is not only maths or physics related, but lie in the field of the original concept author, which may not be the field of interest of the person that asks the question. A perfect example is the Dirac question you cite. If it were to belong to some other place than hsm, it should be in physics, not maths. For this reason, in this particular example we should stay here.

• The technical motivation is not a motivation any more after the concept becomes helpful in more than one field, which most often is the case. The original technical motivation therefore becomes the historical technical motivation, which brings us back to hsm.

As a more general answer, I would like to state that discussing maths and/or science history does mean, at times, discussing maths or physics. We should not be rebutted by answers that requires some technical knowledge in these, and they totally belong here IMO.

• I'm sorry it took me so long to reply, but here we go: $(1)$ Just because a person doesn't have the formation to understand the technical motivation it means the question becomes historical. If the user wants to understand what's behind, (s)he'll have to study said field. $${}$$ $(2)$ I think pretty much the same as in $(1)$. I believe in very few cases the motivation has a subjective/historical reason, most often it's the understanding of the field you're working with that dictates the definitions. – hjhjhj57 May 4 '15 at 23:19
• @Javier can I have an example? Because in your question, understanding of mathematics would not help. – VicAche May 5 '15 at 8:56
• What's needed is some understanding of dimensional analysis, elementary mathematics, and maybe some physical or mathematical intuition. – hjhjhj57 May 5 '15 at 9:06
• Dimensional analysis is, at least here in France, taught only to would-be physicists, and at university level. What's important IMO in this question his really the setting in which the Dirac was introduced, which is not the only possible "technical motivation" for such a function. – VicAche May 5 '15 at 9:51
• Ok, then it should be migrated to physics. As you can see the accepted answer isn't even a historical one. – hjhjhj57 May 6 '15 at 2:20
• If you don't know where it should be migrated, it's because it shouldn't be migrated - the question is about maths, the answer about physics. The answer is historical: the invention was first introduced in the field of physics, hence it carries its past in its most common written form. – VicAche May 6 '15 at 11:33
• I completely disagree, that's not even the point. Look at the accepted answer, it doesn't have anything to do with history. The user tried to give it some historical context by stating that Dirac was a physicist, nothing else. Edit: I hadn't realized you're the poster of the accepted answer, haha. How can you say your answer is historical? – hjhjhj57 May 6 '15 at 21:17
• Makes it even funier :). My answer is hsitorical IMO as you need to know about the context in which he was working to answer, and not only on the mathematical/physical reason why this was (strangely) retained as the canonical form. I really believe you should post an answer of your own to this question. – VicAche May 6 '15 at 22:15