e[sup]iπ[/sup]+1=0, rather. 
Which, by the way, I don’t think we’re talking about. Actually, I’m not exactly sure what equation we’re talking about. Is it e[sup]iθ[/sup] = cos(θ) + i sin(θ) ? AKA “Euler’s formula”? Because that’s useful a lot more places than just particle physics. It’s one of the most important formulas of all time.
I think this must be what we’re talking about. 
ekrisner, I think what Exapno Mapcase was challenging you on (rather more belligerently than was called for, IMHO) was the claim that pure mathematicians apply for grant money by claiming “What I’m working on might have a practical application some day! So fund me!”
Now that the subject has come up, I admit to being a little bit curious as to whether the government funds any research in pure mathematics, and if/when it does so, what arguments the researchers use to persuade it to do so.
Hey thudlow - I think what’s his name just wanted to argue! Even when I offered to send him my own grant proposal he still proceeded to say that no committee would accept such a proposal! Well we were awarded money for research in functional analysis and one for work done with Lie Groups! Both areas of mathematics (lie groups and functional analysis) fit well in either the pure math or applied math categories! Our results were strictly theorretical! But the proposals discussed how our results tie up with quantum mechanics, neuronal networks, and even something about schizophrenia! These ties were admittedly very far fetched. The one propsal was so hastily written that I was rather ashamed to have my name on it! Anyways these are just two of my own personal experiences! I have peers that also had success! So I guess the short answer to your question is that yes it is possible to get grant money for doing pure mathematics! Whether one can obtain money for doing something like set theory or algebraic topology I have no idea! Maybe our grant expert can fill us in!
That said, grant money has been increasingly tough to come by as the years go by. The grant money expert may be correct that committees may flat out reject proposals that make these far fetched ties to the physical sciences. But I wonder if these committees are competent enough to determine that the claims are as grandiose as they really are!
I think you’re right! I believe the equation at hand here is the one that links the gamma function to the beta function! Since I do not have Greek letters assume that G denotes the gamma function B denotes the beta function! The equation is
B (p, q)= G (p) G (q) / G (p+q)
The function in question is the beta function. Not surprising that is would appear in applications Euler did not consider. While beta function may not be commonly taught in high school, it is not very obscure, and is usually covered in math classes along with the gamma function. It is a step away from being common enough to be included as a function on cheap scientific calculators.
I can speak to algebraic topology. I’ve read dozens of papers on homotopy theory that were grant-supported. Most dated were older, supported by military grants, but they exist.
In Canada at least the applications are not publicly available; there is too much private information on them. I suppose it wouldn’t hurt to make the research proposal public, but a lot of the personal information is private.
In any case, I can affirm that I have used such arguments. And I have three cases of my papers being cited, two by computer scientists and the third in a paper on shuffling of cards.
It is hard to imagine today, but in the mid 19th century, matrix theory was widely ridiculed as an example of utterly useless mathematics that could never ever have any application. I am guessing that maybe group theory was too (but I could be wrong about that). And G. H. Hardy actually reveled in the idea that his beloved number theory could never be applied to anything useful. (Try that, RSA.)
Is it that physics finds itself constrained to available mathematics? Or that mathematicians have a crystal ball (I think not). Eugene Wigner published an article titled “The unreasonable effectiveness of mathematics in the natural sciences” musing on the question.
Two things. Exapno is exaggerating, I think, when he suggests that only one in one thousand “theoretical mathematicians”–if the labels are indeed so neat all the time–get involved with other disciplines. And two, algebraic topology is presently being used in a very real and important way at my university, at least, in the field of DNA research and manipulation.
Yes, exaclty. It was Veneziano who realised that the function could be interpreted as giving the scattering amplitude of some strong force processes. Later, the formula was interpreted by Susskind and others in terms of one-dimensionally extended excitable objects—i.e. strings (the resulting theory being catastrophically wrong when applied to the strong force, with modern day string theory essentially being a reinterpretation at a much higher energy scale).
Imaginary numbers were considered purely theoretical and of no practical use, at first, but turned out to be very useful for anything with phase information (e.g., electronics, which is pretty practical).
Matrix math was pretty much unknown by physicists until it turned out to be useful for handling thermodynamics. At the time a lot of physicists grumbled at having to learn such abstruse math! That seems rather amusing from today’s standpoint.
the way e was explained to me made perfect sense.
Take £1 and apply 100% interest to it once a year. You end up with £2
Take £1 and apply 50% interest to it compounded twice a year - £2.25
25% 4 times a year? £2.4414
and so on and so on.
Splitting the interest and time scales into smaller and smaller amounts you eventually see the answer converging to the value of e 2.7182818 (and on and on and on) but of course you never get to a perfect answer because you can split the time and interests into infinitely small values.
As e deals with “growth” then it is not surprising that we see it in nature.
Pi can be approximated by using the geometric properties of many-sided polygons, and of course you can always go one side more. Sure enough we find that ratio in nature all around us.