Category talk:Mathematics user templates

Userbox changing
I feel that the mathematical expressions used in User mathematician-3 and User mathematician-4 should be exchanged. While complex number are often taught at school level, only a few people know how to use zeta functions. I came upon this idea, while thinking about the solution to a question posed at Template talk:User mathematician-3. I was about to write: "If you know the answer to the template expression, you can use the userbox", when I realized that the next level had an easier expression to evaluate. &mdash; Ambuj Saxena (talk) 17:08, 18 July 2006 (UTC)


 * But the expression on User mathematician-3 is not really about zeta functions; it's about an infinite series which is very common in first-year calculus. And likewise, the expression on User mathematician-4 is not really about complex numbers, but about complex analysis, which is far less common to take.  I think they're in the right order.  Perhaps the right heuristic is that if you can rigorously evaluate the expression, then you can use the userbox. Ryan Reich 17:56, 18 July 2006 (UTC)


 * The rigorous evaluation of the expression in User mathematician-4 is taught in higher secondary schools. The rigorous evaluation of expression in User mathematician-3 would (AFAIK) require use of zeta functions, taught only at college level. &mdash; Ambuj Saxena (talk) 18:08, 18 July 2006 (UTC)


 * Am I reading the expression $$\sum_{i = 1}^\infty \frac{1}{i}$$ incorrectly? It is a harmonic series, which is divergent, which I can prove five ways from Sunday is divergent using nothing more than calculus I learned in my third year of high school.  On the other hand, $$e^{i\pi} = -1$$ can not even be made sense of until you define the complex exponential function, which means you must define analysis in the complex plane, and this is not done until the second year of college at the earliest. Ryan Reich 18:21, 18 July 2006 (UTC)


 * Indeed, the evaluation $$e^{i\pi} = -1$$ requires complex expotential functions, something I was taught in 12th standard. In India we have 10+2 system of education, so making clear that 12th is still considered school level. The harmonic series is a very special series that can be evaluated using zeta functions, and equalls "&minus;½". This is not taught until one takes higher studies in mathematics. &mdash; Ambuj Saxena (talk) 18:30, 18 July 2006 (UTC)


 * It is certainly possible to define enough of complex analysis to get to $$e^{i\pi}$$ in high school, but the equation is properly part of more advanced mathematics. As for the harmonic series, you are clearly mistaking it for $$\zeta(0)$$, and you should read Zeta constant and harmonic series to refresh your memory. Ryan Reich 19:09, 18 July 2006 (UTC)


 * Ah yes...that may be possible. I will look it up. Probably I was thinking about $$\zeta(0)$$ itself. Sorry for the botherations. &mdash; Ambuj Saxena (talk) 19:15, 18 July 2006 (UTC)

Personally speaking, $$e^{i\pi} = -1$$ is utterly beautiful, one of those mind-boggling great truths. The expression $$\sum_{i = 1}^\infty \frac{1}{i}$$ has an important meaning in math, but the gut reaction is that whoever writes such a thing is unclear on the concept. Perhaps, what you were looking for was $$\frac{-1}{12}=\sum_{i = 1}^\infty 1$$ which is $$\zeta(0)$$ which is .. interesting .. and has some subtle, suggestive aspects, but I don't think it implies at any great truths. linas 19:40, 30 July 2006 (UTC)