## Bad maths and climbing: a definitive answer?

*Goguelu Lemoutardier - 04 / 05 / 2023*

The abstract is rather simple: we don't have a clue yet, just a hint.

Our talent for climbing is not homogeneously shared among us. Here is a proof.

When \(a \ne 0\), there are two solutions to \(ax^2 + bx + c = 0\) and they are
$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$
In equation \eqref{eq:sample}, we find the value of an
interesting integral:
\begin{equation}\label{eq:sample}
\int_0^\infty \frac{x^3}{e^x-1}\,dx = \frac{\pi^4}{15}.
\end{equation}

Finally, note that the paper [3] has some interest.

\(\textit{Bibliography}\)

[1]
Olivier Bernardi and Mireille Bousquet-Mélou.
Counting colored planar maps: Algebraicity results.
*Journal of Combinatorial Theory, Series B*, 101(5):315--377, 2011.

[2]
Olivier Bernardi and Mireille Bousquet-Mélou.
Counting coloured planar maps: Differential equations.
*Communications in Mathematical Physics*, 354:31--84, 2017.

[3]
Mireille Bousquet-Mélou.
Counting planar maps, coloured or uncoloured.
In R. Chapman, editor, *Surveys in Combinatorics 2011*, London
Mathematical Society Lecture Note Series, pages 1--50. Cambridge: Cambridge University Press, 2011.