[Richardson's theorem][1] says that it is undecidable to tell whether an expression $E$ satisfies $E=0$, where $E$ is generated by $\mathbb{Q}\cup\{\pi,\ln 2,x\}$ and the composition of operations in $\{+,-,\times,\sin,\exp, \mathrm{abs}\}$.

(I thought this deserves its own answer, even if it's given as a comment on [this other answer][2].)


  [1]: https://en.wikipedia.org/wiki/Richardson%27s_theorem
  [2]: https://mathoverflow.net/questions/11540/what-are-the-most-attractive-turing-undecidable-problems-in-mathematics/11555#11555
  [3]: https://en.wikipedia.org/wiki/Risch_algorithm