There are two databases I have wished for during my studies.
One of notation for various mathematical concepts, covering cultural differences. For example the different ways to denote the open-closed interval, or that different symbols are used for strict subset. LaTeX symbols or macros when they exist, would also be useful. This would have greatly helped me when reading things for the first time and later with writing. Such material is definitely out of scope for Wikipedia.
Another useful database would be of logics and logical theories. These could range from propositional logics to higher order and infinitary logics. The theories should include various fragments of arithmetic, algebraic theories, theories of strings, etc. For each, I would be interested in what is known about decidability (and computational complexity), completeness, interpolation, etc. Currently, I use the Stanford Encyclopaedia of Philosophy and Wikipedia but what I want may often not be there or not succinctly presented for reference purposes.
