Are there any (many) algorithmically undecidable problems in computational (combinatorial/discrete) geometry? Update: the Wang tiles answer the question with "any". (I have somewhat overlooked to ...
Some theorems are magical: their hypotheses are easy to meet, and when invoked (as lemmas) in the midst of an otherwise routine proof, they deliver the desired conclusion more or less ...
Are there examples of sets of natural numbers that are proven to be decidable but by non-constructive proofs only?
What are the most attractive Turing undecidable problems in mathematics? There are thousands of examples, so please post here only the most attractive, best examples. Some examples already appear on ...