Here I discuss four interesting mathematical problems (mostly involving famous unsolved conjectures) of considerable interest, and that even high school kids can understand. For the data scientist, it gives an unique opportunity to test various techniques to either disprove or make progress on these problems. The field itself has been a source of constant innovation -- especially to develop distributed architectures, as well as HPC (high performance computing) and quantum computing to try to solve (to non avail so far) these very difficult yet basic problems.
And the data sets involved in these problems are incredibly massive and entirely free: it consists of all the integers, and real numbers! The first two problems have been addressed on Data Science Central (DSC) before, the two other ones are presented here on DSC for the first time.