No, mathematics like science is purely an invention of the human mind...

One could argue that the entire universe as we know it is nothing more than "an invention of the human mind", leaving no scope at all for discovery, but that is hardly a useful position to take in this context. Even if you did take that approach, mathematics should still be excluded, because mathematical relationships exist independently of human thought. The ratio of a circle's radius to its circumference is tau, and would remain tau even if no human ever existed to discover that fact.

Invention implies an element of creativity, deliberate choice among the available alternatives. The only choices in math are in the selection of axioms. Mathematical axioms may be invented (under significant constraints necessary to keep the results applicable to the physical universe, though there remains some flexibility), but everything beyond that follows mechanically from the axioms—and is thus discovered. Similarly, once your requirements are known, developing a software algorithm comes down to little more than solving the system of constraints described by the requirements—given the requirements specified in a formal language, this is something that could be solved in principle by a search through the solution space using tools similar to mechanical theorem-provers. Intuition helps in narrowing the search space (at the cost of possibly missing the solution entirely), but it isn't essential given sufficient time and memory. Of course, an actual program includes additional elements such as comments, identifiers and code style which are chosen by the programmer and have no effect on the program's behavior; these creative elements would be invented rather than discovered.

Science, moreover, is not "purely an invention of the human mind" any more than mathematics is. It consists of both discovery and invention. Science is essentially the process of making observations and developing statistically consistent models. There is more flexibility here than in math; models can fit the data to a greater or lesser extent, and the best-fitting model is not always the most useful. A useful approximation can thus be considered an invention; just the same, most of science consists of discovery rather than invention of new models, even more so when the goal is simply to fit a standard statistical model to the available data, pure math combined with discovered observations.

BitCoin's main [algorithms] go back about 30 years.

The algorithms have been *known* for about 30 years, but they've always *existed* as a solution to the problem Bitcoin was intended to solve, waiting for someone to discover them.