There are essential differences between chemistry and mathematics.
To discover anything in mathematics, including a new video compression algorithm, you do not need anything else, except a computer. In theory, not even the computer is needed, as you could do everything with pen and paper, but it might require years or centuries.
Chemistry is an experimental science for now, until someone would find a method to solve the equations of quantum mechanics for non-trivial systems.
A lot of mathematics is used in chemistry but at its base chemistry remains experimental, because all the mathematical models used in chemistry to predict some facts use a large number of model parameters that have been determined experimentally. There are no truly "ab initio" mathematical predictions in chemistry.
Using mathematics in chemistry allows a significant reduction in the number of chemical experiments that must be done to discover anything new, but they cannot be eliminated yet.
Any discovery in mathematics can be easily redone again, by someone else, completely independently, and this actually happens extremely frequently.
There do not seem to exist many reasons that can justify why the later discoverers must be punished to pay money to others in order to use the mathematical relations that they have discovered themselves, even if by some chance someone else happened to discover the same relations earlier.
For mathematical discoveries, there are little grounds to claim that the first discoverer should be able to recover any expenses, as most of the strictly necessary expenses are just in the salaries of people and it is very difficult to estimate what percentage of those expenses had actually contributed to the discovery.
On the other hand, for inventions referring to chemical substances, or to mechanical, thermal or electrical devices and so on, a lot of experiments with physical devices must be made and the experimentation costs can indeed be very high, so it can be argued that it might be good for a society to encourage such experiments by promising a temporary monopoly for the exploitation of the results, as long as the duration of the monopoly is not excessive.
For the kind of minor innovations that are the object of most recent patents, a reduced patent duration seems more appropriate, e.g. 10 years.
A patent duration of 20 years or more seems acceptable only for a few patents for which the acceptance criteria should be much more strict than they have become recently, i.e. such patents should really be "non-obvious for those skilled in the field", and not just trivial combinations of formerly known devices or methods.
