I don't know if it was asked here, and it is only a curiosity that can be solved by professors or people knowing such projects in universities or mathematical communities.
When I've heard or read the words Langlands program, or the Erlangen program, I think (for the second one that I know its mathematical meaning, Wikipedia tell us that is a method) that is a project with the purpose to finish an unsolved problem or do a task that need many professors working in it.
Question. What's a program in mathematics? For example, currently what's mean a program and what are its characteristics? How do you describe to someone what's a program, its resources, its purpose...? What's it importance (when such project can be called a program?) Are more common in any subject of mathematics? Is it possible to say when (why) the mathematical community will accept such project as a program? Many thanks.
I am asking from a divulgative viewpoint. You can add an example, of a program, to illustrate its characteristics.
The Langland program is pictured here : http://www.lmfdb.org/universe
It is a list of conjectures (that are known to be true in many special cases) together with a very deep theoretical foundation.
If proven, it would explain how the mentioned objects (*) are related together, and would tell us much on what's necessary and sufficient for generalizing things as the Riemann hypothesis or the BSD conjecture.
(*) $\scriptstyle \text{those objects are amazing because they are related with almost everything in modern mathematics}$