User blog comment:P進大好きbot/Summary on historical background of BMS/@comment-30869823-20180713171021/@comment-30754445-20180803132530

Depends on what you mean by "ignore".

Number theorists most definitely did ignore Fermat's conjecture... with the sole exception of looking for ways to prove it (or at least, prove it for a given subset of exponents).

So you're right that BMS should get the same treatment. We should put our efforts into actually showing that it works (or showing that it doesn't work). More to the point: We should pick one version and one subsystem, and convincingly show that it works the way it is supposed to work. Trying to do anything else, at this point, is putting the cart before the horse.

How about this for a first baby step:

Let's show that BM1 indeed reaches Γ₀ at (0,0)(1,1)(2,1)(3,1).

(since I'm actually well-versed in BM1, I might try my hand at doing this)