Is Methylamine an acid or base?

With respect to what?

Typically it's a proton acceptor, so a base, but you can also take a proton away using a stronger base, like LDA, or KHMDS to form MeNH-, so in that respect it acts as an acid.
the pH is 5, thus slightly acidic.
Theoratically it's a lewis acid.
Teorically is a weak base becase it has a pka of 10.62. It is a base because when you put in water it produces OH- (Arrenius or Bronsted theory) and it posess a pair of solitary electrons so is a Lewis base.

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