Every example project suggested by the GP can be easily externally verified, so it has built-in protection against crackpotism. Secondly, it may be very difficult, but not impossible.
I think maybe the most likely outcome, if they were really motivated and somewhat capable, is that they learn lots of mathematics well—but maybe not quite to, "... through graduate level" (that phrasing is a bit ambiguous though; self-teaching 'up to' graduate level is definitely doable).
I think maybe the most likely outcome, if they were really motivated and somewhat capable, is that they learn lots of mathematics well—but maybe not quite to, "... through graduate level" (that phrasing is a bit ambiguous though; self-teaching 'up to' graduate level is definitely doable).