> I could be more persuaded with an example of something that is undecidably a number.

Simple case:
```
In [10]: e=(x+1)**2-2*x-x**2

In [11]: ii=Integral(y,(y, 0, e))

In [12]: ii.is_number
Out[12]: False
```

Actually, it's not undecidable, but heuristic (this time in master) - produce wrong answer.