# Tagged Questions

**5**

votes

**4**answers

1k views

### On similar concepts in mathematics whose similarity is a non-trivial fact.

Recently, while undertaking a study of commutative algebra, I learned three concepts: (i) a local ring, (ii) a regular local ring and (iii) a regular ring.
At the end, I found myself asking this ...

**9**

votes

**2**answers

2k views

### What are examples of theorems which were once “valid”, then became “invalid” as standard definitions shifted?

That is, results established by correct proofs within some framework, yet the manner in which their author or the general mathematical community at the time would describe these results would, in ...

**50**

votes

**16**answers

7k views

### Can a mathematical definition be wrong?

This question originates from a bit of history. In the first paper on quantum Turing machines, the authors left a key uniformity condition out of their definition. Three mathematicians subsequently ...