[ZackOfAllTrades]

Thought: my linear algebra teach this past semester told me that some of the greatest mistakes in mathematics came from people assuming something was obvious without a proof. After building a huge intricate structure around the assumption, they would watch everything fall apart as it turned out the obvious fact wasn't true. Now, whenever I hear somebody say "it's obvious" I always get skeptical now.

[motxilo]

You are just describing what motivated Bertrand Russell to write Principia Mathematica.