Checking Quotes (3 quotes)
Mathematicians can and do fill in gaps, correct errors, and supply more detail and more careful scholarship when they are called on or motivated to do so. Our system is quite good at producing reliable theorems that can be backed up. It’s just that the reliability does not primarily come from mathematicians checking formal arguments; it come from mathematicians thinking carefully and critically about mathematical ideas.
People are usually not very good in checking formal correctness of proofs, but they are quite good at detecting potential weaknesses or flaws in proofs.
To see every day how people get the name “genius” just as the wood-lice in the cellar the name “millipede”—not because they have that many feet, but because most people don't want to count to 14—this has had the result that I don't believe anyone any more without checking.