But Thurston does not find mathematics unreliable. Rather, his point is that the reliability of mathematics arises not from formal proof, but from mathematical understanding: 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 solidly backed up. It is just that the reliability does not primarily come from mathematicians formally checking formal arguments; it comes from mathematicians thinking carefully and critically about
...more
