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I don't think the mental process is necessarily all that different in pure mathematics. The process of creating new structures and proofs in mathematics definit
by tangentspace 11y ago
I don't think the mental process is necessarily all that different in pure mathematics. The process of creating new structures and proofs in mathematics definitely involves a lot of trial-and-error and vague intuition. When the evidence mounts that a particular approach is likely to succeed, more effort goes into refining the intuitive approach into a valid proof. Further iterations often build on the original proof by tweaking the parameters to make it more general or change the context, just to see what happens.
- amelius 11y agoYou have a good point. But at least in pure mathematics, you end up with a rigorous proof, whereas in deep learning, you end up with a system that may-or-may-not work. This means that in pure mathematics you can build on your previous results, but in deep learning you cannot (without danger).
- tamana 11y agoRigorous proofs are a formality that gets less attention than you'd guess at first.