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Agreed, partially. In mathematics, proofs really have two purposes. The foremost purpose is obviously to assert the logical necessity of the statement being pr
by newt0311 18y ago
Agreed, partially.
In mathematics, proofs really have two purposes. The foremost purpose is obviously to assert the logical necessity of the statement being proven. The second not so widely publicized purpose is to gain insight into mathematics. A proof is not just a way to prove that you are right. It is also a way to see what could be further explored. Thus the importance of elegance and insight in proofs.
Automatic proof systems are great for the first purpose but they detract from the second. That is why they should not be considered the begin-all-end-all for mathematics. That is not to say that they are not useful or not an advancement. They are certainly that. Just that they are not a replacement for elegance.