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RE: The significance of mathematics - and why it can prove its own incompleteness
It is a pity I have missed this discussion, as I would have loved to participate. That is my only regret of this meetup: not enough time to chat with everybody.
To come back to your post, what most people have difficulties is the concept of a proof by itself. In science, proving something has a well defined meaning (that could be different in different fields).
Yes, I'm glad to have stayed until Sunday to visit the city and connect with people. Time was really flying that weekend.