Rigor and Simplicity --- and Hints for Talks

In his famous 1900 lecture on 23 Mathematical Problems at the Paris International Congress of Mathematicians, David Hilbert asserted:

"... it is an error to believe that rigor in the proof is the enemy of simplicity."

For me, this is a powerful observation. It also has a corollary that speaks to the question of how one might more clearly organize talks in statistics, machine learning, or mathematics.

I often see people try to give "intuitive" explanations that are in fact too vague (or inaccurate) to be honestly followed by even a sympathetic well-prepared listener.

For goodness sakes, people, start off by giving us a clear and complete statement of what you have really used, proved, computed, or analyzed.

After we understand what is what, then we can start smoothing out the boundaries, looking at analogies, arguing by metaphor, or just generally shooting the bull.

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