Seen today on my Google+ feed:

“Even failed experiments and theories teach valuable lessons.”

Not entirely disconnected, here is an email I recently received from Jason Knapp of Ohio:

For what’s it worth – I have a great amount of respect and admiration for what you’re doing, and what you have achieved with your Academy. My son loves your Number Theory book – it’s his favorite out of the AoPs set.

[anecdote for your classroom]

I have a mathematics background, and I direct research for a small biotech company. I’m honestly dismayed by the ever increasing difficulty of finding people with good problem solving skills – from finding interns to hiring PhD level scientists. I have actually recommended some of the AoPs books to some of our interns (kids working on their masters – smart, but poorly trained). Not because they need to know power-of-a-point or sum-of-cubes, but because the process of solving those types of problems is remarkably the same as that used to solve *real* problems: getting organized, searching for patterns, thinking of a simpler problem, changing your point-of-view, etc …

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