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Has anyone / does anyone know anyone who's cold-emailed a professor at a random university to say "hey I think your research is cool, I have skills/knowledge/connections I can bring to the table here, interested in teaming up?"

If so, were they receptive? Did anything come of it? What help did they need?

I got a free textbook  (that cost some insane amount of money on Amazon) once from a professor when I asked if he could share a copy of his work for reference in a video game I was making at the time. I don't know if that counts, but seems worth mentioning.

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