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https://blogs.ams.org/matheducation/2019/01/15/reflections-on-teaching-for-mathematical-creativity/When instructors develop an environment where students are willing to put themselves “out there” and take a risk, interesting moments often happen. Those risks can only build one’s creativity, which is the most sought-after skill in industry according to a 2010 IBM Global Study.

I don't want to make the discussion exclusively a pedagogic one, which is why I posted it here. Personally, I think mathematics is far more creative than commonly thought - at least if I take the many comments about mathematical rigor which I've read over the years into consideration. In my experience, one learns a lot and gains many different views on a topic, if forced to teach it. Every student you want to convince of a mathematical fact has their own way to it, so one needs different approaches. This is part of the mathematical creativity in my eyes, but certainly not the only one.

I'm a regular reader of Terence Tao's blog, which is another great evidence of mathematical creativity. Of course there is plenty of room between Tao's brilliance and the necessity of ideas while teaching. Additionally, other than in physics, a new idea is usually easy to decide: either you can prove it or not. And if there is a proof, it is automatically no longer a personal theory - just more or less of interest.

What are your views?