Euler... Thinker Extraordinaire

1) Probably any mathematician would rank Leonhard Euler as one of the greatest mathematicians of all time (he pretty much shows up on anyone's top five list). And Professor William Dunham reveres Euler as the very top of the heap. In this video he entertainingly makes the convincing case for Euler -- Dunham talks for about an hour, followed by 30 mins. of question-answers -- for such a long presentation it maintains interest well:

You'll learn what i^i equals (and how Euler computed it), as well as Euler's better-known contributions, all accomplished in an era long before computers and calculators.
One odd, quirky side-note: it turns out that of the top 5 mathematical formulas/results (as voted on somewhere) 3 come from Euler and the other 2 from Euclid... just an interesting twist that mathematicians with 2-syllable names beginning with "Eu" are responsible for so much powerful math! (...uhh, in the future, please just call me Eushek).




2) No promises that it'll get you thinking as sharply as Euler, but the below post offers a nice primer on mathematical thinking/proof (based on logic and abstract reasoning), which I think may be similar to the approach Keith Devlin takes in his Coursera MOOC course on the same subject (but someone feel free to correct me if the comparison is off-base).

http://amininima.wordpress.com/2013/07/25/how-to-prove-somethin/