There's a discussion going on at the Foundations of Mathematics mailing list about the purpose and value, actual and potential, for formalized proofs in mathematics. Harvey Friedman asked Jeremy Avigad to comment; he sent this super-useful list of references, republished here with his approval.
John Harrison and I recently wrote a survey on formalized mathematics, for computer scientists:
Jeremy Avigad, John Harrison, 2014, "Formally verified mathematics." Communications of the ACM 57:
I was observing a new teacher today, and one of the lesson resources was Symmetry Artist from Mathisfun.com. I was so excited by this resource that I could hardly focus on the lesson. If you've never seen this resource before, it looks like the screenshot below: My five year old created the drawing above. When she was finished I told her to pick a different number of "petals", and she chose 9 (shown below).What an amazing resource!
“Martin has turned thousands of children into mathematicians, and thousands of mathematicians into children.”~Ron Graham on Martin GardnerThe 294th day of the year; 294 is a practical number because all numbers strictly less than 294 can be formed with sums of distinct divisors of 294.EVENTS1621 Kepler's Mother, Katherine, during her trial for witchcraft was shown the "instruments of torture." "The whole case was now passed on the law faculty of the University of Tübingen, Kepler’s Alma […]
This new arXival by Chris Oates, Mark Girolami, and Nicolas Chopin (warning: all colleagues & friends of mine!) is a variation on control variates, but with a surprising twist namely that the inclusion of a control variate functional may produce a sub-root-n (i.e., faster than √n) convergence rate in the resulting estimator. Surprising as I […]