This is the third installment of M.~Pitici’s annual collection of articles on mathematics including its history, teaching and philosophy. For the previous two volumes see [Zbl 1221.00020; Zbl 1230.00019]; these reviews also explain the general layout of the anthology. The contributors include three Fields medalists and many well-known mathematicians, but also performing artists-cum-mathematicians. I found all the articles in this compilation very interesting and well worth reading. Among others, the collection contains the following articles: “Is mathematics discovered or invented?” by {\it W.T.~Gowers} (see also [in: Meaning in mathematics. 3‒12 (2011; Zbl 1236.00013)]), “Structure and randomness in the prime numbers” by {\it T.~Tao} [\url{http://terrytao.files.wordpress.com/2009/07/primes1.pdf}], “Dancing mathematics and the mathematics of dance” by {\it s.-m.~belcastro} and {\it K.~Schaffer} (see also [Math. Horiz. 18, No. 3, 16‒20 (2011; \url{doi:10.4169/194762111X12954578042939})]), “How to be a good teacher is an undecidable problem” by {\it E.~Flapan} (see also [Coll. Math. J. 42, No. 5, 350‒354 (2011; Zbl 1258.00004)]), “The cycloid and Jean Bernoulli” by {\it G. L.~Alexanderson} (see also [Bull. Am. Math. Soc., New Ser. 48, No. 4, 525‒530 (2011; Zbl 1228.01011)]), “Was Cantor surprised?” by {\it F. Q.~Gouvêa} (see also [Am. Math. Mon. 118, No. 3, 198-209 (2011; Zbl 1229.03002)]).

Reviewer:

Dirk Werner (Berlin)