Judith V. Grabiner

Augustin-Louis Cauchy was one of the giants of nineteen century's Mathematical Analysis. His importance in shapping the field and definitely steering the subject into the rigorous mathematical discipline we know today, can be gauged by the number of times his name appears connected with mathematical objects and results of present day currency (Cauchy sequence, Cauchy criterion for series, Cauchy root test, Cauchy-Hadamard theorem, the Cauchy-Riemann equations, the Cauchy integral formulas,...) this not to speak of the very notion of limit and continuity, whose rigorous definition is very much Cauchy's work, or the first rigorous definition of integral (now disused, but nevertheless of history intereste.) However great Cauchy was, he did not work alone or ab initio. He was one, admitedly a very important one, of a plethora of great mathematicians that helped build one of the most impressive of humanity's intelectual achievements: the rigorous foundations of Mathematical Analysis. The story, of course, does not end with Cauchy, but this excellent and enticing book actually centers its action on the work previous to Cauchy's as well as on Cauchy's own achievements: in it, the importance of Euler, D'Alembert, Ampère, Poisson, Lagrange (of course), and the unjustely somewhat forgotten Bernand Bolzano, is properly addressed, in addition to a very stimulating account of Cauchy's own work.… (mere)

Modern calculus is such a beautiful and coherent theory that it sometimes appears to have sprung full-blown from the head of Zeus. But at the end of the 18th century, the state of the calculus was very different. Grabiner details how Cauchy re-purposed and built on the work of his predecessors to help transform the calculus into the rigorous system we know today. While her writing is rather dry, and at times repetitive, The Origins of Cauchy's Rigorous Calculus provides a glimpse into a fascinating period of math history. Caution: This is a book about math, not a biography. A year of calculus is pretty much a prerequisite for reading this book. [2007-05-25]… (mere)