Review of The Art of the Infinite by R. Kaplan, E. Kaplan 324p(2003) Michael Starks ABSTRACT This book tries to present math to the millions and does a pretty good job. It is simple and sometimes witty but often the literary allusions intrude and the text bogs down in pages of relentless math--lovely if you like it and horrid if you don t. If you already know alot of math you will still probably find the discussions of general math, geometry, projective geometry, and infinite series to be a nice refresher. If you don t know any and don t have a natural talent for it, you will find it very dense or impossible. Being somewhere in the middle I skimmed thru most of it and slowed down when it got interesting. If you have only a little time I would suggest the last chapter  The Abyss` about Georg Cantor and transfinite arithmetic. At points they wax philosophical and ask the perennial question: is math is out there in the world or in here in our heads. Why not ask this about art or music or literature or computer programs or philosophy itself? In a very general way math must come from the same place that words and ideas and images come from---our brain evolved to make them and they must in many ways (every way?) reflect the structure of our brains, which reside in our DNA, which was shaped by natural selection, which was shaped by the geology of the earth and the structure of our universe, which comes from particle physics which comes from the laws of nature which are just there. I have written extensively on the nature of math and language and mind and how they are all one in my many other reviews so please see them if these topics interest you. Those interested in all my writings in their most recent versions may consult my e-book Philosophy, Human Nature and the Collapse of Civilization Articles and Reviews 2006-2016 662p (2016). This book tries to present math to the millions and does a pretty good job. It is simple and sometimes witty but often the literary allusions intrude and the text bogs down in pages of relentless math--lovely if you like it and horrid if you don t. If you already know alot of math you will still probably find the discussions of general math, geometry, projective geometry, and infinite series to be a nice refresher. If you don t know any and don t have a natural talent for it, you will find it very dense or impossible. Being somewhere in the middle I skimmed thru most of it and slowed down when it got interesting. If you have only a little time I would suggest the last chapter  The Abyss` about Georg Cantor and transfinite arithmetic. At points they wax philosophical and ask the perennial question: is math is out there in the world or in here in our heads. Why not ask this about art or music or literature or computer programs or philosophy itself? In a very general way math must come from the same place that words and ideas and images come from---our brain evolved to make them and they must in many ways (every way?) reflect the structure of our brains, which reside in our DNA, which was shaped by natural selection, which was shaped by the geology of the earth and the structure of our universe, which comes from particle physics which comes from the laws of nature which are just there. I have written extensively on the nature of math and language and mind and how they are all one in my many other reviews so please see them if these topics interest you. Those interested in all my writings in their most recent versions may download from this site my e-book 'Language Games of Philosophy, Psychology, Science and Religion Articles and Reviews 2006-2016' by Michael Starks First Ed. 648p (2016).