Mathematics in Life and Thought.....Reading from Gateway to the Great Books

As with the other readings in this series, all students (and most math teachers) would benefit from the philosophy that is present. While there are some occasional items that are dated, the readings are extremely beneficial, especially in terms of qualitative reflection-an item sorely lacking in much theoretical mathematics that calls for application of theories without full comprehension.

Within Mathematics, in Life and Thought by Andrew Russell Forsyth, there is much for enjoyment and reflection. In contrast to the emphasis on "practical results" of some modern mathematics, Forsyth, says, “If utility should come, well and good: but we need trouble no more about immediate utility as an aim than the Greeks troubled about the utility of their conic sections or Newton troubled about the utility of the gravitation theory” (46). In the same line of thinking Forsyth states, “Ever since man has attempted to acquire ordered knowledge, the science that deals with number and deals with form has been pursued for its own sake because, thereby, the human spirit can find unending satisfaction and unending occupation. And the creations of mathematical science have been the glory of the nations” (45). No doubt, some ancient mathematicians would take issue with the term "creations" as opposed to "discoveries." This is a key, but rare distinction.

Forsyth is in the majority of mathematical camp that asserts “Mathematics as a pure science of progressive knowledge” (45). It is on this basis that he and others speak well of Newton and yet recognize a move past Newton. “The Newtonian theory is still alive sufficiently to provide man with a working hypothesis of the natural universe in which he lives” (44). PBS did a series some years ago on Newton that should be required viewing. While there was some chronological snobbery hoisted against Newton, much of the series was respectful and insightful.