Bertrand Russell's The Study of Mathematics: Gateway to the Great Books Vol. 9 Mathematics

     When most Christians hear the name of Bertrand Russell, they are likely to be aware of his most famous (or infamous) essay which is entitled "Why I am not a Christian" (which, all Christians should read). In truth Russell should also be known for being a mathematical polymath. There are a number of insights one can glean from his writings on mathematics, beyond the very nature of math itself. One quote that Adler gives of Russell that is representative is, "The habit of mind that is developed in defining the obvious will stand you in very good stead when you enter the world of abstract thought. Your definitions will be your only landmarks." (83) 
     A point of import Russell makes that is well worth recurring reflection is, "At this stage, it is well to study afresh the elementary portions of mathematics, asking no longer merely whether a given proposition is true, but also how it grows out of the central principles of logic." (89)  It is here that Russell is asking the student of math to not only be able to crunch the numbers, but to be able to give an explanation for why things are the way they are in math.
     Even if one does not appreciate Russell's views of Christianity, one can certainly appreciate his view that, "As respects those pursuits which contribute only remotely, by providing the mechanism of life, it is well to be reminded that not the mere fact of living is to be desired, but the art of living in the contemplation of great things." (84)
     Unlike most mathematicians of the modern world, Russell was aware of the deep history of mathematics, especially as it is connected with philosophy. Russell speaks well of the roots of mathematics in Plato and other ancient Greek philosophers. He also notes the relationship between math and poetry, math and beauty, and of course math and logic. Russell makes one brilliant insightful comment about the understanding of Euclid and geometry. (87)
     As a teacher of Great Books, I have long been opposed to textbooks for their inadequate ability to actually teach students to think through disciplines. I was encouraged to read Russell had similar convictions, "In the great majority of mathematical textbooks there is a total lack of unity and method and of systematic development of central themes." (89)
     While there is certainly much in this brief essay to appreciate and even learn from Russell, there are also a number of elements that one would want to question.  More than once Russell makes claims for the nature and power of mathematics that may not be defensible. (91)
     Among the many things that a Christian reader can appreciate from this essay on mathematics, one could certainly affirm Russell's convictions against skepticism and his  argument for objective truth.  As a matter of fact he ends this essay with some of the most encouraging words for the defense of math one will ever read. "Every great study is not only an end itself, but also a means of creating and sustaining a lofty habit of mine; and this purpose should be kept always in view throughout the teaching and learning of mathematics." (94)