Abstract #3

Will the Digital Computer Transform Classical Mathematics?

Summary
“Technology is permeated by mathematics.” (Rotman, p 1675) This article describes how mathematics and technology go hand in hand. It discusses the effect of the digital computer on mathematics. The author describes the local and global transformations that have come around since the invention of the digital computer. This article went on to describe how mathematics has changed since computers have been invented, and how it will continue to change as the computer becomes more advanced. The author describes the three theoretical discourses of mathematics: idea, symbol, and procedure. Rotman defines each of these discourses and briefly describes how they affect mathematics. “The digital computer was spawned by modern mathematics and metamathematics.” (p 1676) The author discusses mathematics at a local transformation and a global transformation, and how these transformations started and will continue in the future. In the conclusion portion of the article, the author attempts to sum up his article and clarify the most important parts. “The computer is a machine whose conception, operation, construction and infrastructure are digital: it is antagonistic to the analog and to notions of smoothness and unbroken continuity associated with it.” (p 1688)

Reflection
Again, I found an article that seemed more interesting than it really was. The title of this article made me think that is was going to be about how to use technology (the computer) to change traditional mathematics. Unfortunately, this article did not live up to its title. This article included technical language that made it very difficult to understand. The overall theme of this article was extremely advanced and made one examine our own beliefs about the relationship between computers and mathematics.

The most interesting part of the article was the conclusion. In the conclusion, the author quickly came to the point. “Of course, the computer will transform classical mathematics; surely this is no longer in question. And it is reasonable to predict that it will do so along the same lines–machinic, digital, material–which have determined the changes it has so far wrought.” (p 1688) The author tried to use real world examples to make his point. To me, this was not as helpful as it should have been. Although I struggled reading this article, I still found it interesting and insightful. Once a person got past the technical language, the article made very interesting points about the connection between the digital computer and mathematics.

Reference
Rotman, B. (2003). Will the Digital Computer Transform Classical Mathematics? Philosophical Transactions: Mathematical, Physical and Engineering Sciences. 361(1809), 1675-1690.