Mathematical tools in a digital world

Abstract

There are many vantage points from which to gain a perspective on digital culture. The intersection of mathematics and mathematical tools with all things digital is one such vantage point. This implies an inspection of mathematical software. The broad lines that can be taken are the practice, education and application of mathematics. This thesis focuses on practice and application, disregarding education.

With regards the former it is shown how the practice of mathematics itself has been affected by the increasingly pervasive computational nature of our world. From visualisation to theorem proving no area has been untouched. I programmed a subset of the fractal universe, L-Systems, into the thesis to demonstrate this. In the latter case those who apply mathematics have been aided by the automation of their tasks: be they engineers or academics or artists. I have focused on the recent growth in mathematical art to highlight this.

Culture and ideology affect all areas of life, and the development of software is no exception. At heart are issues of control and freedom, lock-in and transparency. How one develops software can have ethical/pragmatic considerations, it can have legal ramifications, when we get into how mathematics software is used in science there are increasing epistemological issues, finally there are economic ones. First I looked backward in time to survey the history of copyright and intellectual property rights – then I considered how these frameworks operate in the software world.

In order to compare and contrast free and open source mathematical software with proprietary software I composed a set of questionnaires and used the methodology of digital ethnography. In the end this meant talking to users and developers of the open-source Sage project and users and developers of the proprietary Mathematica package. I also gave a detailed overview of both systems prior to analysing the responses.