![]() Even material that is presented as introductory, requires advanced basic understanding in at least algebra, number theory, geometry and a solid grounding in set theoretic concepts as well as the need to become familiar with specialist notation. On deeper reflection, this is not all that surprising since Algebraic Geometry is typically taught at the second or third year for mathematics majors at the undergraduate level, and for the most part is regarded as a graduate programme in the United States. In fact there is not a single course on Algebraic Geometry either on EDx or MIT Open CourseWare. Firstly there is the inevitable fact that Algebraic Geometry is a fearsomely difficult area of mathematics, and secondly, for all it's pivotal role in advancing the limits of modern mathematics in the past century and a half, there is virtually nothing that is available on the internet that can serve as an introduction for the non-specialist. Anyone starting off with more a more detailed study of Category Theory, and who is determined enough to get past the initial thicket of specialist terminology, soon comes face to face with the fact that any serious deep dive into Category Theory means having to come to terms, at least nominally, with Algebraic Geometry. ![]() A small group of readers of my category theory articles were sufficiently motivated to ask me about follow up reading or courses, which of course I was delighted to provide - and that is where the problems started. Turning back now to the reason for this artice. However my lasting love affair is wholly based on an approach that is rooted in the 'pure' maths itself and I am delighted that here at Cambridge Quantum Computing we are working on an active collaboration in this area with Bob Coecke's team at the Oxford University Computer Science ( here for details) that is pushing my own boundaries. Applications of this most beautiful of mathematics within computer science are well documented, including the section in my last article that outlines an emerging link between Category Theory and Quantum Software. The same cannot be said about Category Theory. Quantum Computing has become my vocation, not just an avocation, and as such, it is not only a science but a technology that will be important in our daily lives as early stage quantum computers start to become more than mere curiousities. I should, of course, add at this stage, that in Quantum Computing I admit to having a dual objective in this process of 'de-mystification'. These are typically highly successful people in their own fields who are more than adequately equipped with the intellectual wherewithal to go beyond the equivalent of starng through the shop window In fact one of the great pleasures of this aspect of writing these articles is the rewarding feedback from professionals in a variety of different fields who have a deep seated fascination with maths and quantum computing and who have not been able to exploit that interest due to a lack of accessible explanation. In the case of my articles on Category Theory, I felt that even if I could generate one small gasp of excited comprehension where there was previously only confusion, then the articles were worth writing. Whilst it is clearly not possible to become an expert overnight, and it is certainly not my objective to try and provide more than an introduction (hopefully stimulating further research and study), I remain convinced that with a little effort, non-specialists and even self confessed math-phobes can grasp some of the core concepts. One of my objectives with such articles, whether they be on aspects of quantum computing or about aspects of maths, is to try and de-mystify as much of the associated jargon as possible, and bring some of the stunning beauty and wonder of the subject to as wide an audience as possible. This short article is the result of various conversations over the course of the past year or so that arose on the back of two articles/blog pieces that I have previously written about Category Theory ( here and here).
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