Reply to A (very) gentle comment on Algebraic Geometry for the faint-hearted | Ilyas Khan

Replied to A (very) gentle comment on Algebraic Geometry for the faint-hearted by Ilyas KhanIlyas Khan (LinkedIn)
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). 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. 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. 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.

I just finished a course on Algebraic Geometry through UCLA Extension, which was geared toward non-traditional math students and professionals, and wish I had known about Smith’s textbook when I’d started. I did spend some time with Cox, Little, and O’Shea’s Ideals, Varieties, and Algorithms which is a pretty good introduction to the area, but written a bit more for computer scientists and engineers in mind rather than the pure mathematician, which might recommend it more toward your audience here as well. It’s certainly more accessible than Hartshorne for the faint-of-heart.

I’ve enjoyed your prior articles on category theory which have spurred me to delve deeper into the area. For others who are interested, I thought I’d also mention that physicist and information theorist John Carlos Baez at UCR has recently started an applied category theory online course which I suspect is a bit more accessible than most of the higher graduate level texts and courses currently out. For more details, I’d suggest starting here: https://johncarlosbaez.wordpress.com/2018/03/26/seven-sketches-in-compositionality/

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2 responses on “Reply to A (very) gentle comment on Algebraic Geometry for the faint-hearted | Ilyas Khan”

  1. Hi Chris. In many respects John Baez has become the ‘godfather’ of Category theory, but there are some amazingly talented young mathematicians who are exciting in their own right. i am hoing that we find soon have a category theorist landing the Field’s. If you are not familiar with Emily Riehl you might want to look her up.

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    1. Thanks for the tip. I grew up in the math department at Johns Hopkins in the early 1990’s where I got my two engineering degrees, so I’m aware of Emily Riehl’s excellent work there, though I haven’t been able to travel back in the last several years to catch her in person. I’ve got both of her books and a pile of her papers. It’s been fun watching her, Eugenia Cheng and, more recently, Tai-Danae Bradley popularizing the subject.

      Sorry I don’t spend much time on LinkedIn (other than to occasionally check for your updates and one or two others I follow), so I hadn’t seen your response until now. I suspect I ought to turn my email notifications on…

      While I’m thinking about it I’m curious why it seems that LinkedIn is your sole “social” platform? Given that you’re publishing here somewhat regularly, it might be more worthwhile to have your own website/blog where you publish directly and then syndicate copies to LinkedIn, Twitter, Medium, et al. for broader reach/audience as a means of better science communication. If you’d like I could build you such a set up that makes some of the back and forth easy and simple–in fact, I’d love to do it just to have the available RSS feeds for the real-time notifications of your new posts without needing to have a reminder to visit LinkedIn every few weeks. I’m happy to discuss it if you’re interested.

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