I don't think this is a fair comparison. The modern computer is really distinct from everything that came before. That's because it was built according to the theory of Turing Machines.
One of the most important historical papers for the development of modern computers was the Report on the ENIAC by Von Neumann[1].
Von Neumann took the idea's of others working in the field, and was able to apply his understanding of mathematical logic to formulate the principles which led to the first working modern computer, which Von Neumann built in the basement of IAS. At that time, there was a major debate at IAS between Einstein and Von Neumann, which centered around whether or not to only do pure math at IAS, with the idea that building a computer was part of experimental science. [2]
> Regarding the arrow of influence: a Fields medalist spent a decade coming up with a new foundation of mathematics (or at least algebraic topology), only to realise that the computer science department already teaches Coq to undergraduates!
LOL! That is an interesting and funny story. However, I don't think this example demonstrates that in the future, mathematics will not be the source of improvements to code writing standards.
Question: if code writing standards improve, where else will these improvements come from other than pure mathematics? I consider this question to be a problem type similar to maximum compression algorithms, i.e. its a question whose solution can only be verified using the language of pure mathematics. Therefore it seems likely these improvements can also have their roots in pure mathematics as well. At least, I would not say it "seems unlikely"
[1] https://en.wikipedia.org/wiki/First_Draft_of_a_Report_on_the...
[2] https://www.amazon.com/Turings-Cathedral-Origins-Digital-Uni...
- The Conquest of Happiness by Bertrand Russell was a pretty good one. He has a lot of ideas that were ahead of their time (positive psychology, etc). You can see a lot of parallels between his ideas and modern Stoicism (although Russell criticized it elsewhere, I think he came to some of the same conclusions).
- Introduction To Mathematical Philosophy by Bertrand Russell. Another Russell one. I think this is probably the clearest and easiest to understand explanation I've ever read of the underpinnings of mathematical foundations. It's written in a style that should be accessible to almost anyone with a high school education. He wrote it while he was in prison (for refusing to be drafted) during WW1. Apparently he left a copy of it to the prison warden.
- An Enquiry Concerning Human Understanding by David Hume. This is worth reading because it is the motivation for basically all of modern philosophy of science (at least in the west). It's also pretty easy to read and if you read it you'll be able to more easily understand other books and papers that are responses to it.
- Turing's Cathedral by George Dyson. This book should be required reading for every programmer or aspiring programmer IMO. I learned so much about the history of computing that I didn't know before reading this. You will not regret buying this one.
- I Am A Strange Loop by Douglas Hofstadter. Obviously everyone knows about GEB, but he also wrote a shorter follow up that in my opinion expresses his ideas much more clearly. I think that even if you disagree with him, it's worth reading because there are so many things you can take away from this book. For example, he talks about his wife's death, and ties that into his theory of mind and explains the unstated purposes of why we have funerals/wakes for people.
- An Introduction to Information Theory by John R. Pierce. For someone like me who doesn't really have a very strong math background, this was a very clear intro to the ideas behind information theory, and why they're important historically. I would recommend this to anyone who feels like they need a gentle intro to the ideas and motivation for them. Dover mathematics books in general are great.
- Borrow: The American Way of Debt by Louis Hyman. This is a fantastic historical overview of personal credit in the US that covers the past 120 years or so. I learned a ton from reading this that I had no clue about. Recommended to anyone who wants to understand the origins of credit cards / loans, and how society came to embrace being in debt.
https://archive.org/details/in.ernet.dli.2015.222834/page/n7
https://people.umass.edu/klement/imp/imp-ebk.pdf
https://archive.org/details/humeenquiry00humerich/page/n7
https://www.amazon.com/Turings-Cathedral-Origins-Digital-Uni...
https://www.amazon.com/Am-Strange-Loop-Douglas-Hofstadter/dp...
https://www.amazon.com/Introduction-Information-Theory-Symbo...
https://www.amazon.com/Borrow-American-Debt-Louis-Hyman/dp/0...
https://www.amazon.com/Information-History-Theory-Flood/dp/1...
https://www.amazon.com/Turings-Cathedral-Origins-Digital-Uni...
http://www.amazon.com/Turings-Cathedral-Origins-Digital-Univ...?
http://www.amazon.com/Turings-Cathedral-Origins-Digital-Univ...
Other great titles I'd recommend is Steven Levy's "Hackers" http://www.amazon.com/Hackers-Heroes-Computer-Revolution-Ann... and Phil Lapsley's "Exploding the Phone" http://www.amazon.com/Exploding-Phone-Untold-Teenagers-Outla...
Hope you enjoy!
The Information: A History, A Theory, A Flood http://www.amazon.com/The-Information-History-Theory-Flood/d...
Turing's Cathedral: The Origins of the Digital Universe http://www.amazon.com/Turings-Cathedral-Origins-Digital-Univ...
Nine Algorithms That Changed the Future: The Ingenious Ideas That Drive Today's Computers http://www.amazon.com/Nine-Algorithms-That-Changed-Future/dp...
https://www.amazon.com/Turings-Cathedral-Origins-Digital-Uni...