Here are the key themes from the Hacker News discussion:
Relevance of the Suggested Reading List
A primary theme is the debate over whether the suggested reading list accurately reflects the path to mastery in mathematics, particularly given the domain name's implication of mathematical science. Some users found the list to be too conventional or lacking in certain areas.
- One user expressed, "Safe, conventional, non-controversial choices here. Given the domain name, I expected more category theory." (TimorousBestie)
- Another noted a lack of specific mathematical fields: "(1) Didn't see anything on the math of probability or stochastic processes, e.g., nothing from Dynkin, Neveu, Breiman, etc." (graycat)
- The user "asplake" clarified the site's intent: "About the domain name, I don’t thought that too. But its stated intention is “to accelerate the development of prospective mathematical scientists”, hence the lean to physics and to certain authors."
Feasibility and Timeline for Learning
Several commenters questioned the feasibility of the suggested "two or three years" timeline for working through the material, especially for full-time study. The density and depth of the recommended books were highlighted as significant hurdles.
- "I dunno about “two or three years,” though. It would take me about a year to get through all three volumes of The Quantum Theory of Fields alone (~1500 pages of extremely dense physics!)" (TimorousBestie)
- "3 years still sounds optimistic to me ... even full-time, if we are talking reading through the material thoroughly." (jhanschoo)
- The "greedy" nature of learning was brought up, suggesting that a linear, globally optimal path might not be how humans learn best. "This is wrong. In Computer Science language, human learning works in greedy way. We make locally optimal decisions in life. We cannot learn something in globally optimal way. We learn something in locally optimal way. And by repeating that we can reach somewhere at some point." (lsc4719)
Pedagogy and Textbook Choices
The utility and effectiveness of specific textbooks, as well as broader pedagogical approaches, were a recurring point of discussion. Some users found certain classic texts to be dense or outdated, suggesting better alternatives have emerged.
- The user "stared" observed, "I am not sure if I agree with the list. I mean, one red flag is the frequent mention of Landau & Lifshitz. It is considered a "standard textbook", but I feel it stuck there by inertia. There are quite a few choices of both less boring and more insightful. (Back when I was reading such stuff, 20 years ago, the Feynman Lectures provided orders magnitude more insight. And fun.)"
- Regarding linear algebra, "lambdas" commented, "Shivlov for the one and only text in linear algebra is rough. IMO, it’s a little terse and fast paced. Efficient if you’re already well versed enough to be dangerous, but otherwise I think might slow down the beginner to a crawl in places."
- The same user also critiqued Hartshorne's Algebraic Geometry, stating, "Same for Hartshorne’s Algebraic Geometry. Neither of these are bad textbooks at all, they both have a place on my bookshelf, but certainly better options have appeared through the years (for AG, I’d be remiss to mention Ravi Vakil’s fantastic The Rising Sea, due for a physical publishing October, and Ulrich Görtz & Torsten Wedhorn two part series)."
The Role of Computing and Mathematics
The relationship between computing, software engineering, and mathematics was touched upon, with a distinction drawn between computer science and software engineering in terms of their mathematical rigor.
- "CobrastanJorji" stated clearly, "Computer science is math. Software engineering is not math."
Website Technical Issues and Hosting Choices
A distinct theme arose concerning the website's technical implementation, specifically the "Error establishing a database connection" message. This led to a discussion about the benefits of static site generators versus dynamic platforms like WordPress, especially for sites that might gain unexpected traffic.
- The error message itself prompted a reaction: "Oof. Not usually one to comment on technical issues, but that's a rough one to get for a (presumably) completely-static site! Dr. Sheaf, please consider serving your site via a dedicated service like S3. This is a solved problem <3" (bbor)
- The platform choice was also questioned: "He probably doesn’t know how. This message is em from Wordpress. There are many WP providers where you just signup and start writing. They don’t tell you that if you get to HN front page, your db will die." (figassis)
- Another user provided a contrasting recommendation: "Bear Blog comes to mind (no connection): https://bearblog.dev" (easygenes)
- The preference for static sites was strongly articulated: "It stings be a bit that people use Wordpress in times of really wonderful static sites generators AND vibe coding. They are both pleasure to write, make it easy to tweak style however you please, can cost nothing (just host it on GitHub pages), no maintenance, and if something hits Hacker News, no risk of an outage." (stared)
The "Payoff" or Rationale for Intense Study
One user raised a fundamental question about the ultimate purpose or benefit of undertaking such an intensive, multi-year study regimen, beyond the acquisition of knowledge itself.
- The query was posed: "After working through all those books, cancelling nearly everything else in life for some years, just what is the result, the payoff, the reason? Academic research or something in the mainstream economy, technology, etc.?" (graycat)
Philosophical Interpretation of "Error Establishing a Database Connection"
Amusingly, the technical error message also inspired a more abstract, philosophical interpretation within the discussion.
- "Obviously it's not meant literally. The database represents your mind, and the error represents all the mathematical proofs you haven't written yet. By solving the error (proofs) you learn mathematics. /s" (klipt)