I have been looking for a general all around math text since last century (as an amateur / recreational mathematician). I m starting to look at this. It seems to cover lots of ground. Any observations?
While there are a lot of of textbooks flown around, I'd like to prop up ROB201 textbook, which I came across recently, also aims to cover a lot of ground and is accompanied by videos.
There is no one book which can give you the overall sweep of Mathematics. However, you might find the following (though not textbooks per se) useful.
1) The Princeton Companion to Mathematics by Timothy Gowers et al. and The Princeton Companion to Applied Mathematics by Nicholas Higham et al. - The closest you have to a Modern Encyclopedia of Mathematics. You get unmatched breadth after which you can move on to dedicated books as needed. Well worth the money.
2) Mathematics: Its Content, Methods and Meaning by Aleksandrov, Kolmogorov et al. - Absolutely brilliant overview of Basic Mathematics. Published by Dover and hence very affordable.
3) Elements of Mathematics: From Euclid to Gödel by John Stillwell - Written as sort of an update to the great Felix Klein's Elementary Mathematics from an Advanced Standpoint books. The Topics are particularly well chosen given modern advances; they include Arithmetic, Computation, Algebra, Geometry, Calculus, Combinatorics, Probability, Logic.
If I were to write such a text, it would have a lot more about building intuition for advanced mathematical concepts. This intuition is extremely valuable, but missing from almost all advanced-level texts. On the other hand, it’s very difficult to put into words, and probably quite personal.
> Math Academy is an AI-powered, fully-automated online math-learning platform. Math Academy meets each student where they are via an adaptive diagnostic assessment and introduces and reinforces concepts based on each student’s individual strengths and weaknesses.
What is edutech and why is it unsuitable?
I don't want a computer in the loop when I learn math, plain and simple. My preferred style of learning is instructor led with a mix of Socratic method and hand holding. But bar that, reading texts and using a pen and paper.
As far as I can tell, most of its value comes from having a reasonably thorough dependency tree of math topics and corresponding exercises (which can be solved with pen and paper) and describing it as "AI" is how you get investors to fund a math textbook.
The “ai” is an expert system yes to calibrate to your ability to answer questions it throws at you. The questions are all human written. I had your initial scepticism as well, I can reassure you that the ai is not an LLM.
Also the guy Justin skycak who built it has put a lot of thought into its pedagogy
My experience with MathAcademy is very positive. So is my experience using ChatGPT 5 as a math teacher in learning mode. I'm as fed up with AI slop as most people, but for me this is a domain where it excels.
https://grizzle.robotics.umich.edu/education/rob201 - "ROB 201 Calculus for the Modern Engineer"