51–53 of 53 posts
It is the one and only two dimensional spreadsheet that works in arithmetic with no need for algebra or its notation. Kind of like a hand calculator running around a blank sheet of paper.
There is no royal road to mathematics[1], and it's incredibly arrogant to think that any person can provide a single optimal path. For me for example the next steps are Axler, Abbott and Herstein[2]. That's where I am at the moment, and it's way earlier than the books listed here. It would be far from optimal for me to try to bang my head stubbornly on this list. Mathematics demands you put in the work to build a fou…
Have an apoplectism https://agorism.dev/book/math/ag/royal-road-algebraic-geomet... Also iirc, various books titled Royal Road to Geometry , which might make more sense given that IMO geom was the first to get crushed by chatbots Ymmv, but denying existence of royal road to math seems like a narcissism limited to the most elite layity
Not sure I fully understand your point about narcissism and laity. If Euclid and I are laity then I think I'm happy to be called that though. For me the "royal road" refers to the idea that you can take shortcuts and understand things without putting in the work. That just does not ring at all true to my experience with maths anyway.
The author misunderstands knowledge and mastery. Mastery comes from problem solving and practice - not from reading books. So, I would advise students to limit what you read, but spend a lot of time in problem solving. Get the basics in place. Start with euclid's elements and master that first.
Weird! I think Euclid is fine as a historical document and interesting in a broad sense, but its kind of silly to start with a document from 300 BCE when you could start with, for example, "How to Solve It" (Polya). And even that text could use a rewrite to make it much more readable. I have completed substantial education in both mathematics and physics and I would say one of the weaknesses of the standard system of…
I meant that the foundations of what it means to do math can be found in as elementary a text as the Elements. Most importantly it shows how an abstract world (what we feel as space around us) can be modeled as Geometry with a set of axioms, along with a way to demonstrate statements without doubt. Just understanding this very deeply (in your bones) with a lot of problems would make you a better mathematician than if you read all the books listed above, at least in my view. Other areas of mathematics model different kinds of abstract worlds, but the activity is largely similar.
The problem I see is the focus on gathering knowledge without properly assimilating it (ie reading a lot of books). By assimilating I mean, being able to explain how something is constructed from the very basic first principles of how the conceptual structure was built.