#Should I try to follow a Newton-style learning journey through math & physics and can it be valuable

17 messages · Page 1 of 1 (latest)

stiff wagon
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Hi everyone,
I've been really inspired by how Isaac Newton learned, starting from basic arithmetic and Euclid, then building up his own understanding of algebra, geometry, calculus, and eventually applying it all to physics.

It made me wonder is it possible (or even useful) to take a similar path today? Like starting with the fundamentals and slowly working through historical texts (Euclid, Descartes, Galileo, maybe even Newton’s Principia or Waste Book) while trying to deeply internalize each step before moving on.

My questions:

Can such a "first-principles" learning track still be valuable in today’s world of pre-packaged knowledge?

Is there a logical or rewarding way to recreate this path using modern (or historical) books?

Would it help build a deeper intuition in math and physics, compared to learning topics in isolation (as school often does)?

Has anyone tried a similar long-term, self-directed study project like this?

I’d love any advice on:

What books or resources to include (modern or old)

What order makes sense

Pitfalls to avoid

How to balance it with more modern, efficient learning methods

This is more about thinking deeply and understanding the foundations, not just passing courses.

Thanks to everyone in advance.

marble ruin
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Like, we basically completely reinvented math in the early 20th century to be exactly the kind of singular system of logic you're talking about studying it as, partly because of problems introduced by Newton, ironically enough.

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But like, there's a path of study from more to less fundamental, which starts at ZF(C), and then there's a path of study from more to less intuitive, which would probably start with Peano arithmetic.

fossil crypt
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Possibly there is a better suggestion but if I were to start I would probably go through the following resources:-

  1. (Any book which would teach me school level mathematics)
    Basic Mathematics by Serge Lang is widely recommended
  2. Precalculus-Sullivan
  3. Calculus-Stewart or Thomas
  4. How to Prove it-Velleman
  5. Understanding Analysis-Abbott
  6. Algebra Notes from the Underground-Aluffi
  7. Linear Algebra-Friedberg
  8. Topology-Munkres
  9. Principles of Mathematical Analysis(Baby Rudin)-Rudin
  10. Real and Complex Analysis-Rudin
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I am confused what to read next, mathematics is too broad today

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I think at present times, it is better to get familiar with some mathematics before actually understanding the logic system we fundamentally use, it would help to understand why the system is like that and what are the consequences of the axioms of ZFC

stiff wagon
# marble ruin I mean, if you want to learn all of math from first principles, you need to star...

That's a great point and honestly, I hadn't thought about it from the formal foundations angle. I am not much educated about ZF(C), but I heard it is the base.
That said, I think there’s a distinction between foundational logic and historical development. My focus is more on understanding math the way it grew, with all the human intuition and trial-and-error baked in, not necessarily building it axiom by axiom from set theory (though that’s super interesting too).
Still, I appreciate you pointing this out it's a reminder that “first principles” can mean very different things depending on the view.

stiff wagon
# fossil crypt Possibly there is a better suggestion but if I were to start I would probably go...

That’s an excellent roadmap really solid choices for building a strong foundation and then advancing into deeper areas.
I agree with the last point too: getting comfortable with core math topics first helps make sense of why foundational systems like ZFC exist and what their role is. Diving straight into set theory axioms without context can be overwhelming.
Thanks for sharing this list and thanks for the advice.

marble ruin
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I don't think history is a particularly good guide to learning math. Especially not with the whole foundational shakeup thing.

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Like, The Elements by Euclid is the canon historical geometry textbook, but its axiom set is known to be incomplete. To actually study geometry, you'd need something like Hilbert's axioms.

hexed yarrow
# stiff wagon Hi everyone, I've been really inspired by how Isaac Newton learned, starting fr...

I don't think this is a good way to learn modern, contemporary math. Pedagogy has been streamlined a lot in the past 2000 years, and what people give a shit about has changed a lot too. However, if you're less interested in learning math and more interested in learning about the history of math, I assume it'd be useful - though specialized books on the history of math written nowadays would also be useful.

stiff wagon
stiff wagon
harsh current
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May I ask which grade are you in?

buoyant iron
harsh current