Does Principia Mathematica Live Up to Its Name?

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Discussion Overview

The discussion centers around the book "Principia Mathematica" by Whitehead and Russell, focusing on its mathematical content versus its philosophical and logical aspects. Participants express their experiences and opinions on the book's suitability for learning mathematical proofs and its relevance to broader mathematical study.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • One participant feels that "Principia Mathematica" is more philosophical than mathematical and questions whether it becomes more math-focused later in the text.
  • Another participant recommends George Polya's "How to Solve It" and "How to Read and Do Proofs" as helpful resources for learning proofs.
  • Some participants argue that "Principia Mathematica" is overly specialized and not suited for the average mathematician, with one recalling a review that deemed it a waste of time for those interested in learning proofs.
  • Concerns are raised about the lengthy proofs in "Principia," such as the extensive justification for basic arithmetic, which some find unengaging.
  • Recommendations for alternative resources include "How to Prove It" by Velleman and introductory Linear Algebra books that also cover proof techniques.

Areas of Agreement / Disagreement

Participants express a range of opinions on the value of "Principia Mathematica" for learning mathematics, with some viewing it as overly complex and not practical for proof learning, while others acknowledge its significance in logic and foundational mathematics. No consensus is reached regarding its overall value.

Contextual Notes

Some participants note the limitations of "Principia Mathematica" in terms of its accessibility and relevance to typical mathematical study, highlighting the dependence on individual learning preferences and goals.

skywo1f
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so I've been studying principia mathematica by whitehead and russell.
it seems like its all principia and no mathematica. it just feels like I am taking philosophy logic again.

does it get more mathy later?

any books that will help me with math proofs?
 
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For proofs, have a look at George Polya's How to solve it. Another book that has been recommended to me (but I have less experience with it) is How to read and do proofs.

Principia is extremely specialized. The old joke about it is that it takes hundreds of pages to "prove" that one plus one equals two. If you're really interested in the topic then by all means delve into it, but that sort of logic doesn't map well into the deep structures of my brain. In my humble opinion, I don't think it really has much to do with a lot of the rest of mathematics. There's a lot of other cool stuff out there if Principia isn't your cup of tea.
 
I don't think Principia is suited for the average mathematician. I remember mathwonk reviewed it (from a mathematician's standpoint) and basically called it a waste of time lol. If you're just trying to learn math proofs, I'd agree. I never felt comfortable with trying to prove extremely basic things like the commutativity of natural number addition. This never seemed any more or less obvious than the concept of a set, so if I take one for granted, why not the other?

Yeah, I know the basics of natural numbers are classic topics in a first year grad course and that it's better to limit your axioms, but I really don't care. A book taking 100 pages to prove that 1+1=2 just doesn't seem like fun. I guess if you agree then it's not for you.

I like "How to Prove it" by Velleman, and most introductory Linear Algebra books double as a sort of introduction to proofs book, so you may look into those.
 
Tobias Funke said:
I remember mathwonk reviewed it (from a mathematician's standpoint) and basically called it a waste of time lol.

They were hoping to make a complete and consistent system, ridding any paradoxes they knew about. Then a man named Godel came along and...
 

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