Does Principia Mathematica Live Up to Its Name?

[skywo1f]

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?

 

[Cantab Morgan]

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.

 

[Tobias Funke]

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.

 

[Focus]

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...