Can you call yourself good at math if you're good at calculating and solving problems but can't prove anything worth shit?
I mean, I can learn proofs for exams but if you were to wake me up in the middle of a night 4 months from then I wouldn't be able to do it.
Can real mathematicians, say someone with a Phd in math prove most given theorems at any given time?
Proving things is literally problem solving.
>Can real mathematicians, say someone with a Phd in math prove most given theorems at any given time
Yes. That's literally where everything important comes from. The type of math you're doing, where you get a question and end up with a number as an answer, is something a computer can do for you. Proofs are the only way to understand exactly what you have to do to figure something out - under any condition. It's what real mathematicians do for a living.
Well then how do I get better? I want to think like a true mathematician.
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get this cancer out of here
This reminds me of those /pol/ collages with the fake quotes.
>not starting with baby rudin
Not gonna make it
No. That's why college professors and teachers are revising their teaching material constantly.
What's wrong with this image?
Everything
This isn't the only important thing in mathematics. Being able to apply maths to model real world systems, for example, is very important and something many mathematicans do.
In general these images are made from books that one person who made the image has read.
There are many ways to learn mathematics, it's better to browse until you find a subject you like than to focus so hard on fundamentals.
Fundamentals can always be improved at any point so don't worry about reading a huge list like this before reading what you actually want to.
Read more math, do more proofs, see enough proofs to notice patterns so that you can develop techniques and tricks.
have wrote it right - proving theorems is the core of what real mathematicians are doing.
In order to get better in proving, as stupid as its sounds, you should prove more things. For example, when your are preparing to exam instead of learning a proof given in textbook first try to come up with your own.
Proving things is a central activity of mathematics, and arguably the central activity of mathematics, as this user has said. The point of a proof is the creation of knowledge. How can you claim to know something if you can't demonstrate, in some way, that it's true? I would certainly agree that if you can't prove things, then you're not really doing math, and you're definitely not a mathematician.
All of that being said, proofs are also not the end-all be-all of math. A complaint that is made in math sometimes is that "just proving a bunch of shit" without giving context as to why it's useful in one way or another, /whether in pure math or in the pleb RL world/, amounts to nothing more than stamp-collecting, and so becomes dull.
What topics does baby Rudin cover?
DO NOT FOLLOW THIS
But in what way is the image a "wrong" way to approach the study of mathematics?
He explained it to you. It is just boring and inefficient to focus so much on fundamentals instead of trying to learn what you're actually interesting in.
It creates mustard gas?