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Working mathematicians thread.
How do I evolve from a student into a professional mathematician? I've been researching "heavily" in philosophy of mathematics, yet I cannot find still the secret sauce that makes up a good mathematician.
People who are undergrads or haven't published a maths paper need not reply.
Pic related is an image of how I currently perceive philosophy and practice of mathematics. The math world (Platonic or otherwise) is split into two groups - objects and properties. And then proofs are derived from conjectures, and consist of discourse between objects and properties.
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bump! :-)
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>>8060024
You need to figure out where theorems start to break down, implications of theorems that no one thought of yet, equivalences over different branches of mathematics, etc.
Learn about methods of mathematical proofing, you either want to expand the current tools of mathematics, bridge gaps between current ones, make corrections, or simplify things. This is easier to do at the "limits" of complicated or new theorems. Essentially, if you have an idea, write it down, disregard if it's good or bad at first.
I will remind you that if you don't add any new knowledge to the field you have failed
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>>8060081
>>8060024
Reminder that new knowledge is not necessarily a complete new branch or theorem, it just may be a new way of making applied mathematics such as a more efficient algorithm for modelling softwares and such taking known theorems.
Also, yuge amounts of autism
I work in a lab that makes modelling of proteins and genomic metabollism, and we have large difficulties because those fields are like the wild west
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OP again, trying to get 4chin to work properly.
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Not sure if it will help, but I saved these books after reading Ian Stewart's Letters To a Young Mathematician. Maybe you can take a look at them:
1. The Psychology of Invention in the Mathematical Field - Jacques Hadamard
2. The Mathematician's Mind - Jacques Hadamard
3. Advanced Mathematical Thinking - David Tall
Also, check his other books: http://homepages.warwick.ac.uk/staff/David.Tall/
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>>8060161
OP here, thank you. I have checked out the Jacques Hadamard book and even have ventured down the "what's the psychology of mathematicians" route to not much fruitful results.
I find Philosophy of Mathematics to be much more intriguing than Psychology of Mathematics, but that's just a personal preferrence. Perhaps because I really despise a lot of the foundational mathematics "dead white males" people who believe everything in the Universe is a set.
As for books, I'm currently devouring
What is Mathematics, Really? by Reuben Hersh
http://www.amazon.com/What-Mathematics-Really-Reuben-Hersh/dp/0195130871
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>>8060177
Everything IS a set you troglodyte
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>>8060238
Sets are gross.
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>>8060024
Have you tried taking candies? (Aka amphetamines)
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>>8060261
Lol what
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>>8060413
Bump^2
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