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As I got further in my Mathematics degree what really made it all "click" was classes on Philosophy. The logic and approach you forms in Philosophy give a great

As I got further in my Mathematics degree what really made it all "click" was classes on Philosophy. The logic and approach you forms in Philosophy give a greater understanding of how mathematical proofs are formed and how to approach problem solving. A series of lectures from a Philosophy 101 course would do a lot to help with the mindset you speak of so look to any of the MIT, Stanford, etc online courses.

HuShifang 6y ago
As someone who studied mathematics as an undergrad and then intellectual history (with an emphasis on philosophy) postgrad, I second this. I would add too that learning how to write effective philosophy papers is an excellent way to improve your writing, and argumentation, and analytical ability more generally. (I often share the Jim Pryor's guidelines [1] with students.) [1] http://www.jimpryor.net/teaching/guidelines/writing.html http://www.jimpryor.net/teaching/guidelines/writing.html
- panabee 6y ago
  this is interesting. thanks for sharing! these guidelines seem like they would apply well to science papers, or really, any writing where the objective is to prove an argument or perspective.
omosubi 6y ago
A friend of mine once said that if he could do college over again he'd major in math and philosophy. He said something to the effect of philosophy teaches you to argue from a set of premises, math teaches you to argue with a given conclusion.
- cousin_it 6y ago
  I don't think math is about arguing, and neither is good philosophy. Both are about truth. You could view math as arguing, if you studied it by endless theorems and proofs, but a better way to learn math is by trying to solve problems whose answers you don't know (and picking up theories as needed). That way you learn to be curious for the truth out there, not just a convincing argument. That's the best approach to philosophy as well.
  - omosubi 6y ago
    I think the way we're taught math in school might lead us to believe that it's not but it is. you're right that the best way to learn math, or anything really, is to take a problem or project or whatever that's just outside your current skillset and work towards achieving it, getting help where necessary. But when you are seeking new knowledge, the best tool you have for verifying truth is argument with others. Math researchers and really anyone doing research of any kind spend a lot of time arguing methods and results - this is how you seek truth. Philosophy is the same way - someone makes a claim and uses evidence to support that claim. Others argue either for it or against it, refining the argument until they feel they have a better understanding of a given topic.

HuShifang 6y ago

As someone who studied mathematics as an undergrad and then intellectual history (with an emphasis on philosophy) postgrad, I second this. I would add too that learning how to write effective philosophy papers is an excellent way to improve your writing, and argumentation, and analytical ability more generally. (I often share the Jim Pryor's guidelines [1] with students.) [1] http://www.jimpryor.net/teaching/guidelines/writing.html http://www.jimpryor.net/teaching/guidelines/writing.html

panabee 6y ago
this is interesting. thanks for sharing! these guidelines seem like they would apply well to science papers, or really, any writing where the objective is to prove an argument or perspective.

omosubi 6y ago

A friend of mine once said that if he could do college over again he'd major in math and philosophy. He said something to the effect of philosophy teaches you to argue from a set of premises, math teaches you to argue with a given conclusion.

cousin_it 6y ago
I don't think math is about arguing, and neither is good philosophy. Both are about truth. You could view math as arguing, if you studied it by endless theorems and proofs, but a better way to learn math is by trying to solve problems whose answers you don't know (and picking up theories as needed). That way you learn to be curious for the truth out there, not just a convincing argument. That's the best approach to philosophy as well.
- omosubi 6y ago
  I think the way we're taught math in school might lead us to believe that it's not but it is. you're right that the best way to learn math, or anything really, is to take a problem or project or whatever that's just outside your current skillset and work towards achieving it, getting help where necessary. But when you are seeking new knowledge, the best tool you have for verifying truth is argument with others. Math researchers and really anyone doing research of any kind spend a lot of time arguing methods and results - this is how you seek truth. Philosophy is the same way - someone makes a claim and uses evidence to support that claim. Others argue either for it or against it, refining the argument until they feel they have a better understanding of a given topic.