Is there a key to thinking more mathematically?

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Anti Hydrogen
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Are there some fundamentals or elements for thinking mathematically?

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  • #2
Dr. Courtney
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Lots and lots of practice and hanging around other people who think mathematically is how I got to be good at it.

I don't think there are any short cuts. But there can be some organizing principles for approaching different classes of textbook type problems.

A solid foundation for solving lots of textbook type problems in physics, chemistry, and math eventually provides a big toolbox for other kinds of problems that occur in other contexts. But building up the toolbox takes years of practice and homework in courses with lots of textbook type problems.
 
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  • #3
Anti Hydrogen
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Lots and lots of practice and hanging around other people who think mathematically is how I got to be good at it.

I don't think there are any short cuts. But there can be some organizing principles for approaching different classes of textbook type problems.

A solid foundation for solving lots of textbook type problems in physics, chemistry, and math eventually provides a big toolbox for other kinds of problems that occur in other contexts. But building up the toolbox takes years of practice and homework in courses with lots of textbook type problems.
Thanks for replying. Once I read in Quora that some of most important theories in maths are: Set theory, number theory and functions
 
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fresh_42
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Are there some fundamentals or elements for thinking mathematically?

Thanks
Always ask "why" and don't be satisfied by an answer which didn't convince you. Because the professor said or because it is written in the book are no valid answers.
 
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  • #5
Klystron
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Are there some fundamentals or elements for thinking mathematically?
One fundamental from information theory that helps me think mathematically and solve difficult problems can be called step-wise refinement in the context of the modular hypothesis, now theory. Given a large intractable problem, breakdown or refine the problem into simple steps that you can solve. Faced with a difficult landscape, consider simple shapes that combine to define or map the actual terrain.

Examples abound such as how NASA solved the unique problem of putting people on the moon. The early manned rockets launched astronauts into space with recovery, then into orbit around the earth. Later refinements had spacecraft dock in space and then orbit the moon and return. Finally, these various steps combined into a successful lunar landing, docking in orbit and a safe return to earth.

The Apollo spacecraft consisted of many modules performing diverse functions such as the large boosters to lift from earth, smaller modules for life support and flight control, and the lunar excursion module (LEM) that conveyed astronauts to the lunar surface, provided habitat then launched the explorers into orbit to dock with the service module for return to earth.

Even pure mathematical problems may be refined into sets and functions as you describe to either solve the problem or demonstrate lack of a viable solution.
 
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  • #6
Borek
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Thanks for replying. Once I read in Quora that some of most important theories in maths are: Set theory, number theory and functions

You are mistaking tools for skill.
 
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