Open thread, Oct. 27 - Nov. 2, 2014

MrMind

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If it's worth saying, but not worth its own post (even in Discussion), then it goes here.

Notes for future OT posters:

1. Please add the 'open_thread' tag.

2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)

3. Open Threads should be posted in Discussion, and not Main.

4. Open Threads should start on Monday, and end on Sunday.

I usually think about math nonverbally. I am not usually doing such thinking to come up with proofs. My background is in engineering, so I got a different sort of approach to math in my education about math than the people who were in the math faculty at the university I attended.

Sometimes I do go through a problem step by step, but usually not verbally. I sometimes make notes to help me remember things as I go along. Constraints, assumptions, design goals, etc. Explicitly stating these, which I usually do by writing them on paper, not speaking them aloud, if I'm working by myself on a problem, can help. But sometimes I am not working by myself and would say them out loud to discuss them with other people.

Also, there is often more than one way to visualize or approach a problem, and I will do all of them that come to mind.

I would suggest, to spend more time thinking about math, find something that you find really beautiful about math and start there, and learn more about it. Appreciate it, and be playful with it. Also, find a community where you can bounce ideas around and get other people's thoughts and ideas about the math you are thinking about. Some of this stuff can be tough to learn alone. I'm not sure how well this advice might work, your mileage may vary.

When I am really understanding the math, it seems like it goes directly from equations on the paper right into my brain as images and feelings and relations between concepts. No verbal part of it. I dream about math that way too.

I only got to a nonverbal level of understanding of advanced math fairly recently, and the first time I experienced it I think it might have permanently changed my life. But if you dream about math...well, that means I still have a long way to go and deeper levels of understanding to discover. Yay!

Follow-up question (just because I'm curious): how do you approach math problems differently when working on them from the angle of engineering, as opposed to pure math?