Exploring Different Perspectives on Mathematical Thinking

[Mgkov18]

I was talking to a friend recently when he said he thinks about math like sentences and when he sees formulas he acts like he is speed reading through a book, although this did not really make much sense to me, it must make a lot of sense to him because he is great at math. This just got me thinking off all the different ways people think about math, so I was curious to ask on here.

 

[micromass]

I was talking to a friend recently when he said he thinks about math like sentences and when he sees formulas he acts like he is speed reading through a book, although this did not really make much sense to me, it must make a lot of sense to him because he is great at math. This just got me thinking off all the different ways people think about math, so I was curious to ask on here.

Speed reading math? Seems like a horrible idea! What's his level of math?

I think of math visually. I try to visualize everything I see. And I certainly spend a lot of time on each sentence!

 

[vela]

I'm guessing he means that when he sees a formula, he can read it as if it were a sentence in another language. I get that. Sometimes it's easier to communicate a concept through mathematical expressions rather than trying to explain it in words.

 

[Blackberg]

All of math could be written in a spoken language. It's actually precision shorthand for surprisingly long sentences. Try reading Newton's Principia, you'll appreciate the current notation.

 

[Hepth]

I do this too.

When you start to see so many repeated patterns all the time $\int \frac{d^D \ell}{(2 \pi)^D}$ , $|H_{v} \rangle_{\infty}$ , $\tilde{F}^{\mu \nu}$ , etc, you brain goes though stages of translation as it learns them.

First you think about them and what they mean and maybe go look it up. "Oh, this is a loop integral over the momentum $\ell$, and the $D$ means they're doing it in dim-reg probably. I wonder what their subtraction scheme is. ..."

After a while you say in your head "loop integral over $\ell$" as you read it, and move on.

Then after the Nth article you say in your head "unghh" and it just MEANS something. There doesn't even need to be a literal word. I think this is the point at which you're speed reading. You don't need to translate the math to english, then understand the english and get a concept out of it. You just translate the mathematical equation to a concept immediately.

 

[Dembadon]

I try to visualize everything. For example, when I see $$\nabla\cdot{\bf D} = \rho$$
I note the equipotential surface for which it's relevant, and then visually apply the physical concept to the current scenario (point charge = sphere, line charge = cylinder, etc). Then I draw figures/pictures.

 

[gleem]

I just read that seeing an equation stimulates the same part of the brain that a work of art does.

 

[Fooality]

I try to visualize everything. For example, when I see $$\nabla\cdot{\bf D} = \rho$$
I note the equipotential surface for which it's relevant, and then visually apply the physical concept to the current scenario (point charge = sphere, line charge = cylinder, etc). Then I draw figures/pictures.

I think realizing that many approach it visually is a huge part of increasing math literacy. I'm more of a creative type, and I was math impaired until I got a program that did graphing in 2d and 3d of functions. Finally math started to speak to me, and things like calculus made enough sense for me to care. Abstract math still isn't my thing, but once one can make the link between math and a tangible thing/space it describes, it becomes very interesting. We need to be willing to teach it in a multi-sensory way to engage more kids.

 

[dlgoff]

I think of math visually. I try to visualize everything I see.

This is very interesting to me personally for a couple of reasons. Having hearing problems as a child, reading (or even hearing words correctly) was a big problem; still plagues me today and is probably part of the reason I'm that kind of "visual" person today. I know that I would never have gotten a Physics degree had I not used this technique in mathematics; albeit not to the extent you have used it.

I'm guessing he means that when he sees a formula, he can read it as if it were a sentence in another language. I get that. Sometimes it's easier to communicate a concept through mathematical expressions rather than trying to explain it in words.

Exactly. See above.

 

[Kevinkevinkevin]

I read math pretty slowly, and continue to reread it until I can grasp it visually. To me, it's more than just solving equations, its understanding what they mean in the real world.