Do you translate mathematics or understand it natively?

[austinuni]

I've been reading an introductory textbook on Mathematical Logic by Richard Hodel, and I often find myself translating the logic into English sentences, or translating it into some other form like a graph that helps me understand what is being stated.

I realize this is probably a very poor way of reading the book, but so far it's the only way I've been able to make forward progress with it (very slowly too). I have a Computer Engineering background and I'm reading the book for fun.

When you look at a mathematical equation, do you sub-consciously translate it into some other form, or can you just look at the equation or steps in the proof and understand it without this translation? Is it just a matter of practice to understand math without doing a translation or do you think some people have this inherent knack for it and others do not?

 

[Borek]

Whatever works for you. There is no one "correct" way of learning and understanding.

Don't be surprised if one day you will start to think differently, when you get more intuition and experience. But as long as you get things right, doesn't really matter how you do it.

 

[nuuskur]

I study math in Estonian, I have most materials in Russian and I learn extra from the web in English. Biggest problem for me is the terminology in a respective language. I have a table where I have a termin in the language I know and then I frantically search for their meanings in the other two languages. I speak 3 languages, so it's not that hard. There are people who speak 7+ languages on a professional level - meaning they have every piece of terminology down to the last symbol in every language (though I admit, a lot of the languages are similar), but it's still an astonishing feat.

I am most comfortable in Russian (it's not my native language, most of my material is in Russian), but I make effort to translate it into Estonian and English, but English is not the primary source of information, hence it's not that important and that's why I often struggle with names of theorems in English :D

 

[symbolipoint]

austinuni,

Look for information about the concept of Subitizing.

Although that concept is about identifying a number of objects visually and without consciously counting, this is very likely to correlate with becoming intuitively familiar with looking at expressions and equations, and almost immediately being aware of several characteristics about them as well as what can be done with them. This might also be a way of becoming familiar with graphs of algebraic and transcendental functions.

 

[Silver_rose]

I consider Math to be a language on its own, so when I find there's a lack in understanding there is a need for translation.
So if I understand it, I read it as it's native. If I don't and it needs further thought, I translate it back to English sometimes to cement the process.

 

[audire]

I think this nurture/nature debate over talent vs skill in mathematics and mathematical applications is a long-standing one that still really isn't answered..

There are definitely examples in history and in modern-day life that point to talent being somewhat intuitive as in what genetics you are granted... for example my father and mother hold medical doctorates and whether it be expectation or natural talent I've always found myself good at understanding math and mathematical concepts