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There are certain problems, I am noting that I am unable to solve because I cannot comprehend what exactly is being asked. The problems themselves might be non wordy, but I try to formulate it in english sentences while solving and I get all lost and I dont know where I am going. It is impossible to write down everything abstractly, and I am not accustomed to thinking in my native language using english words interspersed. For example, I wouldnt know the words in my language that stands for permutations and combinations distinctly.

I find it much easier to do symbolic manipulations than comprehending worded definitions, theorems and problems. Do I belong to the category of people who are yet to develop a reasonable facility in stating and understanding abstractions or might it be possible that language is a factor.

To give some background, I was schooled in a country where we spoke "X". This was the language I used at my house, with friends, while buying grocery, etc. But in the math classroom, the language was english. I was good at school mathematics, for example , I once did the manipulations to show that $\zeta(n) =\sum_{k=1}^\infty k^{-n} = \Pi \frac{1}{1-p^{-n}} $ in class. My teacher was impressed and recommended some advanced textbooks, I would read definitions and theorems again and again yet would fail to develop any connections whatsoever. I got so discouraged that only now have I picked up maths again to re-learn it

Now I am facing the same problem. Has anyone, or does anyone know of someone, who comes from a non-english background also has trouble with these kinds of problems or am I just one of those people who havent been promoted from formula manipulation to abstract thinking.

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I don't think it's anything to do with "abstract thinking". How do you write down maths in your own language? Do you prefer symbols ($\forall$ and the likes) or words. As for me, I don't like symbols, whether in french (my language) or english: I find it much more understandable to write "for all $x\in\mathbb R$" rather than $\forall$. Maybe you're just the opposite? – Sebastien May 23 '11 at 4:57
Personally, I find that I can either think about a problem in Spanish or in English; I cannot mix them up. There are portions of basic group theory and large portions of Calculus that I have had essentially to learn twice, once in Spanish, and later in English, so I could "think fluently" about them (for Calculus, in order to teach them; for group theory, in order to go on to more advanced material that I only knew in English). I still do most of my elementary arithmetic in Spanish, and have to pause if I'm speaking to do it mentally and "translate" back, which sometimes leads to problems. – Arturo Magidin May 23 '11 at 5:00
Also: My undergraduate advisor was born in Barcelona; was sent to Russia during the Spanish Civil War, and eventually emigrated to Mexico. In his head, he did arithmetic in Catalan, calculus and basic level math in Russian, and advanced math in Spanish... – Arturo Magidin May 23 '11 at 5:16
I've long suspected that language affects reasoning. I would advice you not to just read theorems but to try to do more manipulation. For example if you read about a theorem, you should try as much as possible to explore it in every direction, look for counterexamples and look for why it actually works. Don't just read theorems, learn why they work! I know this may slow your learning but that's the best way to conquer this problem. (Note: I didn't post this as an answer because the question is not mathematical it should probably be on a psychology forum) – Obinna Okechukwu May 28 '11 at 0:31
Sometimes when I face this problem, if it a problem in a relatively small piece of text, i.e. a theorem, I can try to re-write it in simpler English and expand it into more verbal steps. This helps a lot. However for larger texts, like whole textbooks, I .. uh, just find another textbook which is more non-native-speaker-friendly :) I once read a paper which its author is pretty much well-educated that he extensively use latin phrases. That one drove me both crazy and angry. – M. Alaggan Aug 21 '11 at 4:04

Were the advanced textbooks in English or in X? I understand that translating all the mathematical names between languages is difficult and often not at all intuitive.

"Reading definitions and theorems" is fruitless labour by itself; when a teacher brings them to life in your imagination, and you do a lot of exercises using them, only then you can understand. That's the way to comprehend "worded definitions, theorems and problems".

Try sitting into a math course at a close-by university, and make sure you also attend the exercises. You could also try books of the other language, but make sure you do the exercises.

If you already have a problem you try to solve, applying the theorems and comparing with exercises might also help (tackling the problem plus understanding theorems + problems). This applied learning might also be more motivating than dry reading.

Some things are also plain hard, so make sure you don't set your slope to steep. No harm done going back in the book to studying simpler things once in a while. All the best!

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