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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.

kuch nahi
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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 04:57
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    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 05:00
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    I flagged the question for the moderators, suggesting that this should probably be a community wiki question. – Arturo Magidin May 23 '11 at 05:01
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    The short answer: People are very different in this respect.

    In my country, English mathematical words are commonly used (just like German words like schlicht and eigen were introduced to English), so I have no problem whatsoever to use a mix of my native languge with some English math terms. OTOH, I think nonverbally a lot of the time. Especially with permutations and similar, I hate verbal classifications with and without repetition because I have a nonverbal idea in my head. When I do manipulations on formulas, it feels like manipulating an object with my hands, not like speaking.

     – Phira May 23 '11 at 05:14
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    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 05:16
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    There are many non-native speakers of English at my university doing mathematics and some of them do very well despite not being able to speak English fluently. (But perhaps they have excellent reading comprehension? I don't know.) I haven't paid enough attention to notice whether they gravitate towards courses with more equations and formulae though... – Zhen Lin May 23 '11 at 09:16
  • I also disagree. I live in Korea, where both grammar and language structure differ significantly from English. But I have seen many people who have difficulty speaking English fluently but nonetheless possess excellent mathematical ability and have little problem reading English mathematical material. Also, verbally, my colleagues often use English words for advanced mathematical concepts, while the rest of conversation still done in native language. But this seems not to restrict mathematical thinking, if we put aside the situation where I am forced to speak or write in English just like now. – Sangchul Lee May 23 '11 at 13:52
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    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 00:31
  • You wrote "I would read definitions and theorems again and again yet would fail to develop any connections whatsoever." Possibly the problem is the lack of a comprehensible example. Or you may have skipped some necessary background material. If you are trying to learn from a textbook, do the problems. – phv3773 Jun 20 '11 at 18:40
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    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. – Mohammad Alaggan Aug 21 '11 at 04:04
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    I don't have a problem mixing my languages, although note-taking in mixed languages can lead to a question for the speaker in the wrong language. I still do arithmetic in my native language in my head and most of my colleagues from different countries do so. I suggest to use "permutation" inside a reasoning in your native language without any scruples. – Phira Oct 14 '11 at 23:10
  • "I was schooled in a country where we spoke X": Why so coy? From your name, I would guess that perhaps X = Urdu -- but why would you want to keep that secret? – TonyK Jan 04 '12 at 21:53
  • @ArturoMagidin Your being able to do arithmetic fluently only in your native language is apparently universal. A story I heard once is that during WWII, German spies who were posing as native speakers of another language (and spoke it seamlessly) were unmasked when asked to solve long division problems out loud. – user43208 Oct 20 '13 at 12:59

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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!

j13r
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