Do people whose native languages are read right-to-left experience mathematical statements differently? [closed]

When I see the equation

$$A = B$$

the first idea to occur to me is that $A$ can be transformed into $B$. Although of course

$$B = A$$

has the same content, to me it connotes rather that $B$ can be transformed into $A$. I imagine that this is because English is my native language and I read left-to-right.

Native speakers of Arabic or Hebrew, do you find that the opposite is true for you? Do you find that you experience written mathematics differently at all?


My native language is English, but I have taught many international students from countries that read right to left. My observation is that in very simple examples such as your $A = B$, it makes no difference at all, roughly for the reasons mentioned in Comments.

However for long displayed equations, it does seem to me that these international students are more likely to look at the end first. Sometimes this gives them valuable orientation as to motivation. I often suggest that all students browse through the whole equation to get an idea what is going on before plunging into the details of justifying each equal sign, inequality, or implication (from left to right).

On a related matter, many students in north Asia are taught to deal with the denominator of a fraction before the numerator. This has more to do with training and habits than with language differences. However, there sometimes seems to be a real advantage to looking at the denominator first. One example of this is in probability problems with combinatorial solutions: if both numerator and denominator count ordered arrangements, this is often more quickly seen by looking at the denominator first. Also, looking at denominators first is sometimes an advantage in something as simple as adding fractions that need a common denominator.

This is indeed more a psychology question than a mathematical one, but there may be important implications for math education. The relatively strong advantage of looking at denominators first, may give added credence to my claim that there is a (somewhat weaker) advantage in looking at the end of an equation first.

For everyone, I think the lesson is to 'size up' a math problem from several 'angles' before plunging in.


Another point: Sometimes when you write $A=B$, it does have a different content from writing $B=A$. This is not emphasized in algebra classes, AFAIK.

For instance, $$(x+1)(x-1)=x^2-1$$ is "expanding", and $$x^2-1 = (x+1)(x-1)$$ is "factoring". However, they're the same equation. (Or they're isomorphic. Or something like that.)


In the end, I think it's all isomorphic.

An example where the right-to-left reading is more natural than left-to-right is with the function notation $fg(x)$, where $g$ is applied first, despite being written after $f$. But we Westerners got used to that, right? 8-)

BTW, 2000 years ago, Chinese mathematicians did Gaussian Elimination, but they wrote the equations in columns, not rows (because Chinese is read top-to-bottom).