Am I missing out by not knowing another language?

Solution 1:

This alone is a poor motivation for the enormous effort required to learn a language.

• The majority of contemporary results seem to be published in or translated to English
• A foreign workmate or friend can be asked to summarize important results of the paper
• Mathematical results are technical, not artistic, so there is no danger that the "spirit of what is being done" is lost in translation

Solution 2:

Although I agree with what has been said, I'd like to make a remark. I had two years of French in high school. And it has been years since I've practiced it. If I were asked to speak it, I would probably sound funny to anyone who speaks French well. And higher powers have mercy on me if I'm asked to recount what somebody said in French. However, my recent research has led me to reference several papers in French. And I was surprised by how quickly I was able to understand what was being said. Honestly, the hardest part of the reading was dissecting what 'elementary' assumptions were being taken for granted. Of course, there were a handful of words that I didn't know. Mostly prepositions and adverbs. But those are quick to look up, and that's kind of the point I'm trying to get at. Math presentation isn't usually "flowery". And just knowing the sentence structure, the syntax, the grammar, and an elementary vocabulary was enough for me to `muddle through the French.'

But of course, two years (even if it was a while ago) is a significant amount of time to study a language. Perhaps more than you have time for. And I have the benefit that English is my mother tongue---which has no small borrowings from French. So, I don't know if this cursory knowledge of a language would be easily as applicable to something like Russian.

But just like math doesn't change around the world, math presentation doesn't change much either. The kind of troubles you face in reading math in your mother tongue (why are they doing things in this order? what assumptions are they working from? how does that follow? what they claim here doesn't seem obvious to me... ) are going to be exactly the same wherever you go.