This study investigates the impact of language on students' learning of mathematics. A comparison has been made between English and Korean speaking university students' discourses on "infinity". In Korean, unlike in English, there is a disconnection between colloquial and mathematical discourses on infinity, in that the mathematical word for infinity is not a formalized version of a colloquial word but a novel sound, inspired by a Chinese term for infinity. This difference was expected to be paralleled by certain dissimilarity between the ways the discourses of the two groups developed toward the mathematical discourse on infinity. Data with the help of which we intended to test this hypothesis were collected through surveys and interviews. A total of 132 English speakers and 126 Korean speakers participated in the survey and then twenty paired representatives were selected from each group for follow-up interviews. It was found that in spite of the comparable levels of mathematical performance, there was, indeed, a visible dissimilarity between mathematical discourses on infinity of Korean- and English-speaking students. In general, whereas no group could pride itself on a well-developed mathematical discourse on infinity, the mathematical discourse of the English speakers, just like their colloquial discourse, was predominantly processual, whereas the Korean-speaking students' talk on infinity was more structural and, in an admittedly superficial way, closer to the formal mathematical discourse. (Contains 8 tables and 2 figures.)