The choice of preposition is largely dependent on your said mathematical "things": - The function *f* attains its maximum value **at the point** *x=0*. - The function *f* attains its maximum value **on the interval** [0,1]. - The function *f* attains its maximum value **in the subset** *M*. Alternatively, one may write - *x=0* is the point **at which** the maximum value of the function *f* is attained. - *[0,1]* is the interval **on which** the maximum value of the function *f* is attained. - *M* is the subset **in which** the maximum value of the function *f* is attained. Though, in mathematical writing, one usually shuns beginning a sentence or phrase with a mathematical symbol. Hence - The point *x=0* is the point **at which** the maximum value of the function *f* is attained. is always preferred in mathematical writing. See [How to Write Mathematics by Halmos][1]. If the last formulation sounds repetitive, go with the first set of phrasings. [1]: http://alpha.math.uga.edu/~azoff/courses/halmos.pdf "How to Write Mathematics by Halmos"