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.

If the last formulation sounds repetitive, go with the first set of phrasings.

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.

If the last formulation sounds repetitive, go with the first set of phrasings.