Terence Tao was born in 1975

Optimistic Oliver must have made a calculation mistake.

For any number, $N$ with prime factorization, $N=p_1^{i_1}p_2^{i_2}\cdots p_n^{i_n}$ , the total number of factors can be calculated to be $n_f=(i_1+1)(i_2+1)\cdots(i_n+1)$ .

Now, analysing the last digits of $N$ in the problem, we can see that the number ends in $\cdots 1975$ .

Now noting that for any $a$ , $\frac{10a+5}{5}=2a+1$ , and any number has to end in $5$ or $0$ to be divisible by $5$ ; we can conclude that $N$ divides $25$ , but is not divisible by $125$ .

$\frac{N}{5} = \cdots 395, \frac{N}{25} = \cdots 79$

From this, we get that $N = 5^2p_2^{i_2}\cdots p_n^{i_n}$ and therefore the number of factors would be $n_f = 3(i_2+1)\cdots(i_n+1)$ .

The number of factors should be divisible by $3$ . $1975$ is not divisible by $3$ . Hence, Oliver is wrong.

Of the other two choices provided, $\boxed{1974}$ is divisible by $3$