I have before me a copy of "The Indian Mathematician Ramanujan", by G. H. Hardy (not actually related to me, as far as I know), which appeared in volume 44, number 3 (March 1937) of *The American Mathematical Monthly*, on pages 137‒155.

One of the theorems of Ramanujan stated there is this:

If $\displaystyle F(k) = 1 + \left( \frac 1 2 \right)^2 k + \left( \frac{1\cdot3}{2\cdot4} \right)^2 k^2 + \cdots$ and $F(1-k) = \sqrt{210} F(k)$, then \begin{align} k = {} & (\sqrt 2 - 1 )^4 (2-\sqrt 3)^2(\sqrt7 - \sqrt 6)^4 (8-3\sqrt7)^2 \\ & \cdot (\sqrt{10} - 3)^4(4-\sqrt{15})^4(\sqrt{15}-\sqrt{14})^2 (6-\sqrt{35})^2. \tag{13} \end{align}

Of this Hardy wrote:

An expert on elliptic functions can see at once that $(13)$ is derived somehow from the theory of "complex multiplication", [ . . . ]

What does the phrase "complex multiplication" mean in this context?

The Man Who Knew Infinity. Far more recently a movie inspired by that book appeared, with Jeremy Irons and Dev Patel. $\endgroup$ – Michael Hardy Oct 27 '16 at 5:33