However, her grandmother has other ideas. She believes that gifted children should be groomed for success, and she wants Mary prepared to work on the Navier-Stokes problem as her mother did. (The film exaggerates a bit when it suggests that solving the Navier-Stokes problem could earn someone a Nobel Prize in physics, but it correctly portrays it as a real, difficult and open problem in mathematics.) In one scene, the grandmother takes the little girl to a gallery in which seven picture frames are hanging on a wall at MIT, one for each of the Millennium Problems. All but one (which has a picture of Grigori Perelman) are empty, and she suggests encouragingly that Mary could have her picture in the one reserved for the mathematician who answers the open questions relating to the existence and smoothness of its solutions. She gives Mary a laptop with an ebook called "Transitions in Advanced Algebra" on it, but the little girl says she's already read that book and has "kinda moved on to differential equations, now."

In another scene, she takes Mary to see an MIT professor who challenges her to prove that an improper integral converges to a specified value. The girl is unable to do it and the grandmother disappointedly takes her away, only to learn that the girl recognized that it was a trick question and just did not want to say anything about it. She takes her back to the board where Mary is able to correct the problem by adding a minus sign and absolute value bars, proving it converges to the desired value by converting it to a double integral. In all of this, it does seem as if the proud grandmother wants what is best for Mary.

The grandmother is less admirable when talking with her son. She unsympathetically says that her daughter was too "weak" to solve the problem, and that he (a former philosophy professor who gave up academia to care for Mary) is pathetic. If she gains custody of the child, she will raise her without friends or normal childhood fun, as she did Mary's mother.

I feared that this was going to be yet another movie which suggests that one has a choice between mathematical success and human happiness, but that fear turns out to have been unfounded. I recommend you watch the film yourself. It is a bit saccharine and sometimes cliche, but I liked it. Or, if you'd prefer not to, read on and I'll tell you how it ends.

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It turns out that Mary's mother did solve the Millennium Problem. She showed up at her brother's house with the notes, but instead of being ecstatic, she was depressed, unsure what she would do with her life now that this one goal was accomplished, and unhappy about rewarding her mother with this success. She made her brother promise not to publish her work until after her mother's death.

The uncle is able to use this leverage to get the grandmother to leave Mary in his care. In the final scenes we see that she is studying advanced mathematics, but also is a Girl Scout and plays with other children like a normal girl her age.

Note Added Aug 2017: I just learned from The AMS Notices that mathematician Jordan Ellenberg appears in the film. I think he is the one teaching her advanced mathematics that I mention at the end above!