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NOTE: This spoiler was submitted by Jeremy
Frank Adler (Chris Evans) is trying to get his niece Mary (Mckenna Grace) to come out of the bathroom. She is not fond of the outfit she has to wear for what is to be her first day of school. Frank and Mary live in a small home with their one-eyed cat Fred. Frank then goes to drop Mary off at the bus stop. After she's gone, Frank is spotted by his neighbor Roberta (Octavia Spencer). Roberta follows Frank into his house and tells him that he needs to do something for Mary or else he will lose her.
Mary begins her first day of first grade in math class taught by Ms. Bonnie Stevenson (Jenny Slate). Bonnie asks basic math questions, but Mary is displeased since she knows more advanced math than the rest of the class. She solves a multiplication problem on her own and even states the square root of the number. Principal Davis (Elizabeth Marvel) enters the room and Mary shouts at her to call Frank and get her out of class.
After school, Frank picks Mary up. Bonnie runs outside to catch him and discuss Mary's incredible knowledge of math. Frank says that Mary studied the Trachtenberg method to allow herself to memorize equations and arithmetic computations. Bonnie later looks up the Trachtenberg method to see what Frank was talking about. She also looks up Mary's mother/Frank's sister Diane, who was a brilliant mathematician until she committed suicide when Mary was only six months old.
Frank takes Mary out for a day at the beach on a boat while also lecturing her on why she shouldn't have yelled at the principal. Mary does appear to show remorse. Later, Frank goes to a bar he visits every Friday night and finds Bonnie coming in to approach him. She confronts Frank about what he did and did not tell her truthfully about Mary. Frank explains how Diane came to him one night and he did not realize what she would do later. He found Diane on the bathroom floor and has had Mary ever since.
Mary is on the school bus and sees her classmate Justin (Michael Kendall Kaplan) walking with a zoo diorama that Mary finds better than the one she made. Another kid named Ricky (Brody Rose) trips Justin and causes him to break his diorama, mocking the poor boy in front of the other kids. Mary yells at Ricky for what he did, and when he asks what she'll do, Mary grabs a textbook from another kid and whacks Ricky in the face, breaking his nose.
Frank is called in after the incident. Principal Davis considers expelling Mary but then suggests granting her a scholarship to attend the Oakes Academy for Gifted Education, as someone with Mary's intellect would be more suited for that environment. However, Frank refuses to allow it, feeling that Mary needs a normal education and childhood.
Mary later apologizes to her class for hitting Ricky, but then takes the opportunity to mention how great Justin's diorama was, leading the class to applaud the boy.
Frank and Mary receive an unexpected visit from Frank's estranged mother Evelyn (Lindsey Duncan). She gives Mary a laptop as a gift. Evelyn then takes the time to criticize Frank's living arrangements and Mary's form of education, which doesn't surprise Frank. She claims she is looking out for Mary's best interest and asks Frank what Diane would think if she saw how Mary lives now. Evelyn wants to take Mary and put give her the best education she can get to put more potential in her future.
Frank and Evelyn then become involved in a custody battle. Evelyn brings her lawyer Aubrey Highsmith (John Finn) while Frank is represented by Greg Cullen (Glenn Plummer). Highsmith argues that Frank illegally gained custody of Mary, while Cullen defends Frank's living conditions. It is settled that Frank and Mary will be checked on while Evelyn will have some time to herself with Mary.
Frank leaves Mary with Roberta for the evening while he goes out for drinks with Bonnie. They eventually hook up, although Bonnie is initially hesitant. The two sleep together, and Mary unexpectedly goes over to her house the next morning while Bonnie is there wrapped in a bed sheet. Mary catches her, and Bonnie leaves extremely embarrassed. Frank scolds Mary for leaving Roberta's home when she wasn't supposed to, so Mary thinks Frank can't have a personal life because of her.
Evelyn takes Mary to Boston. She shows Mary pictures of Diane and tells her about Diane's research into the Navier-Stokes problem, which Diane had devoted her life to. Evelyn takes Mary to meet her colleague, Seymore Shankland (John Sklaroff) to review an equation he tried to solve. Mary appears confused by Shankland's work, which he dismisses as her simply not being able to comprehend just yet. As Evelyn takes Mary away, Mary states that she was confused because Shankland's equation was wrong. Mary returns and solves it herself. Meanwhile, back in Tampa, Frank and Bonnie continue seeing each other.
Mary starts seeing a psychologist named Pat Golding (Julie Ann Emery). Pat learns much about Mary's life, including that she has no friends her age and that she sees Roberta as her closest friend. Pat appears concerned when Mary mentions that she and Roberta watch UFC fights every week.
During the next court hearing, Mary's biological father Bradley Pollard (Keir O'Donnell) testifies on behalf of Evelyn. Cullen presses Bradley over his non-involvement in Mary's life, not even being able to know her middle name. The judge rules against Bradley for any sort of custody. When Mary learns that her father was around, she breaks down in tears over him not bothering to visit her. To cheer her up, Frank and Roberta take Mary to the hospital to see a family gathered as they await the birth of a new child. When they learn that a boy has been born, the family cheers. Frank tells Mary that this is what it was like when she was born, and it was he that stepped out to deliver the news.
Frank and Evelyn return to court. Highsmith grills Frank as he testifies regarding his current job doing freelance boat repairs when he used to have a job as an assistant professor at Boston University, as well as a previous arrest for assault. Highsmith continues to insist that Frank is depriving Mary of a potentially fruitful future. Cullen in turn presses Evelyn about the circumstances surrounding Diane's passing.
Cullen later goes to Frank's home and tells him that he and the judge have come to an agreement where Mary would be placed in foster care until the age of 12 when she can decide where to live, out of fear that they will lose the case and Frank would lose full custody of Mary. Cullen urges Frank to take the deal.
Frank meets the foster parents and sees that they have a nice home and family. He leaves Mary there, and they have a tearful goodbye where Mary begs Frank not to leave her. Frank must regrettably walk away even as Mary cries and screams for him. After a while, when Frank tries to visit Mary, the foster father tells him that she doesn't want to see Frank.
Bonnie comes across a flyer for a missing cat - Fred. She sends the picture to Frank, who later goes with Bonnie to the animal shelter, as he seems to know what is going on. Not only does he get Fred back, but he gets two more cats as well.
Frank goes to the foster home and finds out Evelyn is staying in the guest home and has two tutors present for Mary. Although Mary is initially angry to see Frank, she breaks down and hugs him. Frank then goes to Evelyn and presents her with something she had never known of before - Diane's completed work on the Navier-Stokes problem. Evelyn thinks it's fake and that Diane would have wanted it published soon. Frank reveals that Diane had requested not to have the work published until after Evelyn's death. This hits her quite hard. Frank says he will have the work published on the condition that Evelyn give up custody of Mary to Frank, otherwise the work will remain unpublished until Evelyn dies. Frank leaves. Evelyn breaks down in tears and she calls Shankland.
Mary is back home with Frank. She has begun to take afternoon college courses. Frank picks her up and brings her to the park to join with Bonnie and the other students.
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Frank Adler has raised his 7-year-old niece Mary after her mother committed suicide when she was only 6 months old. Mary has an incredible knowledge of math and arithmetic equations, which does not go unnoticed by her educators. However, Frank doesn't want Mary to have a prestigious education, but rather a normal one like her mother would have wanted.
Frank's distant mother Evelyn shows up to try and claim custody of her granddaughter so that she can be taught in the best schools and have a bright future. This leads to a custody battle between Frank and Evelyn. Frank's lawyer feels that they will lose the case and that it would be in the best interest of everyone if he accepts a deal where Mary would be placed in foster care until she is 12 and can decide where she wants to stay. Frank makes the hard choice to let Mary go.
After learning that Evelyn is maintaining some level of personal custody, Frank brings her a completed problem that Mary's mother had tried to solve (she was a brilliant mathematician prior to her death) and says that he will have it published if Evelyn gives up custody back to Frank, or else it won't be made public until after Evelyn dies.
Frank gets Mary back and she is allowed a normal childhood/education while also taking college courses.