There’s a sequence early on in “Hidden Figures” that might touch the hearts of geeks everywhere. A young child wearing glasses proves to be so extraordinary, a school administrator has a special conference with her parents. Shapes from a stained class window, float into the air before the young child who instinctively understands geometry and other abstractions. She sees and thinks differently.

That child was the person who would become Katherine Johnson. The movie doesn’t tell us that she was the youngest of four children. Nor does it tell us that her father, Joshua Coleman, was a handyman, nor that her mother, Joylette (Karan Kendrick), was a teacher. The film does show modest parents earnest in their support of her education even though Katherine was a black girl in Virginia.  Katherine would graduate from high school at 14 and from college at 18 with a major in math (1937) but the film jumps forward, skipping her years as a teacher, her first marriage to James Goble in 1939 and his death in 1959.

When the movie begins, she is not a teacher any more, but single mother of three girls, Katherine Goble, working at the NASA Langley Research Center in Virginia. She’s stuck on the road behind the wheel waiting for her acting supervisor, Dorothy Vaughan (Octavia Spencer), to fix the car that is stalled at the side of the road while their co-worker Mary Jackson (Janelle Monáe) smokes a cigarette.

When a white cop rolls in, he’s surprised (“There are quite a few women working on the space program”), but turns out helpful although it’s clear that the women don’t expect friendly. As Mary notes, “Three negro women are chasing a white policeman down a highway in 1961. That is a God-ordained miracle.” At work, they are women first, but also colored.  Black women are segregated into a different pool from the white female human “computers” or research mathematicians.  The colored computers have a different water fountain and a separate colored bathroom. Dorothy has been acting supervisor without the extra pay, but she also has a determination that is to be reckoned with.

The white cop isn’t the only one who underestimates this threesome. When Katherine first meets Lt. Colonel James A. Johnson (Mahershala Ali), he thinks secretary rather than research mathematician. “Hidden Figures” does touch upon their romance, but greater emphasis is on how Katherine gains the respect of the director of the Space Task Group Al Harrison (Kevin Costner playing a fictional person based on several actual staff members) and then the grudging cooperation of one of the head researchers Paul Stafford (Jim Parsons). Harrison is task-oriented; he’s probably already gone through the entire white female computer pool.

One isn’t quite sure what disturbs Stafford more–that his work is being checked by a woman or by a person who is not white. One of the research group members doesn’t want to share the coffee pot with a black person and a small separate coffee pot is marked “colored” just for her.

For those women who have worked in the white-collared world with the uniform mantra of skirts, pearls and pumps, you’ll sympathize with Katherine as she has to trek half a mile across the broad NASA campus to the colored bathroom until finally one day she returns, soaking wet after running in heels through the pouring rain. Confronted by Harrison about her absence during a crunch time, Katherine explains the situation, harnessing an anger that has been percolating for decades. Harrison responds with practicality, removing the colored bathroom sign and desegregating the whole restrooms.  He’s more worried about the race with the Soviet Union into space and the moon than the concept of separate human races.

The bathroom facility issue is dealt with lightly in Allison Schroeder and Theodore Melfi’s screenplay, and deftly filmed by director Theodore Melfi. The allegro staccato of Johnson’s heel tapping while she’s sitting down going over figures precedes her departure. Her run across a parking lot in heels while carrying a large stack collated of figures she’s checking is desperation hemmed in by a skirt. It might seem comical unless you’ve been in those heels, perhaps just looking for the women’s restroom in a predominately male area or industry.

Restrooms are one thing; glass ceilings are another. Dorothy has managerial qualities, but she’s black and under the supervision of her white counterpart, Vivian Jackson (Kirsten Dunst), who is courteous, but not pleasant nor helpful. Dorothy is not being paid for her extra work nor is she being respected as a person.  Yet the script shows that Vivian isn’t the only person who turned Dorothy away or underestimated her. When the new IBM computer rolls in, Dorothy understands she’s in danger of being replaced and she’s not complacent. At the local library, she meets with more resistance because books on computers aren’t in the colored section.

Mary also wants more and becomes interested in wind tunnel experiments (The wind tunnel experiments help calculate the forces that the space capsules must be able to withstand). With the encouragement of a supervisor, she eventually goes to court to gain admittance into all-white all-male courses in order to become an aerospace engineer with the support of her husband, Levi Jackson (Aldis Hodge).

All three women went on to do great things, but it was Katherine who worked on the Mercury project calculating trajectories, launch windows and the emergency return flights. In 1962, at a crucial moment, the late John Glenn (Glen Powell) asked specifically to have Katherine double check the calculations of the IBM computer, a system that had only been recently introduced into the space program and this moment is shown in the movie.

The Soviets put the first man in space (Yuri Gagarin on 12 April 1961), but Glenn would follow on Friendship 7 (20 February 1962). Coming back, Glenn’s journey experienced a few scary moments, but his success was the breakthrough needed by the US space program.

The movie doesn’t follow the women past John Glenn’s flight into space but does provide a short epilogue that shows how these women were the first and showing what they looked like in real life.  Only one of them lived to see this movie.

Katherine Johnson (1918) retired as an aerospace technologist from NASA in 1986. The Katherine G. Johnson Computational Research Facility at the Langley Research Center was dedicated to her in May of this year. Last year, she was awarded the Presidential Medal of Freedom.

Dorothy Vaughan (1910-2008) retired from NASA in 1971, having specialized in electronic computing and FORTRAN programming. She was on the SCOUT (Solid Controlled Orbital Utility Test) Project tests. According to The Human Computer Project, Dorothy championed women both black and white who deserved promotions or pay raises.

Mary Jackson (1921-2005) did eventually become an aerospace engineer and worked on wind tunnel experiments before becoming an administrator, working as the Federal Women’s Program manager in the Office of Equal Opportunity Programs and the Affirmative Action Program manager.

The movie is based on a 2014 book of the same name by the Virginia-born Margot Lee Shetterly whose father worked at the NASA-Langley Research Center and Shetterly founded The Human Computer Project in 2013, hoping to keep a record of the women who worked as research mathematicians for NASA. According to The Human Computer Project website, when NACA (National Advisory Committee for Aeronautics) transitioned to NASA, segregated facilities were abolished in 1958 (and not in 1961 as portrayed in the movie).

The film fully embraces a glorified visual view of the early 1960s, the wonderful era cars, the color full fitted dresses with matching jackets for the women. The women stand out against the mundaneness of the men’s “uniform” of white shirts and dark ties and medium grey pants. That along with the upbeat music provided by Pharrell Williams, one of the producers, and the light comic tone make this a family movie.

“Hidden Figures” provides a a positive image of women as researchers. They aren’t lonely tortured souls, but determined individuals who balanced their personal lives with their intellectual aspirations. They overcame the additional obstacle of race with poise and grace. If you know children who have questions about what practical applications math has, this movie aptly demonstrates that exploration and adventures in space are mathematical problems. “Hidden Figures” is about three brilliant women who thought differently. It’s a movie about breaking barriers through intelligence that doesn’t veer off topic in search of white saviors, but does allow that for women to achieve they need supportive men.

“Hidden Figures” opens in select theaters on Dec. 25, but rolls out nationwide on January 6.