Katherine Coleman Goble Johnson, NASA Mathematician & Musician: Madeline’s Monthly Musical Tips Blog & Radio Show for October 2025
October 2025 is the Eighteenth Anniversary of “Madeline’s One Minute Musical Radio Show” and the Nineteenth Anniversary of “Madeline’s Monthly Musical Tips Blog/Article”.
Our blog and Radio Show celebrates the life and work of Katherine Coleman Goble Johnson, NASA Mathematician, teacher, and musician.
Many of the world’s mathematicians, inventors, scientists, engineers, medical doctors, researchers, and teachers have studied and played musical instruments since they were children. These eminent individuals have integrated music into their thinking process.
Included is the article “The Corner of Music Avenue and Math Road” by Johnson String Instrument Team.
Our article of the month is “Happy Thoughts to Begin Your Day!” by Madeline Frank, Ph.D.
Feature Question for October 2025: How did Classical music play a part of Katherine Coleman Goble Johnson’s life as a NASA mathematician and musician and what musical instrument did she play?
https://www.madelinefrankviola.com/one-minute-musical-radio-show/
Early Years: Creola Katherine Coleman was born on August 26, 1918 to Joylette Roberta Lowe Coleman and Joshua McKinley Coleman in White Sulphur Springs, West Virginia. She had three older siblings. “Her mother was a teacher and her father was a lumberman, farmer, and handyman. He also worked at the Greenbriar Hotel.” Mr. and Mrs. Coleman wanted the best education for their four children and wanted all four of them to get a college education. (Wikipedia Katherine Johnson)
As a child she was fascinated by mathematics. “She counted everything, from the number of steps she took to get to the road, to the number of forks and plates she washed when doing the dishes.”
Katherine Coleman, “vividly remembered watching her older siblings go to school, wishing so much that she could go with them. When she finally did start school, she so excelled that by age 10, she was in high school.” She graduated high school at 14.
High School: In White Sulphur Springs there was “no high school for black children and the Coleman family were determined that their children would have a quality education. Every autumn, Katherine’s mother moved with her children to a rented home in Institute, Kanawha County, West Virginia, so their children could attend high school there. In the summer they would return around 186 miles to White Sulphur Springs where Joshua worked as a farmer.”
In 1928, Katherine began her studies at West Virginia State High School. She graduated in 1932. She was an excellent student in mathematics and “was taught geometry by Angie Turner King who did an outstanding job in encouraging her students and giving them a love of their subject. She was a tremendous influence on Katherine both in high school and later in West Virginia State College where she also taught.”
Katherine said that King “was a wonderful teacher – bright, caring, and very rigorous.”
“Katherine also became very interested in astronomy while at the high school. This interest came about since she would walk home each evening with the school principal who pointed out stars and constellations to her.”
College & Wonderful Mentors: “Katherine made the natural progression to West Virginia State College having been awarded a full scholarship covering her tuition fees, room and board. This College, was a black college, founded in 1891. She had two years in which to make a decision as to which subject she would major in and she knew it was one of English, French and mathematics. It was a difficult decision for the girl who was talented in all these subjects, so eventually she decided to major in two of these topics.”
At West Virginia State College she was taught mathematics by James Carmichael Evans (1900-1988).
Katherine said, that Professor Evans, who had a B.S. and an M.S. from the Massachusetts Institute of Technology:-… “was one of my math teachers in college – his wife had taught me math in the eighth grade – and because they didn’t have children at that time, I became a kind of child to them. I was always at their house, and he was the sort of person who was always teaching even at home. To please him I always had to do my very best, and he always knew if it wasn’t my very best effort. At that time, I was very interested in French and English studies with Professor Matthews, but Professor Evans said, “I know how good you are in French, but you will also major in mathematics.”
Professor John F. Matthews spoke seven or more languages. (MacTutor Katherine Johnson)
Dr. William Waldron Schieffelin Claytor, an African American mathematician had earned a Ph.D. in 1933 with a thesis on point-set topology from the University of Pennsylvania. He taught Katherine mathematics and “quickly spotted her research potential.” Professor Claytor recognized Katherines “bright and inquisitive mind”.
He said, “You’d make a great research mathematician.” (“A research mathematician does many things, one of which is solving large math problems.”)
Katherine “acknowledged the effort that Claytor put in to help her be successful :- Many professors tell you that you’d be good at this or that, but they don’t always help you with that career path. Professor Claytor made sure I was prepared to be a research mathematician. … Claytor was a young professor himself, and he would walk into the room, put his hand in his pocket, and take some chalk out, and continue yesterday’s lesson. But sometimes I could see that others in the class did not understand what he was teaching. So, I would ask questions to help them. He’d tell me that I should know the answer, and I finally had to tell him that I did know the answer, but the other students did not. I could tell.”(MacTutor Katherine Johnson)
Professor Claytor “made sure that Johnson took all of the math classes she needed to pursue her life’s passion. He even created a class about the geometry of outer space—just for her. Geometry is the study of lines, angles and shapes.”
NASA for kids and students/who was Katherine Johnson grades 5-8.
“When he realized that she would need a background in analytic geometry that the College did not offer, he simply put on a course just for Katherine. She was fortunate to have Claytor as a teacher for he only taught at West Virginia State College from 1934 to 1937. Katherine graduated with a B.S. ‘summa cum laude’ in 1937 majoring in both mathematics and French.” She was 18 years old.
“After graduating, Katherine took a job as a teacher in an elementary school in Marion, Virginia. She was told that she could have the job if she could teach mathematics and French, and play the piano.”
Music: Katherine began to play the piano to be an elementary school teacher. She later joined the church choir, “founded and directed a chorale for her Alpha Kappa Alpha sorority chapter”, and taught piano to neighborhood children.
“She travelled to this school by bus and experienced racism which was all too common at that time.”
“Katherine felt that the racism in West Virginia was less blatant than that in Virginia. As such, she was surprised when on crossing into Virginia from West Virginia the bus came to a halt and all black people were told to move to the back. When the driver said all the colored people were to be put into taxis, Katherine refused until he asked politely. A stand indicative of a lifetime refusal to be thought of as less than equal.” (MacTutor Katherine Johnson)
Teacher: She taught for two years in several schools in Virginia and West Virginia.
Marriage and Children: In 1939, Katherine Coleman married James Francis Goble. They were both students at West Virginia State College and later met as teachers. They had three daughters, Constance, Joylette, and Katherine. Their daughters “became mathematicians and teachers.”(MacTutor Katherine Johnson)
When she married, she gave up teaching. In 1940, “Katherine was asked by West Virginia State University to join their graduate mathematics program.” She thought “that the University was reacting to the Supreme Court decision in 1938 which declared that States had to provide the same educational opportunities for black Americans as for white, either by creating separate institutions or allowing them to attend the same institution. Nevertheless, she was keen to take up the opportunity of graduate study. Sadly, she had to give up her studies since her husband became ill and Katherine had to return to teaching to support her family.”
National Advisory Committee for Aeronautics later called “NASA” Langley Laboratory:
When Katherine visited her relatives in Newport News. Virginia in 1952 “she was told that the National Advisory Committee for Aeronautics (NACA) (later to become NASA) hired black women mathematicians. In fact, they had hired women to act as “computers” since 1935 and, with shortages of manpower during World War II, had begun to take on African-American women. Katherine felt that this was an opportunity that she had to grasp so she moved her family to Newport News. Once there she worked as a substitute mathematics school teacher and applied for a position at NACA. In fact, she received both an offer of a permanent teaching post and of a position as NACA in 1953 and she had no hesitation in accepting the position at NACA. Her husband’s health deteriorated and, in 1956, he died from a brain tumor which was inoperable.” (MacTutor Katherine Johnson)
Katherine Coleman Goble “began working for NACA in 1953. Her work in the agency was a day-to-day progression. She started as one of the women who worked on problems assigned from the engineers in what was then the Guidance and Control Branch. As Johnson worked on the problems, she would ask questions. She didn’t want to just do the work — she wanted to know the “hows” and the “whys” and then the “why nots.”
“None of the other women had ever asked questions before, but by asking questions, Johnson began to stand out. She was told that women didn’t participate in the briefings or attend meetings; she asked if there were a law against it. The answer, of course, was no, and so Johnson began to attend briefings. NACA was just beginning its work on space. Space itself may be perceived as a series of plane surfaces, and as Johnson became known for her training in geometry, she began to work with the team more and more. Eventually, she became known as a leader, and the men increasingly relied on her. She remembered quite clearly her experience at the time. “The women did what they were told to do,” she explained. “They didn’t ask questions or take the task any further. I asked questions; I wanted to know why. They got used to me asking questions and being the only woman there.” It was this inquisitive nature that made her a valuable resource to the team and the only woman at the time to ever be pulled from the computing pool to work on other programs. Then in 1962, President John F. Kennedy charged the country to send a man to the Moon. Johnson became part of the team, and she began to work on calculating the trajectory for America’s first space trip with Alan Shepherd’s 1961 mission, an early step toward a Moon landing. She went on to do the calculations for the first actual Moon landing in 1969.” (NASA Katherine Johnson : A Lifetime of Stem)
“When she began working at NACA Katherine was assigned to the office which housed the black “computers” who were loaned to whichever Division required assistance. She was loaned to the Flight Research Division and her work there was so outstanding that this Division became her permanent place of work. Let us quote her own words:” (MacTutor Katherine Johnson)
Katherine Coleman Goble, “We were pioneers of the space era. We worked in secret for about three years, often without knowing exactly what the total thrust of our work was. … You had to read ‘Aviation Week’ to find out what you’d done. The Russians were already attempting to move into space at that point, so our efforts were militarily strategic.”
In 1958 NACA became NASA and all NACA employees became NASA employees.Katherine explained, “Everything was so new – the whole idea of going into space was new and daring. There were no textbooks, so we had to write them. We wrote the first textbook, starting from scratch. People would call us and ask, “what makes you think that this or that is possible?” and we would try to tell them. We created the equations needed to track a vehicle in space. I was lucky that I was working with the division that worked out all the original trajectories, because I guess that is what I am remembered for.”
“Up to 1958 black workers in NACA were segregated. They had to eat separately and had restrooms which were separate from their white colleagues. However, after the change to NASA, this segregation ended. However, there was still discrimination against women and they were not allowed to attend briefings:”
Katherine, “These were such intelligent men, they knew so much, and I always loved intelligence, and so I’d ask what had gone on in the briefings – I’d listen and listen and ask questions. Then, of course, I’d ask why I couldn’t go myself, and eventually they just got tired of answering all my questions and just let me in to the briefings.”
“This was not the only way that there was discrimination against women. They were not allowed to put their names on their research reports:”
Katherine, “We needed to be assertive as women in those days – assertive and aggressive – and the degree to which we had to be that way depended on where you were. I had to be. In the early days of NASA women were not allowed to put their names on the reports – no woman in my division had had her name on a report. I was working with Ted Skopinski and he wanted to leave and go to Houston … but Henry Pearson, our supervisor – he was not a fan of women – kept pushing him to finish the report we were working on. Finally, Ted told him, “Katherine should finish the report, she’s done most of the work anyway.” So, Ted left Pearson with no choice; I finished the report and my name went on it, and that was the first time a woman in our division had her name on something.”
Katherine continues, “This was not any old report. It was Determination of Azimuth Angle at Burnout for Placing a Satellite over a Selected Earth Position. It contained the theory necessary for launching, tracking and returning space vehicles and was used for the famous space flight by Alan Shepard in May 1961 and the flight of John Glenn in February 1962.” This paper was the first of “26 scientific papers Katherine Coleman co-authored while working for NASA.”(MacTutor Katherine Johnson)
Second Marriage: Katherine Coleman Goble, widow, was introduced to James A. Johnson by their minister at Carver Memorial Presbyterian Church in Newport News, Virginia. They both sang in the Choir at their church. They married in 1959. They were married for 60 years. “He had been commissioned in 1951 as a Second Lieutenant in the United States Army and was a veteran of the Korean War.” (MacTutor Katherine Johnson)
Astronaut John Glenn’s 1962 orbital mission:
NASA prepared in 1962 “for the orbital mission of John Glenn, Johnson was called upon to do the work that she would become most known for. The complexity of the orbital flight had required the construction of a worldwide communications network, linking tracking stations around the world to IBM computers in Washington, Cape Canaveral in Florida, and Bermuda. The computers had been programmed with the orbital equations that would control the trajectory of the capsule in Glenn’s Friendship 7 mission from liftoff to splashdown, but the astronauts were wary of putting their lives in the care of the electronic calculating machines, which were prone to hiccups and blackouts. As a part of the preflight checklist, Glenn asked engineers to “get the girl”—Johnson—to run the same numbers through the same equations that had been programmed into the computer, but by hand, on her desktop mechanical calculating machine. “If she says they’re good,’” Katherine Johnson remembers the astronaut saying, “then I’m ready to go.” Glenn’s flight was a success, and marked a turning point in the competition between the United States and the Soviet Union in space.” (Katherine Johnson bio NASA)
Katherine Coleman Goble Johnson was an American mathematician, trailblazer at NASA for 33 years. She was a teacher, wife, mother, grandmother, and musician. She passed away on February 24, 2020 in Newport News, Virginia. She was 101 years old.
“The Corner of Music Avenue and Math Road” (Sep. 17, 2025) by Johnson String Instrument Content Team. “Did you know that there is a strong relationship between math and music?”
“Research has indicated that music activates the same area of the brain that is used for solving spatial-temporal reasoning problems. Conversely, understanding various fundamentals of math can help you learn to read and play music. Similarities in how the brain processes the two disciplines creates a beneficial overlap between the two.”
“Math is helpful when learning music and vice versa, because there are several places where math and music intersect. For example, numbers and mathematical principles can be used to teach or learn music. And when performing music, you rely on time signatures, beats per minute, and formulaic progressions, which reinforce math skills. Good at math? You’re probably capable of being good at reading music. We think of learning math as a logical process and learning to read music as a creative one. In truth, we rely on a combination of logic and creativity to be able to solve a math problem and play a piece of music. One of the strongest correlations between the two is that they’re both dependent on numbers and division of time.” To read more:
https://www.johnsonstring.com/resources/articles/helpful-advice/math-music-intersection/?utm_campaign=What+do+Math+and+Music+have+in+common%3F+&utm_medium=email&utm_source=iPost&campaign_id=534969&iqs=9z4zdii0l349oubt1lrvaa3l8gnndpu8ltv5tq9alo0
Happy Thoughts to Begin Your Day! by Madeline Frank, Ph.D.
How to start your day with excitement and enthusiasm with an air of creativity!
Happy thoughts!
Do you remember as a child waking up at the crack of dawn, filled with happiness, excitement and enthusiasm because it was your birthday or a special holiday?
Do you remember how excited you were?
Do you remember the gift you received and how you enjoyed unwrapping it?
One of the most exciting gifts I received was when I was an eight-year-old child.
It was a violin. That violin was my opportunity to change my life and brought me great joy!
Do you remember receiving a gift that changed your life?
When you remember that gift does it make you happy and grateful?
When I was 12 years old, I took Home Economics in public school. Momma bought me a used Singer Sewing machine so I could make the required clothes for class. I also made things for my younger siblings like bibs, handmade dolls, and aprons. It was a wonderful gift to learn how to do something new. The class also taught us to sew, with nice hand stitching to hem clothes, and cook basic meals! I smile as I remember this!
What is the difference between a day that feels like everything that can go wrong will vs one that feels like everything goes your way?
It obviously starts with the beginning.
I’m sure you know someone who walks into the office every morning, a grimacing look plastered on their face, and they usually look for the negative side of everything.
I’m not sure how this person starts their day, but it probably looks like this:
An alarm blaring at full volume, jolting them awake.
Scrolling through social media (comparing yourself to others).
Reading/watching the news (creating panic, fear, and doubt).
Reading email (letting other people prioritize your time).
Grumbling about going to work/school.
If this is the foundation for your day, what lens do you think you will see life through that day?
You will likely focus on things you do not want.
You will likely look at lack, doubt, and hopelessness with greater importance.
You will likely quash most positive thoughts that enter your mind.
Instead beginning your day like this:
1) Set your alarm clock to ease you awake (most phones have this setting to whisper you awake, rather than jolt you out of bed).
2) Spend a few minutes in silence, focusing on what you are grateful for. It is easy to do this when life is going well…but it is essential to do this when life is not perfect.
3) Move your body in some way, whether it is stretching or slipping into your workout clothes to get your heart pumping.
4) Journal for 5 minutes about whatever flows into your mind. Positive ideas can be captured, and concerns stop renting space in your mind once they are put on paper. Send a note of encouragement to a child, family member, or friend! Write 5 things down you are grateful for!
5) Only read/listen to/watch something growth related or positive.
It’s all about starting your day with gratitude and positive thoughts.
So how can you give yourself a gift like this every day?
Begin your day by thinking of joyful things and gratitude.
Don’t listen to the news.
Don’t check emails for at least two hours after waking.
Set your priorities for gratitude, growth, and challenge for the day (yes…we all need challenges!)
Fuel your mind by reading a positive article.
Write a motivating encouraging note or thank you note to child, parent, or friend.
Thomas Dreier said, “Today should always be our most wonderful day.”
One of the most effective strategies I’ve discovered to set myself up for success is to ask a series of “power questions”.
For example:
What am I grateful for in the past 24 hours?
What am I excited about today?
What am I unsure of, but know I can conquer today?
Gordon Tredgold of Leadership Principles Ltd says, “People are more open to ideas, communication, opportunities, and ambitious goals when they are happy.”
He continues, “Happy teams are productive teams, and this productivity comes from people’s openness to be more inspired when they are happy, it increases their belief in what they are capable of and what they are prepared to try.”
Zig Ziglar, motivational expert and speaker said, “You have to feed your mind daily with the good, clean, pure, powerful and positive.”
So, what is the best way to start your day?
Give this strategy a try for the next 10 days and let me know how it works for you! © 2025, 2023 If you need a speaker or virtual speaker contact Madeline at: [email protected]
https://madeline-firstimpressions.blogspot.com/2023/02/happy-thoughts-to-begin-your-day-by.html?m=1
“Musical Notes On Math” by Dr. Madeline Frank teaches your child fractions and decimals, the fun easy way, through the rhythm of music, Winner of the Parent To Parent Adding Wisdom Award is available in book form, newly updated as an e-book on Kindle, Nook, or iBook.:
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Dr. Madeline Frank’s book “Leadership on a Shoestring Budget: Timeless Principles for Everyday Use, helps businesses stay afloat in times of trouble. She calls her innovative observations, Tuning Up Your Business. For over 25 years she has helped countless people create their great image brand, and communication style that makes them irresistible. Click on the following Amazon.com link to order your copy of “Leadership On A Shoestring Budget
“The Secret of Teaching Science & Math Through Music” shares scientific evidence, medical evidence, test results, and true stories of the world’s scientists, medical doctors, and mathematicians who have studied and played musical instruments since they were children by Madeline Frank, Ph.D. Click below:
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“Madeline’s Midnight Melodies- Music From around the World”. This CD complements her books with a blend of dance music, gigues, tangos, ballet and favorites including “Danny Boy”, Puccini’s “O Mio Babbino Caro”, Debussy’s “Claire De Lune” and others. “Madeline’s Midnight Melodies” CD is now available for purchase by downloading a song, downloading the album click below:
Wishing you and your family a happy October, from Your Non-Invasive Medicine Music Expert, Madeline
For over 30 years, Dr. Madeline Frank has helped children and adults overcome problems through Classical music. Madeline Frank, Ph.D. is an award-winning teacher, author, researcher, speaker, conductor, and concert artist. She has discovered a scientific link between studying a musical instrument and academic and societal success. Madeline Frank earned her Bachelor and Master’s degree from the Juilliard School of Music. Her education has included scholarships at the Juilliard School, Indiana University, and the University of Cincinnati and she has a violin performance diploma from the North Carolina School of the Arts. (C) 2025 Madeline Frank