Katherine Johnson
Katherine Johnson (1918 – 2020) was an African-American mathematician. While working at NASA, Johnson calculated the orbits taken by American astronauts – including Alan Shepard, the first American in space, the Apollo Moon landing program, and even the Space Shuttle.
Her extraordinary ability to calculate orbital trajectories, launch windows and emergency return paths was widely known. Even after the arrival of computers, astronaut John Glenn asked her to personally re-check the electronic results.
In 2015, Johnson received the Presidential Medal of Freedom.
“Katherine Johnson – Timeline of Mathematics.” 2024. Mathigon. Accessed July 31. https://mathigon.org/timeline/johnson.
Goodrich, Joanna. 2023. “Katherine Johnson, the Hidden Figures Mathematician Who Got Astronaut John Glenn Into Space.” IEEE Spectrum. IEEE Spectrum. March 1. https://spectrum.ieee.org/katherine-johnson-the-hidden-figures-mathematician-who-got-astronaut-john-glenn-into-space.
Katherine G. Johnson’s mathematical calculations of orbital mechanics at NASA were critical to the success of Friendship 7 and several other U.S. human spaceflights. She was one of the women featured in the 2016 Oscar-nominated film Hidden Figures.
“Katherine Johnson Biography.” 2024. NASA. NASA. June 28. https://www.nasa.gov/centers-and-facilities/langley/katherine-johnson-biography/.
Grigori Perelman
In 2003, the Russian mathematician Grigori Perelman (Григо́рий Перельма́нborn, born 1966) proved the Poincaré Conjecture, which, until then, was one of the most famous unsolved problems in mathematics.
The complex proof was verified by 2006, but Perelman declined two big awards that came with it: the $1 million Clay Millennium Prize, and the Fields Medal which is the highest recognition in mathematics. In fact, he said: “I’m not interested in money or fame; I don’t want to be on display like an animal in a zoo.”
Perelman also made contributions to Riemannian geometry and geometric topology, and the Poincaré Conjecture is still the only one of the seven Millennium Prize problems to have been solved.
“Grigori Perelman – Timeline of Mathematics.” 2025. Mathigon. Accessed January 2. https://mathigon.org/timeline/perelman.
“Grigori Yakovlevich Perelman – Biography.” 2025. Maths History. Accessed January 2. https://mathshistory.st-andrews.ac.uk/Biographies/Perelman/.
Grigori Perelman is a Russian mathematician who proved the Poincaré Conjecture and who refused to accept a Fields Medal or the $1 000 000 Clay Prize.
“Grigori Perelman.” 2024. Wikipedia. Wikimedia Foundation. December 17. https://en.wikipedia.org/wiki/Grigori_Perelman.
Grigori Yakovlevich Perelman (Russian: Григорий Яковлевич Перельман, born 13 June 1966) is a Russian mathematician and geometer who is known for his contributions to the fields of geometric analysis, Riemannian geometry, and geometric topology. In 2005, Perelman resigned from his research post in Steklov Institute of Mathematics and in 2006 stated that he had quit professional mathematics, owing to feeling disappointed over the ethical standards in the field. He lives in seclusion in Saint Petersburg and has declined interview requests since 2006.
Goutay, Nicolas. 2015. “How Grigori Perelman Solved One of Maths Greatest Mystery.” Medium. Medium. https://medium.com/@phacks/how-grigori-perelman-solved-one-of-maths-greatest-mystery-89426275cb7.
The Poincaré Conjecture, formulated in 1904 by the French mathematician Poincaré, remained one of the most challenging open questions in the twentieth century, until it was proven in 2002 by Grigori Perelman. It has been considered by the Clay Mathematics Institute as one of the seven Millennium Prize Problems that, if ever solved, would grant a one-million dollar prize. Grigori Perelman was attributed a Fields Medal for « his contributions to geometry and his revolutionary insights » that led to his outstanding proof. He refused both the prize and the medal. My researches showed me that the history of the conjecture and the mathematical path that led to Perelman’s proof is, besides related, at least as interesting as Perelman’s peculiar personality and particular conception of how Mathematics should be conceived and studied. As topology, the field of Mathematics in which the Poincaré takes place, is rather a topic of interest than my speciality, the mathematical developments in this article will not be technical, but enough to comprehend the extend of the Conjecture and the idea behind Perelman’s proof — and do not, in my opinion, require any advanced mathematical knowledge from the reader.
Steven Strogatz
Steven Strogatz is the Susan and Barton Winokur Distinguished Professor for the Public Understanding of Science and Mathematics at Cornell University. After graduating summa cum laude in mathematics from Princeton in 1980, Strogatz was a Marshall Scholar at Trinity College, Cambridge. He then did his doctoral work in applied mathematics at Harvard, followed by a National Science Foundation postdoctoral fellowship at Harvard and Boston University. From 1989 to 1994, Strogatz taught in the Department of Mathematics at MIT. He joined the Cornell faculty in 1994.
Strogatz has broad research interests. Early in his career, he worked on a variety of problems in mathematical biology, including the geometry of supercoiled DNA, the dynamics of the human sleep-wake cycle, the topology of three-dimensional chemical waves, and the collective behavior of biological oscillators, such as swarms of synchronously flashing fireflies. In the 1990s, his work focused on nonlinear dynamics and chaos applied to physics, engineering, and biology. Several of these projects dealt with coupled oscillators, such as lasers, superconducting Josephson junctions, and crickets that chirp in unison. In each case, the research involved close collaborations with experimentalists. He also likes branching out into new areas, often with students taking the lead. Over the years, this has led him into such topics as the role of crowd synchronization in the wobbling of London’s Millennium Bridge on its opening day, and the implications of “the enemy of my enemy is my friend” for social and political systems. [SS]
“About.” 2024. Steven Strogatz. Accessed July 31. https://www.stevenstrogatz.com/about.
“Steven Strogatz.” 2024. Department of Mathematics. Accessed July 31. https://math.cornell.edu/steven-strogatz.
I have broad interests in applied mathematics. At the beginning of my career I was fascinated by mathematical biology and worked on a variety of problems, including the geometry of supercoiled DNA, the dynamics of the human sleep-wake cycle, the topology of three-dimensional chemical waves, and the collective behavior of biological oscillators, such as swarms of synchronously flashing fireflies. In the 1990’s, my work focused on nonlinear dynamics and chaos applied to physics, engineering, and biology. Several of these projects dealt with coupled oscillators, such as lasers, superconducting Josephson junctions, and crickets that chirp in unison. In each case, the research involved close collaborations with experimentalists. I also love branching out into new areas, often with students taking the lead. In the past few years, this has led us into such topics as: mathematical explorations of the small-world phenomenon in social networks (popularly known as “six degrees of separation”), and its generalization to other complex networks in nature and technology; the role of crowd synchronization in the wobbling of London’s Millennium Bridge on its opening day; and the dynamics of structural balance in social systems.
“Steven Strogatz.” 2024. Wikipedia. Wikimedia Foundation. June 18. https://en.wikipedia.org/wiki/Steven_Strogatz.
“steven strogatz.” 2024. Steven Strogatz. Accessed July 31. https://www.stevenstrogatz.com/.
Steven Strogatz is an applied mathematician who works in the areas of nonlinear dynamics and complex systems, often on topics inspired by the curiosities of everyday life. He loves finding math in places where you’d least expect it—and then using it to illuminate life’s mysteries, big and small. For example: Why is it so hard to fall asleep a few hours before your regular bedtime? When you start chatting with a stranger on a plane, why is it so common to find that you have a mutual acquaintance? What can twisting a rubber band teach us about our DNA? An award-winning researcher, teacher, and communicator, Strogatz enjoys sharing the beauty of math though his books, essays, public lectures, podcasts, and radio and television appearances.
“The Joy of Why Podcast.” 2024. Quanta Magazine. Accessed July 31. https://www.quantamagazine.org/tag/the-joy-of-why/.
The mathematician and author Steven Strogatz and the astrophysicist and author Janna Levin interview leading researchers about the great scientific and mathematical questions of our time.
Terence Tao
Born in Adelaide, Australia, Terence Tao (born 17 July) is sometimes called the “Mozart of mathematics”. When he was 13, he became the youngest ever winner of the International Mathematical Olympiad, and when he was 24, he became the youngest tenured professor at the University of California, Los Angeles.
Tao has received the MacArthur Fellowship, the Breakthrough Prize in mathematics, as well as the Fields Medal, the highest award in mathematics, for “his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory”.
Together with Ben Green, Tao proved the Green-Tao theorem, which states that there are arbitrarily long arithmetic sequences of prime numbers.
“Terence Tao – Timeline of Mathematics.” 2024. Mathigon. Accessed July 31. https://mathigon.org/timeline/tao.
Srinivasa, Raghava K. “Harmony In Numbers: The Life, Work, And Legacy Of Mathematician Terence Tao.”. 2023. Medium. https://medium.com/the-modern-scientist/harmony-in-numbers-the-life-work-and-legacy-of-mathematician-terence-tao-4cd5e46e7b7d.
Terence Tao is a mathematical maestro who creates beautiful symphonies of ideas. In fields as diverse as harmonic analysis, combinatorics, and partial differential equations, his precocious intelligence has left an indelible mark. Tao, a brilliant polymath and Fields Medal winner, has left an imprint on fields as diverse as physics, engineering, and encryption. His contribution to modern mathematics and the lives of future mathematicians is immeasurable because of his willingness to work with others and his enthusiasm for the classroom.
“Terence Tao.” 2024. Wikipedia. Wikimedia Foundation. July 22. https://en.wikipedia.org/wiki/Terence_Tao.
Terence Chi-Shen Tao is an Australian and American mathematician who is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins Chair in the College of Letters and Sciences. His research includes topics in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing and analytic number theory.
“Terence Tao – Biography.” 2024. Maths History. Accessed July 31. https://mathshistory.st-andrews.ac.uk/Biographies/Tao/.
Gladys West
Gladys Mae West (née Brown; born October 27, 1930) is an American mathematician. She is known for her contributions to mathematical modeling of the shape of the Earth, and her work on the development of satellite geodesy models, that were later incorporated into the Global Positioning System (GPS). West was inducted into the United States Air Force Hall of Fame in 2018. West was awarded the Webby Lifetime Achievement Award for the development of satellite geodesy models.
“Gladys West.” 2024. Wikipedia. Wikimedia Foundation. June 14. https://en.wikipedia.org/wiki/Gladys_West.
“Gladys West: The Hidden Figure Who Helped Invent GPS.” 2020. The Guardian. Guardian News and Media. November 19. https://www.theguardian.com/society/2020/nov/19/gladys-west-the-hidden-figure-who-helped-invent-gps.
Growing up on a farm in Virginia during segregation, West knew education would be her means of escape. But she didn’t know her quiet work on a naval base would change lives around the world.
“Gladys West and the Invention of GPS: Hidden Heroes.” 2024. Gladys West and the Invention of GPS | Hidden Heroes. Accessed July 31. https://hiddenheroes.netguru.com/gladys-west.
All of this would be relatively easy to calculate if Earth itself happened to be a perfect sphere. But while it looks to the naked eye from space like an exact circle of Euclidean perfection, in reality our planet bulges out slightly at the equator, while the poles are flatter than they would be in a true sphere. And Earth’s gravitational fields are also distorted by many of its distinguishing features: tides, mountain ranges, and ocean trenches. To make GPS work, you didn’t just need satellites and atomic clocks. You also needed to know the true shape of Earth’s gravity. And that is what Gladys West figured out.
Jones, Willie D. 2024. “Gladys West: The Hidden Figure Behind GPS.” IEEE Spectrum. IEEE Spectrum. July 30. https://spectrum.ieee.org/gladys-west-hidden-figure-gps.
While working for four decades as a mathematician and computer programmer at the U.S. Naval Proving Ground (now the Naval Surface Warfare Center) in Dahlgren, Va., she prepared the way for a satellite constellation in the sky that became an indispensable part of modern life: the Global Positioning System, or GPS.
Mathematical Mysteries 