Hidden Figures is a new movie that’s coming out next year, telling the story of some pretty awesome mathematicians and physicists! With the popular Turing film The Imitation Game in 2014, and the independent Ramanujan film The Man Who Knew Infinity in 2015, it seems like films about mathematicians continue to spark people’s interest.
Stand and Deliver (1988) might be one of the first popular math movies that was not purely educational. Since then, Hollywood has given us Academy Award winners Good Will Hunting (1997) and A Beautiful Mind (2001), and several others such as 21 (2008). But while the other movies may have been great, in terms of cinematography, what Stand and Deliver did for math more than all of the others was bring the mathematician down to earth — show the public a glimpse of the mind and life of a math teacher and his students, and plant the idea that math was for more than just “unapproachable geniuses”. The films following Stand and Deliver tended to be portraits of these geniuses, who while being important to mathematics, but exasperated the stereotype of the otherworldly mathematician. This is why I am excited about Hidden Figures. The trailer seems to also to showcase mathematicians as people, not gods.
The protagonist of the film is Katherine Johnson, who worked at NASA and computed trajectories for the Apollo 11 space mission. In 2015 she received the Presidential Medal of Honor for her lifetime achievements. The film was originally a book of the same title, written by Margot Lee Shetterly. This article in the NY Times gives a nice summary of the topic, along with comments from Johnson, Christine Darden (another NASA researcher, portrayed in the book), and Shetterly.
Recently, the card game Set has been a trending topic in math circles. A breakthrough came on the topic of finding an upper bound on the number of cards one could lay down without any players finding a set. The problem is a sort of combinatorial problem (it falls under the umbrella of Ramsey theory), but was translated to the language of group theory and algebraic geometry where the authors used the “polynomial method” to get much, much better bounds than ever before, and a very, very short number of pages. See these papers for more information on the math. According to the first linked article, the popularized proof technique has already been used to solve other “cap set” problems, which tend to have applications in fields like computer science and information theory.
The reason I’m interested in the news is that I didn’t realize how many applications the “mathematics of Set” had — both inside and outside of mathematics. I have spent time playing it as a logic game with many students for simply that, that it practices “logical reasoning” which is the foundation on which mathematics is built. To learn that all along, I had been playing a game with these deep connections — and that I could have been telling the students about them! — I felt both excitement and regret.
As mathematicians we get excited about the chase of new ideas, new puzzles, new theoretical structures to explore. But there’s something really special about being able to communicate this excitement to the “layperson” in the terms that they’re already familiar with, like card games. It’s a real struggle in the field of operator algebras to find such connections, since there’s such an enormous amount of structure just built up to define the questions we want to tackle. Often times the connections I do know of seem superficial, in the sense that the applications don’t often drive the problems I’m interested in or the hypotheses I impose. Even so, and even while some of the “technical speak” might be out of grasp for Average Alex, I believe that with enough thought and perseverance I can find ways to phrase the math I do in ways that are intuitive and relate-able. Maybe not ways to get across the finer points, or give those easily-digestible-but-unrealistic-“real-world” applications. What I want is something like Set is to Ramsey theory — a way that will get at the heart of the matter.
Check out this article in the New York Times!
Dr. Mathieu Ossendrijver from Humbolt University translated cuneiform tablets dating around 350-50 B.C., describing how Babylonian astronomers calculated the distance that the planet Jupiter traveled across the sky. They did this by recording its velocity at specific times, and then approximating the area under this graph — i.e. approximating the definite integral.
Photo credit: Mathieu Ossendrijver/British Museum, via the New York Times.
If you haven’t taken calculus yet, the process is still understandable. We know that distance traveled = speed x time; for example, if you travel at 60 miles/hr for 2 hours, you have traveled 120 miles. This works if you keep your speed roughly the same. On the other hand, if your speed keeps changing, you could instead calculate this on small time intervals, and then add them all up to get the total distance traveled. That is what the Babylonians did.
We’ve known many ancient cultures — China, Greece, etc. — used versions of what we now call the definite integral to calculate areas of shapes. However, this is the earliest documented instance of where the “shape” was a velocity curve (a much more abstract object than say, a circle). Previously, the earliest instance of this we knew of was in England in the 1300s.
If your library has access to the journal Science, you can find more details in:
Ossyndrijver, Matthieu. “Ancient Babylonian astronomers calculated Jupiter’s position from the area under a time-velocity graph.” Science. Vol. 351, Issue 6272, pp. 482-484.