Math is a star in the movie Hidden Figures

Hidden Figures is a 2016 biographical drama based on a book of the same name. The movie celebrates the work of three mathematicians/engineers/computer programmers whose work helped propel America into space and win the space race against the Soviet Union. It garnered positive reviews from critics and has been nominated for numerous awards.

Scientists and mathematicians are not hard to find in a place like NASA, currently as well as in the time period in which the story took place (1950s and 1960s). What set these three individuals apart is that they were female and African Americans. They are Katherine Goble Johnson (played by Taraji P. Henson), Dorothy Vaughan (played by Octavia Spencer) and Mary Jackson (played by Janelle Monáe). Thus this movie touches several dimensions – race, gender, history of the space race, and of course the gripping human stories of these three individuals as they struggled to excel in an endeavor they were not expected to excel in.

Math is not just the backdrop of the story; it is front and center in the movie. Of course, the movie does not delve into the details of the math (if it did, it would not gross $129 million worldwide). But the movie is a story of the triumph of math. The math equations worked out by the central characters helped make the space flights safe and successful. There is another sense that it is a story pf the triumph of math.

According to this piece from The Atlantic, math at one point in time was the province only for those who were white and male. Johnson, Vaughan and Jackson and other human computers (later turned mathematicians and engineers) at NASA were allowed to play a pivotal role in the space program because of their math prowess. In fact, due to the societal stereotypes and racial biases of the time, they would normally not even be hired in the first place.

Katherine Goble Johnson was a child prodigy and for a while her talent was underutilized. Then her moment came when NASA needed someone who had skills in geometry and could apply the skills in the calculation for flight trajectories in the Mercury program. The stake was obviously high. NASA was under tremendous pressure to catch up with the Russian. Wrong or inaccurate calculation could mean loss of life and national disgrace. This tension is best dramatized in a scene in which John Glenn wanted to have the numbers checked by the girl (i.e. Johnson). As Glenn was about to be sent off for his orbital mission in 1962, Glenn insisted on having Johnson run through the equations to make sure the trajectory was safe.

Here is a post that focuses on the mathematical achievements of Johnson.

So math is an equalizer. These mathematicians and engineers had a seat at the table because of math. This is an all around wonderful story. This article from Scientific American gives more information on the mathematical and programming work of Johnson, Vaughan and Jackson. This is a piece from NASA on human computers.

Math is as much of an equalizer now as then. I hope the movie inspires youngsters to pay more attention to math and science. Math makes space travel possible. Anyone can learn and excel in math. A whole new realm of possibilities is awaiting for the next generation to explore and unlock.

Due to the popular movie, the story of Johnson, Vaughan and Jackson is now well known. A lot of results come up from Googling their names and the movie. Here’s one piece from Forbes. Here’s the Wikepedia entry about the movie. Here’s two articles (here and here) from npr.org.

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A fascinating read about Terry Tao

I just came across an article in New York Times about the famous mathematician Terry Tao, who, a one-time math prodigy turned Fields medalist, is a prolific researcher working in diverse areas of mathematics. The title of the article is “The Singular Mind of Terry Tao”. Here is the article.

With Terry Tao being a one of the greatest minds in 21st century mathematics, I know this would be an interesting read. Indeed, it gives a vivid picture of the world of Terry Tao – a prolific mathematician producing important work, a former child prodigy, a husband, father and so on.

It turns out that it is also a gentle introduction of various math concepts. For example, the article has a great short introduction of prime numbers that gives readers a sense that prime numbers are a simple construct that arises out of a concept of numbers and the four arithmetic operations (addition, subtraction, multiplication, and division). Knowing these basic number concepts is all you need to spot the prime numbers. Thus prime numbers are elemental objects in mathematics. It goes on to say that any alien species in other parts of the universe is probably very different from us but “we can be almost certain that their mathematicians have discovered the primes and puzzled over them”. It also points out that “scientists have uncovered deep connections between primes and quantum mechanics that remain unexplained”.

The short intro to prime numbers is to lead the readers to the discussion of the Green-Tao Theorem, which led to the award of the Fields medal for Terry Tao.

Another interesting thing about the article is that it gives the readers a sense of what it means to do mathematics. It is not a static pursuit of solving algebra problems from stale old math books. In fact, “The ancient art of mathematics, Tao has discovered, does not reward speed so much as patience, cunning and, perhaps most surprising of all, the sort of gift for collaboration and improvisation that characterizes the best jazz musicians”. Mathematical research is a fundamentally creative act. It is a very difficult pursuit. It is akin to a struggle with the devil (as the article playfully suggests). Mathematics research is a long game. Doing math research requires courage; it may take weeks, months and years if success comes at all.

Another interesting tidbit of information is the letter of recommendation written by Paul Erdos, the revered Hungarian mathematician, in supporting Terry Tao’s application to Princeton.

    “I am sure he will develop into a first-rate mathematician and perhaps into a really great one,’’ read Erdos’ brief, typewritten note. ‘‘I recommend him in the highest possible terms.”

Based on what we know of Tao, Erdos’ prediction is spot on. The full article is here.

Cheering for Yitang Zhang

If you Google the name of “Yitang Zhang” recently, you will find many entries with keywords such as “twin primes”, “twin prime conjecture”, “bounded gaps between primes”, along with “University of New Hampshire”. Here’s three of the entries: UNH professor solves ancient mathematics riddle; UNH lecturer stuns the math world; The Beauty of Bounded Gaps. Here’s a piece from New York Times: Solving a Riddle of Primes. The reason for all this attention from the mainstream media that normally don’t pay attention to math? Mr. Zhang made a huge breakthrough toward solving an ancient problem about prime numbers. This is a brief account of his achievement.

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A prime number is an integer greater than 1 that has no divisor other than 1 and the number itself. For example, 3 is a prime number because 1 and 3 are the only positive integers that evenly divide 3. However 6 is not a prime number since 3 evenly divides 6 in addition to 1 and 6. The first several prime numbers are: 2, 3, 5, 7, 11, 13, …

A pair of prime numbers are twin primes if they differ by 2, for examples, 3 and 5, 5 and 7, 11 and 13, 17 and 19 and so on.

The Greek mathematician Euclid gave the oldest known proof that there are infinitely many prime numbers around 300 BC. Euclid also conjectured that there are infinitely many pairs of twin primes.

The statement that there are infinitely many pairs of twin primes is called the Twin Prime Conjecture. Note that the Twin Prime Conjecture is saying that there are infinitely many pairs of primes such that the gap within each pair is exactly 2. Many great mathematical minds since ancient time had been trying to prove this conjecture but to no avail. But there were incremental progress throughout the twentieth century and in the first decade of the new century.

Mr. Yitang Zhang did not prove the Twin Prime Conjecture. He proved that there are infinitely many pairs of prime numbers such that the gap within each pair is bounded is at most 70,000,000 (70 millions). In other words, Mr. Yitang Zhang proved the Bounded Gaps Conjecture.

The gap of 70 million seems like a large number and may not seem all that significant to non-mathematicians. Now that there is now a proof that the gaps between pairs of primes do not have to increase without bound (as some mathematicians had suspected), mathematicians can work on narrowing the gaps (may be even reducing the gaps down to 2).

Indeed, since the announcement of Mr. Yitang Zhang’s result in May, some mathematicians had narrowed the gaps down to mere millions (in one case down to hundreds of thousands)!

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His achievement is even more impressive considering the background of Mr. Yitang Zhang. Mr. Zhang did earn a PhD in mathematics in 1991 from Purdue University. In the tough academic job market after graduation, he could not find any academic position. He worked as an accountant for a period. He even made sandwiches at a Subway shop at one point. He is currently a part-time math lecturer at the University of New Hampshire, a nice school for sure, but far from the elite club of mathematicians working at places like Harvard, Princeton and Stanford.

Some people have this notion that monumental math problems such as the Twin Prime Conjecture are the domain of young math whiz. Mr. Zhang is over the age of 50.

Another handicap for Mr. Zhang is that he is not in the math specialty of number theory, which would be the specialty of the mathematicians who work on problems like Twin Prime Conjecture.

The last academic publication of Mr. Yitang Zhang is from the year 2001. So he is considered an inactive researcher by many in the math community.

Given his background, no one in the math community expects great results from Mr. Yitang Zhang. Apparently he was oblivious of his supposedly “handicaps”. He certainly did not make any excuses for himself. He just kept plugging away, building upon the advances made by other mathematicians.

The story of Yitang Zhang is remarkable in two fronts. One is his mathematical work. The other is the human dimension of the story, which makes his achievement all the more remarkable. Mr. Yitang Zhang is an inspiration to us all.

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More information about Yitang Zhang can be found on the Internet. Here’s a few more entries from an Internet search.