Remembering Katherine G. Johnson : Mother, Mathematician, and a Pioneer for Space Exploration

Many people spend decades writing about an important figure, who has impacted not the life of a single person but an entire race. Writing about this important of a person is really tiresome and it takes sometime to process the fact that one has been endowed with this amazing opportunity. 

 

 For me, It all began with a simple google search of Katherine Johnson's name. 

Portrait of Katherine Johnson via. NASA 

I like to view this as a simple google search that changed the way I perceived the world of Mathematics. An African-American lady who was rejected the first time she applied to NACA ( National Advisory Committee for Aeronautics, which was later changed to NASA ) changed the way I view Mathematics.  

 
Katherine Johnson was simply put an extraordinaire. She was an amazing Mathematician who helped NASA lay it's foundations for Space Travel and also is an inspiration to many and one of the very few awardee of Presidential Medal of Freedom ( Highest honor to any civilian service).  

Born amidst WWI on August 26, 1918 Katherine was the youngest of the four children born to a farmer and a teacher. Katherine as she states loved counting. She used to count the number of steps to church, number of steps of dishes and silverware she washed and so on. Katherine was a child prodigy who was just felt closer to Mathematics than anything other in the world. After graduating from high school at the age of 14, she got enrolled into West Virginia State and graduated with a degree in Mathematics. Whilst being enrolled into West Virginia University,  where she was the first African-American to attend the university for graduate program she dropped out after being pregnant and chose her family. 
 
It was after several years that she was introduced to a job that met her brilliance, A computer. *Before the modern computing era the term "Computer" was referred to a person who was responsible to do several precise calculations of the given set of data on a given day.* When she first applied to NACA for a job as a computer she was rejected but later she found herself working with various other African-American women and computing various data to help NASA conduct its tests. In 1957, the soviet union launched "SPUTNIK", which was a major blow in the face of the organization which aimed to revolutionize space and the leader of the free world but little did the people know that that incident would change the course of action of then NASA, and Katherine Johnson.  
 
Whilst working as a computer Katherine was reassigned to Guidance and Control Division of Langley's Flight Research Division. With the segregation laws still intact in the NASA she worked her brilliant mind to find the accurate trajectory of launch, flight and landing by using Euler's method to solve differential equation involving the position and velocity. She hand calculated 50,000 equations precisely to calculate the trajectory of the APOLLO-11 flight which she says is her greatest accomplishment. 

In the above texts I have taken you through the life of Katherine Johnson and how she brilliant of a mathematician she was. There is one particular thing that I would like all of you to get out of this article, "The Euler's method" 

The Euler's Method 

 

I think of differential equation as a large cloud of entangled ideas that binds all the mysteries in the world. There are a lot of ways you can find a solution to these equations but there is a reason that many engineers and physicists choose Euler's method for solving them. While by using calculus method to solving differential equation we can find the formula for the curve of the equation it is not always valid! So, We use Euler's method to estimate/approximate path of  the curve to any degree of accuracy (i.e. the instance or the interval for which Euler's method is used for approximation). 

Consider the differential Equation : 

 

dydx=f(x,y),  y(xo)=yo {This is always given.} Here, we have to find y(xn)=yn

 

 

According to Euler's method : 

yn=y(xn)=yn−1+hf(xn−1, yn−1) , where h=xn−xn−1 

 

 

This means that if, 

n=1,      y1=y(x1)=yo+hf(xo, yo)

 

n=2,      y2=y(x2)=y1+hf(x1, y1)

 

and so on. 

 

For a single iteration to be completed (say n=2). We will have to find the value of y1

What Katherine Johnson has done for the scientific community is truly un-parallel and I hope that you guys will get inspired reading this article and  abide by her rules "Like what you do, and then you will do great" :) 
 
- Karun Dhakal