National History Day 2016: Math, Physics, and Technology Topic Ideas

The theme for 2016 NHD is Exploration, Encounter, and Exchange History.

History of science topics tend to be underrepresented in NHD, so here are some math, physics, and technology topic suggestions for this year's theme! This year's theme is particularly good for scientific topics because so much of science is about exploration. The theme book encourages pulling in elements of all three parts of the theme, but it's not required, and it's natural for a project to focus much more on one than the others. This post might be updated occasionally throughout the fall!


Math and Statistics
--Paul Erdős and collaboration in mathematics. Erdős was hugely influential in combinatorics and graph theory in general but particularly in a few subareas like Ramsey theory and extremal combinatorics. More importantly, though, Erdős helped build collaborative networks in mathematics. He worked with many different people, connected people with each other, and connected people with problems that he thought they could solve. Read The Man Who Loved Only Numbers and watch N is a Number.
--Newton, Leibniz, and calculus. Newton and Leibniz independently developed calculus and then famously argued over it. This actually had consequences for the communication of mathematics between Britain and the continent for the next century, really negatively impacting British mathematics.
--G.H. Hardy and Ramanujan. Both men were incredible number theorists, and Ramanujan could see connections among numbers better than anyone else. Hardy discovered Ramanujan through letters and then invited him to come work in England. Read The Man Who Knew Infinity.
--Janos Bolyai and non-Euclidean geometry. Bolyai wasn't the first mathematician to explore what happened when we break Euclid's fifth postulate (about parallel lines), but his work was more complete than what had been done previously, and he did it independently. He wrote about this work in a letter to his father and said, "Out of nothing I have created a strange new universe." (Something from that quote would make a great project title!)
--Leonhard Euler. I could put a specific field, but Euler shaped a lot of how we talk about and write mathematics today as well as being extremely prolific in a variety of fields. There are so many possibilities here. Look at the biography Euler, Master of Us All.
--Augustin-Louis Cauchy and complex analysis. A lot of mathematicians believe complex analysis is the most beautiful subfield of mathematics, and Cauchy pretty much developed it all on his own. (Half the theorems in an intro complex analysis course are named after Cauchy.)

Physics and Technology
--The development of the theory of special relativity. Start with the Michelson-Morley experiment and move forward. This is an extremely well-tested theory, and the Michelson-Morley experiment which started hinting towards it was intended to detect aether...and failed.
--Quantum mechanics. There are a lot of possibilities here, and the whole story is really interesting, but especially in thinking about exchange the Bohr-Einstein debates would be a cool topic.
--The Einstein-Szilard letter and the Manhattan Project. Hungarian physicists and Einstein warned the US government that Germany might develop atomic bombs. The result was the Manhattan project.
--The space race. Some of the exchange is more a lack thereof, but this is definitely exploration.