A new study of an ancient Babylonian clay tablet claims to have evidence of the use of calculus techniques. These tablets date back to 350-50 BCE. The same techniques were thought to have shown up for the first time during the 14th century in Europe. There is a link to the article in Science here. Apparently the Babylonians had a graph of the relative velocity of Jupiter over time and used the trapezoid method to measure the area under their curve and then related this area to the relative distance traveled by the planet.
Emmy Noether is one of our most influential modern mathematicians. She lived from 1882-1935. Her main contributions are in a field of algebra called ring theory.
The beginning of her professional career was in Göttingen, Germany where she was not allowed to become a professor, in spite of her recognized groundbreaking work, because she was a woman. She left Germany in 1933 to get away from the Nazi government. The United States was privileged to be her new home as she accepted a position at Bryn Mawr College in Pennsylvania.
So check out: Noether’s theorem, Skolem-Noether theorem, or Noetherian ring to find out more about her work. Also, check out Emmy Noether : the mother of modern algebra from our library to learn more about her life and work.
There is still a lot we don’t know about prime numbers. For instance: are there an infinite number of prime pairs? Examples of prime pairs are (3,5), (11,13), and so on. In 2013 University of New Hampshire lecturer, Yitang Zhang, submitted an article to the Annals of Mathematics. This article established a finite bound on prime gaps. Of course that bound was 70,000,000, but using Zhang’s technique other mathematicians have decreased this number. Zhang was immediately offered a professorship at the University of New Hampshire and a MacArthur award. The conjecture that this number should be 2 was made by Euclid (300 BC), so this is a very old problem. Maybe we will have a proof of this in our lifetime.
The discovery was made by Casey Mann, Jennifer McLoud and David Von Derau.
The illustrations above were taken from The Guardian article by Alex Bellos, which were taken from Wikipedia and Casey Mann.
In finding a shape that tiles the plane the goal is to find a single shape that when repeated (using any 2 dimensional orientation) the “tiling” can cover the whole plane without leaving any gaps. It has been show that all triangles and four sided shapes can. It is not known how many pentagons can tile the plane. In particular the regular pentagon cannot. There is no way to lay regular pentagon shaped tiles down, and not leave gaps.
This new result gives us the 15th pentagon known to tile the plane.