jueves, 28 de septiembre de 2023

 Amalie Emmy Noether: 

Written by: Duy Phuong Nguyen Truong 




Brief history: 

Amalie Emmy Noether was a German mathematician, born on the 23rd of March 1882 to the 14th of April 1935 into a Jewish family of 4 children including her. Her father, Max Noether was also a mathematician who worked at the University of Erlangen. 


At a young age, she showed interest in becoming a teacher of French and English but ended up studying maths at the University where her father worked. From 1903 to 1904, she studied at the University of Göttingen, where she attended lectures given by famous astronomers and mathematicians like Karl Schwarzschild, Hermann Minkowski, Otto Blumenthal, Felix Klein, and David Hilbert. Unfortunately, the University of Göttingen limited the women’s participation so she returned to Erlangen. 


She then returned to the University in October of 1904 where she decided to focus on the study of mathematics under the supervision of Paul Gordan. Eventually, between 1908 to 1915, she decided to teach at the same University she studied, she taught at the Mathematical Institute of the University of Erlangen for 7 years without pay. At this time, women’s talent and work were underestimated and not well recognised.  

In 1915, Noether was invited by David Hilbert, who was a very famous mathematician during this time for his contributions to maths, and Felix Klein to the University of Göttingen. Although their efforts were stopped by philologists and historians at the University. However, the idea of not allowing women to come to the University was protested, Hilbert believed that men or women didn’t matter since it is a place of education 

Not long after Noether had arrived at the University, she demonstrated her talent at the University of Göttingen by proving her own theory, which is now known as Noether’s Theorem. This theory helped to change the view of the principle ideas in physics forever. 

On the 14th of April in 1935, Noether fell unconscious with a fever of 42.8 degrees Celsius and passed away after a pelvis surgery to remove a tumor. She was one of the most unrecognised mathematicians just because of her gender, but to those who know her, like David Hilbert, Albert Einstein, and others, she will remain to be a genius among them. 


Noether’s Theorem: 

In order to know why theorem is so important, first we need to understand what Noether’s Theorem really is.  

Noether’s Theorem is a theorem that connects mathematical symmetry to the Law of Conservations in physics. For example, the Law of Conservation of Energy: Energy cannot be created or destroyed, it can only be transferred. If you drop a ball from a certain height, its Gravitational Potential Energy will be transferred into Kinetic energy causing it to move faster, the closer it is to the ground. In mathematics, symmetry means that the property of a mathematical object will remain unchanged under a set of transformations applied to it.  

Going back to the example of the Conservation of Energy, if you have a timer with 20 seconds and you drop the ball, it takes 2 seconds to drop to the ground and you have the same timer this time it is set to 0 seconds, and you again drop the ball at the same height. This would also take 2 seconds to reach the ground. In conclusion, no matter when you drop the ball, it would reach the ground at the same time and this time transformation leads to the same result of 2 seconds to reach the ground, implying that energy is conserved. In a sense that gravity is always acting on an object, and its gravity always warping the fabric of spacetime. No matter when you drop something or what time you drop it, gravity always remains constant, meaning the time it takes to reach the ground is the same and the same amount of energy is used. 

Her theorem provides a concrete link to the Conservation Laws in physics and mathematics of symmetry. It also shows where the Conservation Laws are coming from and how we can prove that the Laws are correct as well as how they are derived. 

  Amalie Emmy Noether :   Written by: Duy Phuong Nguyen Truong         Brief history:   Amalie Emmy Noether was a German mathematician, bo...