The Consequences of the Riemann Hypothesis
Dhanial Mohammed
Physics
1st
Year of study:
Abstract
Here’s a question; what do infinite sums, complex numbers and the distribution of prime numbers all have in common? While it’s not immediately obvious to most people, a German mathematician called Bernhard Riemann was able to put the pieces together, and in doing so prompted a problem that has remained unsolved to this day.
The problem in question is called the Riemann Hypothesis and it involves determining the nature of the Riemann-zeta function in the complex plane, particularly the values where it equals zero. The truth or fallacy of the hypothesis can have exciting (or devastating) consequences across all fields of mathematics, like the distribution of prime numbers.
The aim of my research is to investigate how the results from the problem can influence other aspects of mathematics and science in ways that most people wouldn’t expect.
I aim to find my results through study of academic papers and articles, mathematical journals and through contact with experts in the field. I will also try to take note of my own observations.
Through my research, I was able to find some interesting and unexpected consequences of the Riemann Hypothesis, such as its connection to the Bose-Einstein condensate, an exotic state of matter that can only exist under specific conditions at low temperatures. It can also play a role in describing certain chaotic classical systems.
This investigation will hopefully help to shed light on how seemingly abstract fields of mathematics like number theory can have real world implications that can impact scientific research and technological development, notably in areas such as cryptography and complex quantum systems.
Bio
My name is Dhanial Mohammed, I grew up the Shetland Islands and I am currently in the first year of my Physics degree. As it is my first year, I have yet to get the opportunities to partake in real world research as of yet, but I will jump at any opportunity do so. From a young age I developed a fascination for physics, particularly cosmology and particle physics. In high school, I started to gain an appreciation for certain areas of mathematics, specifically calculus and number theory. As a result I competed in the UKMT Team Maths Challenge and the Individual Challenge. My interest in mathematics is what lead me to find out about the Riemann Hypothesis. This topic is not exactly something I can just do my own original research on (mainly because I’m not a super-genius celebrity mathematician yet), but I can gain knowledge and insight from publications and real experts in the field and present my findings in a form that appeals to the multidisciplinary audience. I believe presenting my research in this way helps to inform people on the purpose of studying mathematics, even if it’s not completely clear what the point of it all is.