6 Conclusion Sometimes things that seem very disjointed come together to morph into something beautiful. The monstrous moonshine conjecture is one of those things. Bringing together number theory and algebra, and concepts from math and concepts from physics, moonshine gives us the start of a unified theory of how these things fit together. The monstrous moonshine conjecture really starts with the Monster. This huge simple group caught the interest of many in the past half century. Due to efforts to study and understand the Monster, the connection between it and modular functions was found. In every area of study, you need people who are not content with just noticing interesting facts. You need people who are willing to ask “why”, and then put in the work to find the answer. In the area of monstrous moonshine, those people were Conway, Norton, Frenkel, Lepowsky, Meurman, Thompson, McKay and Borcherds, among others. Because of their dedication to finding out why the coefficients of the J-function and the dimensions of the irreducible representations of the Monster are so closely connected, we have this beautiful theory that brings together people and ideas from so many different areas. Far from being the last topic to be explored in this area, moonshine has opened our eyes to how many connections have yet to be discovered. There are many other related theories to moonshine. Subquotients of the Monster have their own moonshine theories. The umbral moonshine correspondence was connected to the Mathieu sporadic group M24. There are questions of correspondences between sporadic groups and some Lie algebras [11]. It will be exciting to see where these theories go heading forward. Connections between group theory and physics could lead to all sorts of new theories. Although moonshine has radically impacted algebra, it has had a far less intense impact on number theory [7]. Perhaps this connection will be explored more from the number theory perspective in the years to come. In conclusion, moonshine connected fields that seemed too different. It explained “coincidences” in a beautiful way. In the future, hopefully the moonshine conjecture will serve as an encouragement to mathematicians and scientists working on obscure or supposedly unexplainable theories. What today may seem like a crazy idea may tomorrow be a huge breakthrough in multiple areas of mathematics. Channels • 2022 • Volume 6 • Number 2 Page 49
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