The Importance of Numbers and the Need to Study Primes: The Prime Questions

Abstract

Problem Statement: The study of prime numbers is important today as it was in ancient times. The level of interest in any form of mathematics of students in Australian high schools is decreasing and furthermore the level of interest in number theory is also less that it was before; prime numbers is not being considered as an area of interest by our younger stars. This paper explores prime numbers and attempts to show some interesting aspects in the study of primes that highlight why number theory studies can be considered important for today's up and coming mathematicians. Approach: The historical review of mathematics and analysis of simpler but accessible proofs can help show clearly the motivations behind the mathematicians work. In depth analysis work may be used to reveal parts passion, politics and dedication played in the study of numbers and construction of equations. The analysis of proofs is also used to provide a further background of prime numbers and why the pursuit of primes. Results: The analysis shows there are a number of motivating factors that may promote real interest in number theory; such as human dramas behind the "prime" mathematics. The paper shows politics and passion also exist behind numbers. If explicated well, this may help drive more interest in research by younger mathematicians by making mathematics human activity. In number theory there are a number of unanswered questions that often attract large sums of money. There are a number of proofs in primes and these are made accessible to the younger researchers so that they appreciate the nature of the problems faced by the history's intellectual minds in their efforts to solve some of the unanswered questions; and those they began to solve. The analysis based on historical works of mathematicians as well as the modern studies reveal surprising "real life" applications for prime number theory. Conclusion: Mathematics can often be thought as only for the enjoyment of pure thought but the study of prime numbers has discovered to have some real life applications. This paper shows that pure study of abstract ideas, importance of numbers, history, politics and real life applications are all important aspects of the study of prime numbers. If these aspects are highlighted, a more realistic picture of the pure mathematics of prime numbers may be presented in classrooms to the younger up and coming mathematicians of today to help promote interest to pursue research work on prime numbers. Allowing for different points of view to the study of mathematics should be well regarded in classrooms that my in itself lead to better understanding of the very building blocks of our numbers system.