Greek Pure Mathematics and the "Infinitude of Primes" | Sociology and Pure Maths | N J Wildberger скачать в хорошем качестве

Greek Pure Mathematics and the "Infinitude of Primes" | Sociology and Pure Maths | N J Wildberger

To understand the sociology of pure mathematics, we need to appreciate the long historical span of the subject, going back at least to ancient Greek times. Euclid's monumental work The Elements set the standard for pure mathematics research and education for more than 2000 years. Mathematicians thus naturally have a lot more reverence for tradition than other scientists, such as chemists, physicists or biologist, who are relatively speaking newcomers to the scene! To appreciate both the way the ancient Greeks thought, and some of the important differences between them and us, we look at Euclid's famous proof of the "Infinitude of Primes". Actually Euclid does not use that language, and it is instructive to see what he actually does. By looking at the argument very carefully, we see that there are actually serious problems with the modern claim that "there are an infinite number of primes". The real truth is in the opposite direction, which we can see more clearly by adopting a more computational frame of mind. This should be a topic of great interest and discussion for mathematics undergraduates and graduate students. Some healthy skepticism regarding the claims of modern pure mathematics is entirely in order! Also a small clarification: Euclid's statement "take the least number measured by A,B and C" literally should be understood as referring to the least common multiple of A,B,C. But if we are assuming A,B,C are (distinct) primes, then this least common multiple is just their product. Video Content: 00:00 Introduction 1:12 Mathematics / astronomy / surveying 3:09 Euclid's Elements 6:34 Prime numbers 10:19 Euclid IX Proposition 20 25:44 Some big primes *********************** My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/... My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things. Online courses are being developed at openlearning.com. The first one, already underway, is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at   / njwildberger   Your support would be much appreciated. Here are the Insights into Mathematics Playlists:    • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист   Here are the Wild Egg Maths Playlists (some available only to Members!)    • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист   ************************