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MF88: The decline of rigour in modern mathematics

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Xuất bản 18/08/2015
Rigour means logical validity or accuracy. In this lecture we look at this concept in some detail, describe the important role of Euclid's Elements, talk about proof, and examine a useful diagram suggesting the hierarchy of mathematics. We give some explanation for why rigour has declined during the 20th century (there are other reasons too, that we will discuss later in this course). Critical in this picture is the existence of key problematic topics at the high school / beginning undergrad level, which form a major obstacle to the logical consistent development of mathematics. We list some of these topics explicitly, and they will play a major role in subsequent videos in this series. This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics. The full playlist is at http://www.youtube.com/playlist?list=PL5A714C94D40392AB&feature=view_all
elementary geometry Mathematics problems proof Set theory limits circular infinite foundations Wildberger rigour Euclid Elements Weiesrtrass Cantor Cauchy Dedekind pure sets integrals Euclidean transcendental exponential inverse