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MF88: The decline of rigour in modern mathematics
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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.
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