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Logical Weaknesses in Modern Pure Mathematics - Real Numbers and Limits - Math Foundations 87

Offered By: Insights into Mathematics via YouTube

Tags

Mathematics Courses Number Theory Courses Logic Courses Mathematical Analysis Courses Applied Mathematics Courses Pure Mathematics Courses

Course Description

Overview

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Examine the logical weaknesses in modern pure mathematics through this 27-minute video lecture from the MathFoundations series. Explore five key problems affecting the field, including inconsistent rigor, problematic definitions, and reliance on axioms. Distinguish between problematic and non-problematic areas in mathematics, and compare applied and pure mathematics approaches. Analyze concepts that are clearly defined versus those that are not, and consider three consequences of these logical weaknesses. Conclude by reviewing four aims for addressing these issues in subsequent videos, inviting further discussion on these contentious yet crucial topics for the foundations of mathematics.

Syllabus

Intro to why modern pure maths doesn't work
5 Key problems
Problematic & Non-problematic areas
Applied and Pure Mathematics
Inconsistent rigour
Concepts defined clearly
Concepts not defined clearly
3 Consequences of logical weaknesses
4 Aims


Taught by

Insights into Mathematics

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