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 jeremykun.wordpress.com
Constructing Topological Spaces - A Primer - Math Programming
| | grossack.site
Life in Johnstone's Topological Topos 1 -- Fundamentals | Chris Grossack's Blog
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| | Chris Grossack's math blog and professional website.
| | siddhartha-gadgil.github.io
Formalizing Gardam's disproof of Kaplansky's Unit Conjecture ยท Artificial Intelligence and Mathematics
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| | [AI summary] The author details the process of using the Lean 4 programming language to formally verify Giles Gardam's disproof of the Kaplansky Unit Conjecture in mathematics.
| | www.jeremykun.com
Constructing Topological Spaces - A Primer | Math Programming
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| | Last time we investigated the (very unintuitive) concept of a topological space as a set of "points" endowed with a description of which subsets are open. Now in order to actually arrive at a discussion of interesting and useful topological spaces, we need to be able to take simple topological spaces and build them up into more complex ones. This will take the form of subspaces and quotients, and through these we will make rigorous the notion of "gluing" and "building" spaces.
| | jaydaigle.net
A Fictional History of Numbers, Part 4: Imagination, Complexity, and the Fundamental Theorem of Algebra
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| We continue our exploration of what numbers are, and where mathematicians keep finding weird ones. In the first three parts we extended the natural numbers in two ways: algebraically and analytically. Those approaches gave overlapping but distinct sets of numbers. This week we combine them to get the complex numbers, and see some hints of why the complex numbers are so useful-and so frustrating.