Welcome!

These pages are the result of a life-long love of learning. Some contain never-before published insights and theorems. Others provide my way of clarifying concepts that many people find hard to grasp. I leave it to the historian to sort out new from old. My aim here is more that of a tour guide.

This isn't Math for Dummies. It's more what Peter Lax called a fighting chance. I'm not the first to notice that mathematics is an oral tradition. Textbooks generally provide no better than a guide for rediscovering for yourself the topic they treat. The sad reality is, that there is an excellent chance that when you found it hard to grasp some concept, it was because your teacher didn't really understand it, either. That leaves you in a nigh impossible position. I had the experience myself of being baffled by a course, only to realize years later that the textbook itself was totally confused.

You deserve better.

Why is Mathematics

The Mathematical Menagerie

Some Subtleties From Logic

Some Subtleties of Sets

The Family Tree

Why is Topology

Why Are Quivers

Why Are Associations

Structure of Algebras

Why Are Categories

Acknowledgements

I'm Andrew Winkler. I hope you've enjoyed exploring these ideas with me. Thanks for your time. If you've got any questions, send an email to 4af502d7148512d4fee9@cloudmailin.net.

This is all still in draft form. There will be errors. Please point them out when you find them. If you're not sure, let me take a look. If you're confused, it's a presentation bug, even if it's not an actual error, and I'd especially love to hear from you.

The Hertz Foundation has been a valuable support, not only during graduate school, but ever since. If you can, please consider supporting them with a donation.

How can I help support this work?

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