Every single day of working with Principles of Mathematical Analysis (Baby Rudin) I hated the book. I hated my teacher for making this obviously non-introductory text the mandatory text for the course. I hated myself for reading through the pages at the speed a 6 year old reads prose. I hated the way a proof would just appear as if out of thin air with no motivating paragraphs as to what was to be achieved or why this or that route was taken. I hated it all — but most of all I hated Rudin himself.
At that point I had already taken 2 years of physics and maths and I thought of myself as having a fairly good grip on things. Sure the stuff I had read wasn’t what I would now call rigorous but it was intuitive. Most of it had been to just apply methods and state theorems rather than really prove why they worked beyond outlining the ‘idea’ or intuitive principles. Sure, there were theorems to be proven in tests from time to time but even then it boiled down to memorizing it and not really thinking much about how a proof is properly structured.That’s totally fine but it had in no way prepared me to think critically about math and differentiating what I knew I could prove and what I knew because I had been told. To from this background make the jump to working with chains of 12+ sequential proofs where every statement is built on another statement running back to the simplest of notions completely overwhelmed me. I felt like my mind simply wasn’t build to keep track of it all.
It took me half a semester to recover my senses and figure out the structure of the book and how to work with it but in the end it was the closest to a transformative things I have experienced it since going to university. I was both humbled and more curious once the course was done and I don’t think I would have been if it hadn’t been for Rudins desire for the book to be (essentially) self-contained and lacking in embellishments, as to the supposed meaning of what — forcing you to think for yourself.
The books still has too many problems for it to be good enough to warrant it’s widespread usage but to me it still was one of the most important reads I’ve made in the past 3 years. To actually have become aware of what I knew, didn’t know, and can know about mathematics way is priceless.