I still vividly remember my first week at Caltech — we got our very first problem set after the inaugural Math 1 lecture. Problem 1: “Using only the field axioms, prove that (-1) × (-1) = 1.” This was just days after international orientation. I’d flown to Pasadena straight from Bulgaria for the first time, alone with two suitcases of not-warm-enough clothing (blame international TV for the California misconceptions), a vacuum-bagged blanket, no cell phone, and barely any sense of what to expect. Back then, the school’s website was about as good as the internet got for information. So we sit in a circle and stare at the problem — all of us internationals looking confused and still jetlagged. “Isn’t it obvious?” a few protest. “Can’t we just prove it by contradiction?” someone else tries. “Wait, don’t we need to prove that any number times zero is zero first?” asks someone who’d actually paid attention during lecture. That “simple” problem ended up sending a handful of us to the TA’s office hours just to get a hint on the right approach. The cognitive dissonance between “this is obvious” and “this needs rigorous proof” was real. Ah, those early days of developing mathematical maturity.​​​​​​​​​​​​​​​​ Thank you, Baby Rudin and Apostol.