The Glory Gaussian Days

So, I wasn't a very good grad student.  My grades were okay, but I was a bit directionless.  On my way to my Master's degree in Physics (which was just supposed to be a waypoint on the way to the PhD but well, you know... stuff happens), I was mostly taking classes.  The thing is, I thought I would understand things better.  It turns out that the old adage "the more you know, the more you know what you don't know", turned out to be very true in my case.  I always felt like I was on the verge of learning/understanding something very cool about physics... but never quite arriving.

There is one glory moment that I like to relive though.  It was in Statistical Mechanics.  I was really looking forward to this class and it was taught by a relatively charismatic faculty member who was about to become the department head of the physics department.  Turns out, he wasn't a very good teacher (if I had a nickel...). He would assume we already knew stuff we didn't know and spend lots of time on something obscure that he found interesting and then he would give us tests that were only tangentially related to what we have been doing in class.  It wasn't just me, all of the students in that class were a bit frustrated with that experience.  (To his credit, after the class, he came by and asked several of us to tell him why it went so poorly so he could do better in the future!).

Since I wanted to understand what was going on, I picked up an old textbook of my father's (I just googled and found that it is still exists, but I'm pretty sure Amazon is making up this edition number!)

On one of the pages, the famous gaussian integral was introduced and there was a brief footnote where they outlined the derivation of this important integral (I can still picture the page and the format of it to this day).  I was fascinated and read it carefully and thought "Wow, this is cool."  Of course, I was still confused about how to apply it, but at least I understood the calculus tricks involved.  

Back to my glory moment (one of only two during my three years of graduate school) in the class:  One day, the prof wrote the integral from negative infinity to positive infinity over e to the ax^2.  He asked if anyone happened to know the answer.  I waited a beat and said casually (assuming others knew), "Yea, square root of pi over a."  He then turned to me in a swooping motion and said "BUT CAN YOU PROVE IT?"  His face lit with joy and anticipation.  My reading fresh on my mind, I responded without hesitation, "Yes, sure - you square the integral, change to polar coordinates, solve that integration over the plane, and finally take the square root."  He stood there and looked disappointed and sad.  He deflated and said "yes, that's basically it."  It was a strange encounter but I felt my fellow students were proud of me in that moment (pretty sure none of them remember it today though like I do !)

This memory triggered courtesy of my son, who does not know any calculus but somehow found this little video cool enough to share with me today after he mentioned the words "gaussian integral" and I said "what do YOU know about gaussians?".  Small world, huh?