4-13-26 - Proud of Myself

Today I was very proud of myself. I have these days every once in a while where I feel like I genuinely understand something I am working on. Without days like this I don’t know if I would’ve made it this far in my program.

Yesterday a few friends were discussing postgrad education and for anyone out there thinking about it, particularly in math, you should be aware that as you likely already have experienced, you will constantly feel outclassed by everything and everyone. Grad school has been the process of constantly feeling dumb, despite knowing that I know more math than almost anyone ever. Because you are around other smart people who also have dedicated even more of their lives than you your days are spent feeling dumb.

The other thing about grad school is you don’t have to be smart to make it. Like if you want to get a Ph.D or a master and have the moeny or time you can do it. The ceritifcation is nice but many Ph.D’s couldn’t explain any hard stuff after 20 years in industry not being forced to think about more than their own cog.

Now I get to be a nerd about what I learned today. I was sitting in on my advisors course on automorphic and modular forms and we were discussing Hecke operators. We gave the classical description as sums over representatives of a double coset and I asked about the relationship to the local spherical Hecke algebra in the adelic perspective. I then spent time on and off for the next week trying to see the fact that the action of char(K(p,0\0,1)K) on the adelization of a modular form should be the same as the action of the classical Hecke algebra and I think I understand it now. I was proud that as I wrote down my understanding on my own I correctly predicted how to translate between the two version (via the SL_2(Q) piece of the strong approximation decompostion). I found some exercises that note this here. https://bicmr.pku.edu.cn/upload/file/2021/20210802/20210802085307_22494.pdf