Beaten into Submission by Maths

Just kidding

• My professor said two phrases this week that made me laugh. The first is “I’ll let you all in on a secret. Mathematics is rotten to the core.” The second was that they get really annoyed when people use the word “natural” because it has a very specific meaning. They said “it means the morphism of functors.” Ha. Can you imagine how triggering it must be to operate in society? So this week was pretty fun.
• The rundown of this week is that I did a lot of Maths and struggled through a lot, but it was worth it. I’ve been trying to get to sleep at a decent time, which is rough on some days when I just have a lot to do. I’m listening to Jim’s last show; I began listening to him in 2010 or something like that, I believe. Wow; that’s a long time.

The promise

• The thing that we were speaking about this week that really resonated with me was the promise of a generation.
• There was a really unfortunate incident that occurred the other day in our local healthcare system in my country that basically amounted to negligence, and the commentary was that someone should have been held accountable for that negligence. Coincidentally, there was also an electricity outage that lasted for a significant amount of time this week, too. I was asking what outrage and discontent was locally, and my dad calmly said “I know what that is; it’s disappointment.” He told me that decades ago, about the time of his generation being young adults (teens, early 20s), when the British left, there was a sense in the air of all the things they could be, in terms of invention, infrastructure, etc without British rule. And a lot of this has to do with the fact that not only were pivotal events like the Civil Rights Movements and the Black Power movement in the air, and a spiralling of countries that declared to be separated from British rule, but there was this great hope for the future of what each nation could become. After all, many of these Empires did pillage and plunder our region.
• However, there was so much more to independence; there is the undoing of brainwashing, an ability to attain self-reliance that is financial, economic, and fostering self-worth and values to build this new future. And within that generation, it didn’t really happen. One of the things I have thought about lately is how archaic our banking systems are in my home country. How many artists and small business owners I know have struggled to obtain funding, making them dependent on a system that seeks out government handouts and makes persons dependent on government funding for funding in the Arts and in local Business? Why are so many of our banks foreign-owned (i.e. from Canada, etc). And what about our local stock index; what does it mean if we stagnate and make it near impossible for persons to grow local businesses? And so, the business wealth remains within a few circles where those few can seek out personal loans, or tap into generational wealth and leverage this wealth.
• My dad said when he was pretty young in the workforce locally, they would send their best and brightest locally to exchange programmes at some of the top universities in the world. So they would have exchange programmes for local persons working in Development, Agriculture, Law, etc to study at Cambridge, Harvard, etc, through semester or year-long exchange programmes with our local Universities. The intent was that we, as a newly independent country, would take knowledge from those institutions and implement and innovate visionary programmes locally when they returned. So there was this cross-pollination of ideas, an excitement for building a new nation, a new region without having to designate everything to a higher power that quite frankly, didn’t care much about our region (besides for the exploitation of our local resources). Even hearing my parents talk about it made me feel excited. You really got the sense that we were on the edge of this new era.
• One of the final things my dad said was that we had a lack of leadership in terms of visionary leaders. He said that Singapore had attained their independence within years of our having independence, but that they had a visionary leader, Lee Kuan Yew. Proper leadership makes a difference. Often, when I write these things, I am relating these broader thoughts to organizations I deal with day to day.
• I had a conversation with someone this week (possibly also my parents) where I said that one thing I have noticed in the Pure Maths department is that the grad students are not afraid to ask for clarification in the middle of a talk, if something doesn’t quite make sense to them, or something was missed. I have noticed this in other groups I had joined in the past, too, with grad students from schools like Brown and Princeton; they speak up. I am not going to lie; when I was first thrown into a group in the middle of these students, it was very intimidating. I did not speak for that entire session and watched as they passed words back and forth like a hockey puck. But part of your training as a researcher is not to be a follower who does not think critically about problems; it is to be a leader. And on many levels, your advisor cannot provide this for you. In fact, if they try too hard, they can end up doing the opposite; coddling you and not giving you the opportunity to bounce back and to be resilient. I have watched the movie “King Richard” quite a few times, and one of the scenes I really liked is one in which Sampras’s coach asks Venus and Serena each what they want. In fact, each coach does, because they know that even with the desire and drive of their parents, Venus and Serena had to want this for themselves, too. And I often think that for many advisors, they can get caught up in what they want for their students, moreso than in what students want for themselves. Once again, my parents said “it looks like you have found the lab filled with leaders.”. It definitely feels that way. They advocate for their group, work together in a focused way, and as I was discussing with my parents, “When a company hires you as a PhD research intern, they are looking for someone who has leadership abilities. If you are sitting there waiting on instructions, why hire a PhD student, who often costs more?”. And I’m really happy to have found a group who embodies these kinds of values that I aspire to long-term.

This week

• I sat in on a Combinatorics Seminar on Probabilistic Graphs and Katz Centrality by Hunter.
• I saw a Category Theory talk by Liam that included functors, Diagrams, Colimits and the Fiber Product.
• In Algebra, we covered functors, sheaves, Bordism Category, manifolds, Brouwer’s Fixed point theorem, natural transformations, adjunctions, functorial, single homology, contravariant functor, forgetful and free functor, limits and colimits (to continue), terminal objects and review of ideals (ACC, Radical Ideals) and Chinese Remainder Theorem as well as proof of UFDs.
• In Elliptic Curves we covered Isogenies: characteristic, algebraic closures, discriminants, torsion points, branch and ramified vs unramified points, roots of unity and ramification index, ramifications of isomorphisms. I am also meeting next week to talk about torsion attacks.
• In Number Theory we spoke about Bounded Primes and Congruence.
• In Random Prob Graphs we spoke about thresholds for subgraphs, Poisson distributions in graphs, and probability generating functions.
• I also got in as a virtual participant for a Number Theory school in March (during spring break) and have a mentor who is a Number Theorist as part of our study group sessions!
• Oh, and I reviewed a functional programming book! I’m very excited about it! :)

Things I learned along the way this week (just reading)

• Minkowski’s bound
• Wordle using Information Theory
• Interesting article on Btc
• I also bought some cursed stickers that should arrive soon. I’ll explain later if the meaning is not understood.

Swag

• I was invited to an event by Jane Street a week ago, and they sent me swag in the mail.
• Trading cards and a t-shirt. I really like that the trading cards say that this is a company that cares about your mind.

Super grateful

• They also gave us a food voucher, that I have yet to use because I don’t eat out that much.
• Where I am also has pretty slim pickings for eating out, anyways; you get a couple small businesses, but to be honest a lot of it is not the kind of food I would trade over food I could cook for myself. And I really enjoy cooking, especially in the evenings.

And that’s it