Two Proofs and a Lady

Sorry

• I just really liked the title :) In a bit of a mood.
• I did a fair number of proofs this week, but this is my life now I guess. We didn’t end up having grad seminar this week, but I was super happy anyways because I got to chat with one of my mentors instead, and catch up with another friend who is coming to vist me! I am so excited!
• A couple things of note that my mentor advised me is that I should not think of a PhD as this lofty thing which can lead to (if I am not doing things perfectly) failure, but rather a space for experimentation. I definitely feel this these days, and I’m a lot happier than when I started in that sense because you also realize that not everyone comes in at the starting line, too. There are students who do come in to be set up ahead of everyone else, or to be groomed for certain opportunities that others are not. There is neglect, and there is regret.
• Humans, as a friend mentioned this week, like to see potential in persons who remind them of themselves, so there’s that, too. And if there aren’t already a lot of people who traditionally are in grad school like yourself, good luck finding mentors! Unconsciously, you may find that seniors grapple with what to do with you, or how to support you. They have little to no context for this. I still think that part of the solution is to admit coming from a place of ignorance with respect to this, but Academia can convince persons with the title of “senior” to think that showing a lack of wisdom in a situation can be viewed as a sign of weakness, so you may get overconfidence and bad advice instead. Be wary for your own sake; if you are ill-advised, learn from it. I think whether to call them out on it is a judgment call (my opinion, open to debate on this). Some seniors take this badly, in that their ego gets in the way if you say “hey, you were wrong about this”, and others will take it for what it is. This is the forest of egos and prestige, in a world where many were told from a young age they were going to excel and that they are special and know things, so retaliation from bruised egos and a stubborness to prove academic righteousness is a thing. Coming from the world of work, some of this is funny to me, and I think that sometimes these people could benefit from a day of pouring concrete, doing customer service or digging ditches, but I digress. Anyways, It’s a lot more challenging being from a smaller demographic not traditionally represented in Academia than getting support from some senior advisors who “see a bit of themselves (when they were younger) in you” (because basically they are all from your background..all of them).
• There is a lot of inexperience, because well, advisors are human and many make a lot of mistakes along the way, and their students further along in their journey get the benefit of all the experience and things they had to figure out that earlier students did not. There is a bit of luck involved in terms of research topic and payoff, too. There are so many things can play into things working out, and you would drive yourself nuts if you were to think about it. As much as one would like to think it’s this meritocratic space, there is also an incredible amount of unfairness. I like to think about it as more of a tipping of scales; how can one increase their odds to gain leverage to do the things they want to do? There is a lot of that going around, which means that if you do achieve some of those odds, you may find that you suddenly have a lot of persons in your company who see you as a good investment or a means to an end. It’s definitely a chess game. I totally understand why people come out with the right kind of skills for leadership positions, even if they don’t have all the skills to be a leader. It shapes your mind to focus on the details of your field, while keeping track of all the “big picture” things you need to navigate that space. If you can’t do both, it becomes painfully obvious, and well, your students (and research) will suffer.
• Most importantly, there is finite time, so it’s really important to not waste your students’ time and have a plan. Speaking of plans, this is pretty wild, but I went down a list of things I had made a while ago and realized I had achieved every one! So the plan thing really works (at least I think so)!

I got snacks!

• The BlackComputeHER Conference sent us (Fellows) some snacks! I regrettably have almost eaten mine out already!
• Apparently I was able to find some fancy plantain chips, guava chips and coconut water, as well as some sweet corn chips that are supposed to be like arepas or something. They were really great is all I can remember! And then they were gone :( So I got more! I also got a bunch of teas because well, tea-person (waves).

I got into another graduate Pure Maths summer school!!

• I am so excited! It’s the Park City summer school focused on Computational Number Theory. There are isogenies and crypto lectures and in total, it will be around 300 of us total attending (undergrads, graduate, etc)! I received full funding, too! How awesome!? And on top of that, my advisor will be there, too! I couldn’t be happier!
• It’s been a dream of mine to attend, too! I don’t know why, but it feels like this particular community has been so welcoming, and I love it!
• My parents say that all I talk about is Pure Mathematics; I seem to be sailing on a cloud of happiness in this space. I know that I have a lot to learn, but I’m really happy here! This past weekend, they said I sound like I am on a high every time I talk about it!
• The parts where we use computers are also more my kind of jam, too. I really like doing things with numbers moreso than building applications. It took me SO long to figure this out when I started learning computer things because that was the advice I was given by most; “learn to build the applications and do the web things”, and I was like “no, I want to just work on small puzzles all day”. As it turns out, you can do this! There is space for this, too, in the field!
• Oh, and my Pure Maths grad student friends apparently refer to me as having “Hermione energy”, which is the nicest thing anyone has said to me this past week! I updated my “about me” page to reflect this! :)

Stuff

• Elliptic Curves: l-adic (Automorphisms), Weil Pairing and Tate Module.
• Algebra IV: did about 5 smaller proofs for this class. I also gave some notes to people this week because that’s what nice people do when their friends miss class! I know we did some Eisenstein Irreducibility stuff and Direct / Inverse Limits aka Projective / Injective.
• Random Prob Graphs: Random Walks (1D) and Stirling Approximation. I am doing homework for this over the next few days.
• Combinatorics seminar: I saw a cool talk on C4 graphs and trivial bounds for B_k(g). Learned about Sidon Sets.
• Number Theory: looked at Euler’s Totient (proof of), Mobius involution.
• Did research meeting with advisor. She promised to give me notes on Topology! I tell you I would be here for another 10 more years to learn all the Pure Maths things!

Other

• I also went to this seminar by Mathematicians in a three letter company and this guy named William gave a talk on cryptology and Kerckhoff’s Principle, and referred to what I am working on as “fancy math” with elliptic curves, which is pretty funny. He was so passionate about cryptology and Pure Mathematics. It was kind of awesome. I also read about some of the first black cryptologists there.
• I’ve been working on a proposal for a month now, and have about another month to submit, so I’ve been slowly chipping away at reading the papers and stuff for that. It’s super interesting, and I often have to tell myself to stop thinking about it so I try to minimize tabs when I am not working on it. I generally love writing proposals and grant things and do them on my own when something interesting pops up (and if I have the time).
• Oh, I reviewed an article for a friend, in of all things, Haskell! And omg the code worked! I am always surprised by this, because I always tell myself I don’t know coding things really well, because quite frankly I enjoy solving puzzles more than building applications. I started going back into doing CodeWars (but haven’t posted my solutions like I used to in the github repo), and I’m still pretty up there in terms of ranking (currently in the top .3% (point three percent) of all users on the platform; at peak mode years ago, I was in the top 300), even though I haven’t been there in a while. Solving puzzles is an itch I have to scratch, but I don’t think I’d be happy building say, a web application or whatever. And yes, you do solve problems when you build applications, but it’s a different kind of problem-solving, I think, and then there is the maintenance aspect. And whatever it is (let’s call it Bob?), I don’t enjoy it (Bob) that much, or taking care of Bob once he is built. I like working on smaller concept things for long periods of time, where my time is uninterrupted. I don’t even mind writing on boards or on paper for most of the time, and writing up the solutions in LaTeX. And that was part of my consideration for grad school. I much more enjoy what I’m doing more, because it’s more along the lines of the solving puzzles in the way I like than in other capacities I may have liked less (and been unhappy about, even though yes, I know those application jobs pay well, too).
• Very funny observation: someone pointed out that they only know software engineers who own houses, and I laughed. That’s completely not true. Perhaps most of your friends are software engineers? At this point, I know a number of persons across fields who own houses (some more than one!) and aren’t in software. It’s a very attainable goal in software (the timeline is shorter, it’s easier to switch from another field, there isn’t much risk associated and there are multiple opportunities / chances to fail along the way and still make it work compared to some other careers where if you fail at any point along the pipeline, you’re filtered out, or don’t come from the “right” background, you aren’t even given the opportunity), but it isn’t the only way. At the beginning of grad school, I met a friend who said she wanted to become a professor because it’s a difficult thing to accomplish (she is absolutely kicking butt in her career right now and achieving every goal btw). Some friends make more than software engineers, too! Some are retired already, in my age group. Some have private chefs; I don’t think I’ve met software engineers who regularly have this, btw. Some will never buy a house because they aren’t interested / it isn’t a goal for them. Software eng is not a career that is associated with getting to know power structures at the highest level unless you “manager up” (nor is it associated with the traditional kind of charisma or charm associated with historical leadership figures), and that has its tradeoffs. Being clear about what goals you want to accomplish (is being a role-model important, is power and fame important? Is having a family important, is legacy important?) is a better metre of prospective happiness than “this makes a lot of money”, even though, yes, it can be a start, particularly for those who do not come from a background of privilege. I have also met several persons who did come from privilege who loathed software engineering or would never consider it, because prestige and having access to power at the highest levels of society runs deep in their family name and heritage, and that is where they seek validation. Prestige can also be cyclical; some career considered “prestigious” or even “financially secure” today may not in the next decade. Some have traded wealth to pursue neither, or for careers with access to power and fame, but with less monetary gains because this is where they find happiness and validation. To each his own. Money (or an abundance of it) is also not a quantifier of happiness for all persons. Do what you love, or find a way to do it. If you change your mind, that’s fine, too. One of the things I’d really like to do moving forward in my career is not be caught up in such a bubble where I can only see the perspectives of people within my field. I would lose my mind because I loathe insular circle-jerking. Life is fun when people along the way can challenge the way you think, or engage in meaningful discussions with you.

So that’s it