Numbing Persistance

Editors Notice

Listen to this while reading for full immersion.
For the sake of authenticity this hasn’t been edited or assisted by LLMs or AI. This is raw, unedited DeGatchi.

Foreward

I’ve made so many unfinished articles in the past 2 months. It’s been a real struggle to sit down and complete something. My attention is naggingly unfocused, my anxiety drowns me and emotions are so numb that I didn’t know something was actually wrong with me. Two day ago someone I was seeing for 5 months broke up with me and I feel like I still remain in this limbo. I was unable to be present in my work and in life, constantly thinking of the next thing and how to progress, unaware of how not being present jeopardises that progression, and even living. I have been in this purgatory of “its okay to rest, do it tomorrow” and then not know how to rest and feel extremely guilty for not progressing. It’s a vicious cycle that never seems to end. Maybe this is why I’ve gotten so far. It’s an uphill battle rolling this concrete bolder…But without the bolder there is nothing for me. I’ll spare the details of my past for now. Maybe in the future i can get myself to talk about it properly.

Learning Math Is Fucking Hard

Humbling Myself

Everyone says “are you in high school” or “this is so trivial”, failing to see the beauty of the fundamentals that are the building blocks of everything else. Like the atoms that form the cells that form you, the basics of algebra, trigonometry, arithmetic form the complexities beyond calculus. I decided to take the route of wanting to understand and seeing the intrinsic beauty of these “trivial” fields, such as the wonderful power of cosine and tangent ratios for automating guiding mechanisms.

It’s a humbling experience going to the complete basics that are meant to be engraved in you from early high school. But the truth is I was never taught properly, let alone truly understand this language. I felt i was always cheating myself of actually knowing these subjects in a rigorous way. Its easy to talk about something and seem like you know it but when it comes to prove why its true everything shatters. You don’t know it. You took it for granted. And how can you expect to do meaningful research when you don’t understand how the tools you use were made and how they get more advanced? How can you make meaningful contributions to the next generation of tools? You cannot advance.

Motivating The Struggle

So my journey so far has been exploring the motivating reasons to go through the humble foundations again. Doing a breadth first search for the past 6 months to realise what i truly want to specialise in: topology and geometry with a side dish of measure theory. I want to master manifolds by gluing them together, morphing their topologies into homotophically similar structures and explore the geometry of them to decide whether the information points are strategically placed. Manifolds spark something in me. I have a deep curiousity for them but it took some time to get there.

I originally thought markov chains were my thing, then stochastic processes, but i always came back to calculus, curves and space. Non euclidean really struct a cord with me. I have this natural nack for curvature. Something about it just speaks to me, like a key perfectly unlocking a door in a single smooth fashion. Its simply satisfying.

But i found myself physically excited for algebraic and differential topology. Something i never truly had until now. I get an adrenaline rush rn thinking about it. Thinking about how i can glue two manifolds together with surgery theory or punch holes into them using morse theory. I get so many creative ideas of what the possibilities are. I yearn to learn more. I want to master this field so badly. I never stop thinking about it. I’m obsessed, to say the least…I hope everyone else can experience such joy in their lives.

Gaining Appreciation For Simpler Things

And as i found this deep appreciation for my future i had gain a new appreciation for the foundations it lies on — i.e., trigonometry. I never really liked it but as time went on i developed a love for it, wanting to know the proofs and why everything worked. It’s amazing, truly. I feel much smarter as my understanding of the world grows exponentially. It’s saddening though. With each step in the direction i know that there is so much more in science i wont be able to do. Or maybe i will? Who knows.

Building a drone has also been a huge motivation spike for learning math such as linear algebra, all for the ideas of computer vision for making the drone fully automatic. Its been really amazing how a side project can spark all these other passions in the originating field.

How To Actually Learn Math

I would also like to mention: learning math isn’t a thing you do once then stop. You don’t just read a single book or youtube video or article about some topic and now you know it. You are kidding yourself. That information is stored in your mental RAM and by the next week it’ll all be gone. It’s only through ruthlessly going through exercises and practice questions will you make any meaningful progress. Proof writing is proving to yourself and others you can actually do something without error. Chug and plug is mindless action without thought. Identifying when to use a formula you don’t deeply understand. Are you learning math to really understand it or just use it blindly.

Master the langauge and demolish those that choose not to understand the building blocks of the fabric that weaves this world. Hostile NPCs will try to shoot you down, but they are rather testimates to how strong your mental dedication is to this path. Math is more than just numbers. Its a way of thinking and a deep want to understand what made up society as we know it, where we came from and what governs our entire existance. This isn’t some fad. It’s the underlying reason for your very existance.

Doing exercises is fucking hard. Its meant to be. If you knew it already you wouldnt struggle! Struggling is where growth is made. Thats why the gym is painful. Why heartbreaks and loss are painful. Each experience of suffering grows you into something stronger. Without the testing of knowledge and the smack in the face of reality you would be deluding yourself, fixated in your fictional world of “knowing” math. Mathematicians ask questions and play around with concepts all the time. You are no exception if you want to contribute. Without questions you are wasting your time if you want to build up your vocabulary. Without questions is the equivalent of doing duolingo and saying you’re fluent in a language without ever speaking to the natives or visitng the country. In most cases the questions teach MORE than the theory itself because you will notice patterns, logical structure, relationships and gaps in your knowledge that will be overwritten.

You know, it’s very releiving that PhDs also have the problem of requiring MANY hours to get through a few pages, e.g., 4-6hrs to read 15 pages of a math book. So don’t worry, you aren’t stupid, we all are. Its just the nature of learning math. Its a language where the vocab needs to be built up from nothing. Each understanding of a world allows you to speak more intricate sentences and understand deeper what someone is trying to convey.

Learning From Others

I’m so obsessed with math that i want to learn everything from others. I listen the to what inspires them, what draws them to their niche fields in math. I read auto/biographies of famous mathematicians to understand how they thought, what lead them to discovering incredible things. Trying to understand how i can create my path while keeping in mind their flaws and desirable traits. What led them to their discoveries? What did they pursue? Is there a commmon trend in interests or intersecting certain topics? I am just fascinated with these people and want to learn everything about them. I love learning about the history of mathematics too. Where thoughts originated from and how it swayed the wars and intelligence of the world. How government funded schools are used as training groudns for the next generation of defense contractors and weapons designers. It’s an incredible world when you open your eyes enough to see in it.

Persisting

Redefining My Identity

Learning the language of math has been brutal. Its something I’ve used to carve out a new identity out of. Ive immersed myself so deep in the field that i talk to PhDs and professors all the time about it. Learning the high level concepts to have decently motivating conversations. Wanting to learn about their niches and being fascinating no matter what it is. I originally hated abstract algebra but now find it one of the most fascinating fields because i found a connection to what i enjoy and discovered algebraic topology and algebraic geometry. Its incredible how a single connection can make you go from hating a subject to wanting to master it. For example, category theory was deeply boring for me until i learned how it abstracts everything away and leaves you with the bare bone skeleton of the topology which allow for rigorous analysis of a space. Its so fucking cool and powerful.

My superpower has always been persistence. I’ve always been extremely lonely all my life with not many IRL friends, being terminally online. Over the years ive become emotionally numb and can endure extreme pain ranging from a special forces military bootcamp training for 8 weeks and extreme isolation. My brain has just adapted to it. Ive experienced my closest family members die right out of high school and have been forced to mature at an accelerated rate. The only control variable i have is not quitting. This is the thing i know that if i continue to do i will be alright in the end and will survive. Leaving my past career in crypto HFT and security for more exciting things like malware and math have been extremely tough mentally but worth it long term.

Past Advice

The only thing i would tell myself in the past is that “be present and enjoy the journey more. you’ll look back at these times fondly and realise you weren’t going to be homeless any time soon. so stop worrying and embrace it for what it is. don’t let it eat you alive and drown out all the enjoyment of daily life. the end isn’t the goal. enjoying the process is.”.

Do What You Can

Doing a little bit each day, no matter how small, has been my motto for my life. I have a roller coaster of ups and downs. I go through hardcore burn out but force myself to continue each day. Trying to watch videos about math despite procrastinating in a negative cycle loop from watching youtube videos for 6hrs wondering where the day went by. In no time ill end up where i want to be. Maybe the 6hrs of procrastination was necessary to achieve that short time of focus on the career. I know when i reach the creative part i will exponentially gain but the learning part is a struggle. I need this support from procrastination.

The point is, if you do a little each day, whether spiritually, mentally, physically, you will reap the rewards long term. Something is always better than nothing. Stop being hard on yourself and show some compassion to yourself like you would to a close friend or family member. Smile in the face of those that doubt you as it is their insecurities and egos wanting to leech your happiness away, the happiness they could never find. You will surpass them and look at them in awe.

Just because they deceived themselves into thinking they know it all and aren’t excited you’re building your way up so they can share passionate ideas with you they instead shoot you down because they are fearful you will surpass them as it’s the thread that holds their ego in tact from ripping away violently. I feel sorry for these people. They are most likely the “smart kids” that never tried hard and fell off because passion was never something intrinsicly burning in their souls. The desire for more. It was null void that never seemd to mend itself. Only widening over time as they observe others overcome the headstart “gifts” they were granted. Oh, how i pity you.

The Journey Becomes The Destination

The original intention of learning math was to learn ML and build models. But i learned that i genuinely enjoy math. It was what i had been longing for. The closest thing to an answer of why i even exist. Sure, ML is incredibly interesting but at the core of it it is simply math. More advanced models will be dictated by the math. And so by that virture one so passionate to go as far as to become advanced while being in the intersection of applying to computer science can revolutionise the world as did Turing, or Hamming or anyone else that was deeply entrenched in math. There is more than meets the eye in this realm. But the price is fair. You will have to sacrifice something for this knowledge. And the higher you go the steeper that price gets.

Progression from legendary geometer, Grothendieck

Final

Theres not much here as I just wanted to get something off my mind onto paper. Not a polished article as my readers may expect from me but, again, something is better than nothing. Maybe this resonates with someone going through a similar time as me. I hope to look back at this fondly and remind myself of the compassion i deserve. Everything will fall in the right place eventually. Persist and you shall be given all you deserve for your pain. Any loss is a lesson, something with a positive outcome in some aspect. You will grow and adapt. I see the world completely differently with each day i do math. Its an amazing feeling to see things others cannot even comprehend. This gatekept perspective is reserved for those that pay the price of mental wellbeing.

Take care of yourself and survive to see tomorrow. One of these suns will sprout the tree that will feed you food life. Until then, we wait in the scorching heat. Remember to pull back like a bow and arrow once in a while to propel forward. And remember that without a destination there is no point being the fastest or most skilled driver. And finally, without health none of this matters. You cut your time short to experience what is truly enjoyable about life. Heartbreaks happen, time goes by, but you will always be the only person in control of your life. Don’t let go of that dream you had many moons ago. Chase it until your body gives out and you mind fails to function no more.

Everything will be okay, anon. Godspeed.