this post was submitted on 26 Oct 2025
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Nothing kills my motivation more than discovering something new in math and then finding out some dead guy beat me to the punch by several centuries lol
Then again sometimes it’s worse when I expect there to be literature on a topic and then discovering there isn’t even a wiki page for it.
Hell, most recently it was bi-intuitionistic logic. Originally studied in the 40s by one German guy who took bad notes. Main body of work done by a single math grad in the 70s (Rauszer) culminating in her PhD. Turns out there were errors discovered in her proofs and it was proven inconsistent in 2001. Only for two relatively young mathematicians to clear up that there are two separate versions of bi-intuitionistic logic which are consistent. This discovery and proof are found a paper that was published only this fucking year.
I asked a simple question about dealing with uncertainty in a logical system and instead of finding a well studied foundation of knowledge I was yeeted to the bleeding edge of mathematics.
Edit: in case it isn’t clear, by “new things” I mean new to me not new to the world; hence the aforementioned dead guys with published works on the topic. And when I say I was yeeted to the edge of math, I should mention that edge is well beyond my capacity to further. I had to learn a lot about notation for logic just to parse the paper, and I’m sure I still don’t fully understand it.
This is literally the heart of science and physics, it's how every single great mind has made advancements and gotten recognized, by building on the works of those who came before them and finding new ways to connect and test models. If you're "discovering" things that other people have before, that means you're on the right track, now you just need to put the work in validating and verifying your model or expanding on the models that others have developed.
You’re right, we build on the backs of giants. The issue is, typically, anything I discover myself is typically very far below the level where new science can be done OR it is far enough above my current knowledge that I just don’t even know where I’d begin.
Bi intuitionistic logic is the latter category. I was expecting truth tables and instead had to add a ton of words to my vocabulary like “Heyting Algebra” and “Kripke Frame” etc. just to understand what the paper was saying (not that I do fully understand what the papers are saying lol)
This is the entire point of academia though. If you were in a math PhD program you would have much better access to the resources to build the background knowledge you need to explore this topic, and then you would literally be paid to research it, and then possibly paid to manage a whole team of people interested the topic, and paid to teach classes on it and publish book chapters, and so on. People have this misconception (not saying you do, but this is a very common sentiment) that academia is this ivory tower which gate keeps knowledge, when the reality is that it's just a framework for enabling knowledge discovery. The reason most people outside of academia don't publish original research isn't some conspiracy. It's because engaging in original research is a full time job which often requires a lot of money and resources normal people don't have.
I know :( the issue is I’m in ME and school is fucking expensive. Oh and I am working in a research lab getting paid for my work, not much though.
I would love nothing more than to stay in school and get like 82 different degrees in various topics. I would love to do a PhD in math, and one in physics, and one in cs, and linguistics, and psychology…
But the world forces me to specialize if I want to have enough money to live well. I chose ME because I knew it had a lot of overlap with a bunch of different fields. And yeah I’m taking grad level math and cs courses, but like you said, lots of the stuff I’m interested in is PhD level stuff.
Also Idk if you’re in America, but the money for research here is getting scarcer every day. It could likely be more effective for me to sell my soul to a defense company and then build my own personal lab with that blood money to do research I want to do than it would be to get a PhD and be a professor and simply hope the projects I want to work on will get funding.
Of course that’s assuming the country doesn’t fully collapse (or kill me) before I enter the job force. And assuming I could work for a defense company without deciding to kill myself out of guilt of building civilian killing murder machines.
Anyway, point is that you are right but I lack the financial security to justify trying to get a PhD in math right now.