CC=community college, I'm a part time teacher. It seems you're still optimistic about academia, even if you see it as work. That's really nice, and will color your grad school experience positively.
Splines (piecewise polynomials satisfying some regularity constraints) are great for a lot of function approximation applications and are relatively cheap to fit to a given set of data points. I'm a fan, and would recommend them to you. Of course a lot of care must be given to which dimensions you select as input and which as output. E.g. if your data is three dimensional, is x affecting y and z? Are x and y affecting z? These questions will shape what structure your approximations will have and are suitable for you to answer more so than a mathematician.
Regarding philosophy of old, I've read newton's principia. He uses the same word for different things, and uses different words for the same thing. It's confusing as hell. Was he a genius who pioneered calculus and furthered the idea of a limit (without epsilons & deltas)? Yes, but his book is unintelligible garbage. A necessary step in the development of calculus, but it should be read by math historians, not by those trying to understand the concepts. The same could be said about many of these old philosophers and scientists. Kant? Garbage. Engels? Garbage and evil. Marx was cool but autocrats coopted it. Studying philosophers of old is important for historical understanding but I don't place these guys on pedestals any more than I would the author of a punchy tweet or a funny meme.
Ohoy! I've also read (mostly read) the principia! We've actually had quite a few "principas" up in the club. You probably know Alfred Northwhitehead and Bertrand Russels "principia mathematica".
I certainly didn't find it (Newtons) to be garbage.
But although i liked reading it - i'd say it is a type of reading of which one should not expect the same result/experience as in reading a favorite modern textbook. You could call it a study of "history" i suppose, but then what is reading a 200 year old novel? I tend to not have strong dividing lines between the types of reading i do like that. I'd rather figure out along the way if what i'm taking from it is history or something else. There's so many things inbetween modern and "old" as well - maybe you've read some Feynman lectures?
Using the same word for multiple things is such a mathematician thing to get fussed about!
I totally disagree with you that these authors should not inform modern thought. I think they are absolutely crucial, if nothing else simply as ways to think *backwards* and *OUT* of ones current paradigms. I have nothing against memes, but i've never found the study of the confession bear to be crucial in understanding my modern use of mathematics... Northwhitehead and Russel on the same point though? *absolutely*. I picked up their book because of Douglas Hofstadter's lectures on metaphor/analogy - and i must say it was a top 3 read in changing my relationship with mathematics and science.
As a child i found Hume and Lockes original texts to be near spiritual awakenings. Perhaps you are smarter/think more clearly than me, but for reading Locke disentangling his concepts of types of ideas felt like the only "clean" thought i'd ever read, showing how to gain any control of the mess in my own head. Now, 20 years study in neuroscience later, are Lockes concepts the main model i have of "innate ideas"? Obviously not. platonic forms, kant's a priori structures, Descartes/Locke/Hume's innate ideas respectively, chomskian universal grammar, premodern bio engram research, etc. etc. they are all crucial for me - it is a luxury of fields of study that can consider themselves more "finished" to move on from and ignore the old perspectives. I constantly find some older view and think "what the hell, this is what we call x in the frontier field of y today!". Karl Friston is a great modern example of someone who constantly reuses older physics/natural philosophy to make real advances in modern science.
As for piedestals - they are no longer alive, so i'm less afraid of accidentally inflating *their* egos. I don't think i worship them, but then again i'm also a typical danish atheist in that i don't really mind going into a church.
I suppose it depends how you view these "systems of knowledge", but i don't even see "calculus" as a finished structure. Or at least, i think we can define it that way if we want - but there is certainly ALSO a version of "calculus" which can be as unfinished as we need it to be. Who knows, if Newton had adapted it a bit, maybe he'd have finally gotten gold to materialize from boiling all that piss of his. I should bring suggest piss-boiling as a work shop in the jjournal club!
I will immediately check out more about "splines", thanks for putting my mind there!
Oh and i actually also sometimes teach at a nearby vesrsion of a danish "community college" (not totally the same, bit lower level, probably inbetween your high school and college) Although i just say no if there's too many students
i only want to do the small classes with like max 10 students, that's awesome!
This post was edited by emiq on Apr 15 2026 04:12pm