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How is this level of math even possible... like... how are people hard-working enough to reach this level of understanding?
by buddyp450 6y ago
How is this level of math even possible... like... how are people hard-working enough to reach this level of understanding?
- EE84M3i 6y agoI don't know about these people specifically, but if you are interested/passionate about it, it probably doesn't feel like work.
- gizmo686 6y agoWe, as a society, produce enough of a surpluss that we are able to pay armies of researchers to do nothing but expand the frontier of human knowledge and pass that knowledge on to the next generation.
- chewbaxxa 6y agoYou could study computer science and then go to a large corporation to help them maximise their ad revenue, or you could study and do something like this instead. Depends what motivates you.
- flafla2 6y agoI upvoted you because there is truth to this sentiment. But I want to add that physics is IMO one of the hardest fields intellectually of our time. Just to get your feet wet, you need to be well versed in an intimidating array of mathematical disciplines. DiffEQ, Discrete Math, Computer Science, Topology, Differential Geometry, High Level calculus,... the list goes on even at the undergrad level. To make a meaningful contribution is quite a feat. I have massive respect for those who bravely tackle the frontiers of Physics; some physics majors have a broader understanding of Math than a mathematician! Though importantly, your average mathematician will have a much deeper understanding of more focused topics. I don’t mean to suggest that any of Math, Physics, CompSci, etc is fundamentally harder than the others. Each field presents different challenges! But they are also intimately related IMO: the recent MIP*=RE proof has convinced me. In short, we’re all on the same side.
- bArray 6y agoJust my 2 cents, but I would suggest from a programmer's perspective, a method of entry might be in game programing. You can explore a bunch of really interesting mathematical properties of the Universe in isolation and visualize (and even feel) them to some extent. On my TODO list for example is to take a look at this project that maps a world to non-Euclidean space [1]. Writing these "simulations" and exploiting their nature to make interesting interactions is just unbelievably awesome. P.S. Another interesting one (by the same person) is "MarbleMarcher" [2]. [1] https://github.com/HackerPoet/NonEuclidean https://github.com/HackerPoet/NonEuclidean [2] https://github.com/HackerPoet/MarbleMarcher https://github.com/HackerPoet/MarbleMarcher
- jeffreyrogers 6y agoI get what you're saying, but people learn the math in 4-6 years or so, so while it's definitely a lot of work (not that many other things that people spend that much time learning), it's also fairly well bounded. You know that if you study hard for long enough you'll know most of what you need to know, and then the parts you don't know yet, you have enough awareness of to know when you need to learn more about them.
- ISL 6y agoIt takes a decade or more of continuous professional effort (treating successful undergraduates as professionals) and mentorship to become conversant. Some of it is acumen, some is community, and a lot of it is time. People can easily ask the same of experts in other technical fields and arts.
- blueprint 6y agoIt takes 10 years of post-undergrad professional or academic work to become "conversant" in physics? Isn't that the undergrad GR and supporting math courses, themselves, generally? Or are you referring to a level of keeping up with the latest modern theory?
- ISL 6y agoI meant the combined study of undergraduate and graduate theoretical physics, to be conversant at the level of the arXiv preprint.
- canjobear 6y agoIt’s not as inaccessible as you think. Once you understand/get used to some hard concept, then suddenly a lot of other ones make sense, and you’re ready to tackle the next conceptually hard thing. It might seem like advanced math is totally unreachable, but in fact it’s only maybe 10 steps away.
- typon 6y agoIt's actually undergraduate level of math (typically General relativity is taught in 4th year). It just seems overwhelming because it builds on top of four years of math courses. I'm not an expert, but this paper is interesting because of its leaps in physics rather than special math.
- oh_sigh 6y agoThis isn't the culmination of a lifetime of math study. You just don't have a basis to understand it, but you could easily understand it with a few years of study in your free time. Chinese may be as inscrutable to you as math is but you understand that you just need to learn it for it to start making sense.... Note I'm talking about the math in the paper, not the paper itself.
- dvanduzer 6y agoWhy do you think understanding math requires hard work?
- esperent 6y agoI have a degree in math. I've since moved onto 3D graphics rather than pure math, but I think I was fairly good at it. I can tell you it was damn hard work to get my degree. The only guy in my year whom it all seemed to come easy, I later found out was the son of one of the professors and had been essentially studying for the degree since he was 13.
- failuser 6y ago<sarcasm> How do you know it’s not entirely genetic? </sarcasm> Reading HN would make one think education is irrelevant.
- ClumsyPilot 6y agoIn more than one way
- laichzeit0 6y agoIf the general hacker news sentiment is anything to go by, then it’s just hard because of the archaic mathematical notation. If we could just use better notation then a simple mathematical bootcamp would make mathematics accessible to all the brilliant self-taught programmers as well /sarcasm.
- pas 6y agoJust the lack of syntax and type checking is a serious burden on folks who don't have those committed to muscle memory. That said, that's the easiest part of mathematics.
- pa7x1 6y agoIf only those pesky physicist and mathematicians would name their variables correctly everything would become self-evident.
- jjk166 6y agoNewton, why do you want to name this the 6th dimensional electron-graviton interference coefficient? Just call it G for gravity!
- deleted 6y ago[deleted]
- TheOtherHobbes 6y agoIQ of >160. If you're down here with us stupids you can spend a lot of time on it, you'll get some insight into the basics, but you won't be good at it - certainly not good enough to do it for a living. Yes, GR is taught at undergrad level. But that doesn't mean most undergrads really understand it, or can do much with it beyond solve a few toy exam problems. Because undergrad GR and QM are introductory courses for beginners. It takes a PhD to start acquiring fluency, and that's years of constant grind doing nothing else but. It's also hugely helpful to have mentors and/or parents and/or other family members who can give personal help.
- paulpauper 6y agoi thought GR is grad level. I know physics grads and they never studied it, but this was a long time ago.
- cthalupa 6y agoIt depends on the university. It is taught in undergrad in some places, not others.
- paulpauper 6y agoThe building blocks are multi-variable calc and linear algebra. The leap from elementary to advanced math occurs when one transitions from dealing with a single function to dealing with parametric arrays of implicit differentials, which are abbreviated in short-hand notation for brevity. Most people , even in tech/STEM, do not get a good foundation in those topics, so that precludes the possibility of deeper understanding.
- nscalf 6y agoThe answer is patience. Everything is easier once you've been working in the field for a few years, steeped in that world. Have you ever read legal texts? Or dug through a graphics rendering library? Or seen a grandmaster play chess? Or etc, etc, etc. Experts in a field can show you how complex things can be when you're working on hard problems and innovating, but that doesn't mean you're not capable of getting there if you're patient.