I’ve had a very similar experience and my solution was to incrementally move into more and more math intensive jobs, starting from regular old SWE working on a web app to working on an aerospace-related web app that involved lots of physics and geospatial calculations and then moving toward MLE/DS jobs. All without a STEM degree, teaching myself the math as I go. It hasn’t been easy but I enjoy what I do more and more over time.
keep the salary. if the goal it to change the world, to understand reality, to have an impactful life, have a good standard of living, etc. math is one of the hardest ways of achieving that. It's such a saturated field. Almost everything you can imagine has been done to the highest possible degree of abstraction. Every stone overturned except for things which may take a lifetime to even try to understand. Writing a blog post is probably way more fulfilling and also a doable challenge. A top mathematician may spend years working on a result that maybe if he is lucky be worthy of a footnote somewhere.
As a field I think math is well past its diminishing returns imho. It's like 'what was the last big philosophical discovery'...yeah...hard to think of one. Maybe the P zombie concept or the simulation hypothesis. But new and important books, fiction and non fiction, are being written all the time.
I'm actually looking into this. Just an hour ago I mailed the local university that I won't be doing any courses there. My initial plan was to do a bachelor at around 50% speed. But working and having to girls (1,5 years and 3 weeks) makes that quite impossible. And looking at photos of myself at 17 makes me feel rather out of place at a university at age 42.
The Open University has an AI master that I'm thinking about right now.
It has about 25% of the math that I want to learn, so that would be a good start.
I did some prep work (an official high school math certificate) last few months and I noticed that I need a schedule to keep me going.
One thing that I'm quite certain about, is that doing math is the most important thing. And doing math leads to more doing math.
Be sure not to retire too late. At an older age, with all the experience you will have under your belt, picking up new concepts and methods will not be a problem, but retaining details in memory will. You have no idea how incredibly hard it will be. So start early.
Same situation, but I've started! I only spend about 30 minutes every other day, and it's extremely slow-going, but so fulfilling. I had the same goal as you -- _really_ learning & understanding math.
I finished pre-Algebra last year and I'm halfway through an Algebra text by Gelfand & Shen now. My friends look at me funny when I tell them I'm re-learning Math from the ground up for fun (esp. with a degree in CS) but it has been so rewarding. I probably won't get to finishing Calculus for another couple years but I'm already having so much fun. Stumbled upon deriving some exponent laws last month by accident and truly understanding the sum and difference of squares has been awesome.
I'm still grumpy that I accepted I knew what real numbers were just because I could recite back the definition given by the teacher. There is so much depth there if you go looking...
In the same boat. One of my dreams is to go back to school, learn vector analysis, differential equation, differential geometry, classic mechanics, electromagnetic, special relativity and finally general relativity.
Actually quite doable as long as one can grit through the Math, some of which do not need a back to back read.
If your goal of learning is for your own benefit, it's much easier than actually going to school and doing exams, assignments, and getting credits which involves a massive amount of formalities.
A good starting point could be MIT OCW 18.01, 18.02, and 18.03. Do all their problem sets and get as much understanding you want. It corresponds to a first year university engineering curriculum.
My lofty future academic pursuit for fun when I can relax from my professional programming career would probably be compsci and then research if I’m still interested. Gonna get really old and tired working in the semicolon mines, then turn around and learn all the stuff I was supposed to learn when I started. At least that’s my picture of my casual retirement interests.
Aim for financial independence on that SDE and you can retire a few decades ahead of schedule. And you’ll have plenty of time for that sweet math learning.
You can’t really learn Math at school. Not really from the perspective of understanding mathematical beauty deeply. I wish there was an outlet or means to do so. I always found schooling to be woefully inept at assisting in learning the craft.
I love Terry Tao’s writing on math. One thing that strikes me about him is that, despite being an absolute technical powerhouse, he writes in a very down to earth style that connects disparate areas of math - e.g. his article on “what is a gauge” https://terrytao.wordpress.com/2008/09/27/what-is-a-gauge/am... where he explains how dimensional analysis might be viewed as a change of coordinates. Too often exposition in math is myopic and fails to impart a unique perspective on the subject, but Tao imbues his writing with a wisdom that I consider the sign of a true genius.
I feel like this is how all domain expertise works, no? Start with intuition which helps you solidify some of the foundation. Flush out the foundation and start building complicated structures. Now that you've built up the experience, go back and use your intuition to figure out new types of buildings to build.
This is remarkably accurate and resonates with me a lot. I did mathematical olympiads in high-school, where intuition to crack problems plays a major role. Then went on to college to study an undergraduate degree in maths (concentration in analysis). Analysis requires, at least in its rigorous foundations, to be careful and have a skilled knowledge of logic/quantifiers (more than elementary abstract algebra in my humble and biased opinion), often very scrupulously. Then in my graduate studies intuition along with the maturity of rigor work to produce new theorems. I'm impressed that several times I look at a paper or series of results and can read them "diagonally" to get the motivation without scanning all the text (of course, if the aim is to cite/build on top of/generalize/apply it then close attention to reasoning should be paid).
You can infer from this how Artificial Intelligence and Logic should be combined: AI enables a "post-rigorous" mode, and Logic is how you know you are still doing something sensible, and how you expand your sure footing.
#2, #3 means being at the stage where you can look at something and be like "no this cannot work" or "maybe this can work" without having to do all the steps.
Which are the newest developments in math? Someone told me Geometric Algebra has been around for a long time but wasn't really useful until some recent theorems.
It really depends on which field you are talking about. I’d say it is very hard to find an area of math that’s completely new , but you will often find existing areas where novel perspectives are driving math forward. Geometric algebra may be a hot topic in some areas, but the ideas of exterior algebra go back more than a century at this point, so is it really new??
Just to humor you though, I think Deep Operator learning is a vastly exciting new field which combines ideas from functional analysis and deep learning in order to do things like solving PDEs.
A proof that no one would understand in not a good proof. The ideal approach to proving theorems, at least according to how Grothendieck did it, is to build a beautiful theory in which the proof becomes elementary.
[+] [-] devnulll|4 years ago|reply
What's stopping me now? That sweet overpaid SDE salary and the endless obligations that come from being an adult. I suspect I am not alone...
[+] [-] stult|4 years ago|reply
[+] [-] paulpauper|4 years ago|reply
As a field I think math is well past its diminishing returns imho. It's like 'what was the last big philosophical discovery'...yeah...hard to think of one. Maybe the P zombie concept or the simulation hypothesis. But new and important books, fiction and non fiction, are being written all the time.
[+] [-] hebrox|4 years ago|reply
The Open University has an AI master that I'm thinking about right now. It has about 25% of the math that I want to learn, so that would be a good start. I did some prep work (an official high school math certificate) last few months and I noticed that I need a schedule to keep me going.
One thing that I'm quite certain about, is that doing math is the most important thing. And doing math leads to more doing math.
[+] [-] Koshkin|4 years ago|reply
[+] [-] ifokiedoke|4 years ago|reply
I finished pre-Algebra last year and I'm halfway through an Algebra text by Gelfand & Shen now. My friends look at me funny when I tell them I'm re-learning Math from the ground up for fun (esp. with a degree in CS) but it has been so rewarding. I probably won't get to finishing Calculus for another couple years but I'm already having so much fun. Stumbled upon deriving some exponent laws last month by accident and truly understanding the sum and difference of squares has been awesome.
[+] [-] foobarian|4 years ago|reply
[+] [-] markus_zhang|4 years ago|reply
Actually quite doable as long as one can grit through the Math, some of which do not need a back to back read.
[+] [-] yobbo|4 years ago|reply
A good starting point could be MIT OCW 18.01, 18.02, and 18.03. Do all their problem sets and get as much understanding you want. It corresponds to a first year university engineering curriculum.
[+] [-] eyelidlessness|4 years ago|reply
[+] [-] qsort|4 years ago|reply
You really can't win :/
[+] [-] stocknoob|4 years ago|reply
[+] [-] mbrodersen|4 years ago|reply
[+] [-] agumonkey|4 years ago|reply
I'm still trying to find a part time dev gig so I can just focus on graphs and advanced combinatorics
[+] [-] postingposts|4 years ago|reply
[+] [-] lupire|4 years ago|reply
Clearly you find earning/spending money more appealing than math.
[+] [-] peterhalburt33|4 years ago|reply
[+] [-] dang|4 years ago|reply
There’s more to mathematics than rigour and proofs - https://news.ycombinator.com/item?id=9517619 - May 2015 (32 comments)
There’s more to mathematics than rigour and proofs - https://news.ycombinator.com/item?id=4769216 - Nov 2012 (36 comments)
[+] [-] mbrodersen|4 years ago|reply
https://softwarefoundations.cis.upenn.edu/
Another good starting point (for mathematicians) would be the Lean community group and the Math lib project:
https://arxiv.org/pdf/1910.09336.pdf
https://github.com/leanprover-community/mathlib
[+] [-] vlovich123|4 years ago|reply
[+] [-] cpp_frog|4 years ago|reply
[+] [-] auggierose|4 years ago|reply
[+] [-] paulpauper|4 years ago|reply
[+] [-] unknown|4 years ago|reply
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[+] [-] ffhhj|4 years ago|reply
[+] [-] peterhalburt33|4 years ago|reply
Just to humor you though, I think Deep Operator learning is a vastly exciting new field which combines ideas from functional analysis and deep learning in order to do things like solving PDEs.
[+] [-] adamnemecek|4 years ago|reply
[+] [-] Koshkin|4 years ago|reply
[+] [-] kazinator|4 years ago|reply
[+] [-] formerkrogemp|4 years ago|reply
[+] [-] unknown|4 years ago|reply
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