I'll use this thread to ask a semi-related question:
Over my years (probably more than most here), I have found no need for math beyond some simple algebra and statistics. This includes 30 years in a tech career. I'm now semi-retired and working in an even less mathy field. That said, I have always felt like I might have missed out on something important in my auto-didactic intellectual development by skipping math.
Given my situation, how would you try to convince me that I should learn math and how would I teach myself the actually interesting parts without getting bogged down by doing lengthy calculations that a computer could do. The standard curriculum is so heavy on the latter and mostly absent of the former.
> Given my situation, how would you try to convince me that I should learn math
I wouldn't. I would say, if you don't need math to accomplish anything you want to accomplish, and you're not interested in it anyway, why bother?
If you are interested in it anyway, then you should not need anyone to convince you that you should learn it. You should just go learn it.
> how would I teach myself the actually interesting parts without getting bogged down by doing lengthy calculations that a computer could do
First, if you don't understand the "lengthy calculations", you will have no way of knowing whether the answer the computer spits out to you is correct.
Second, doing the "lengthy calculations" is sometimes the only way to learn the "actually interesting parts". If you haven't done the grunt work of solving some problems from start to finish in a subject area, you don't really understand it. You might have a sort of vague conceptual overview of it, but you don't really understand it. So you need to decide whether a vague conceptual overview is enough for you (for many people it is, and if you don't need to know the subject for anything essential, it might be), or whether you want to really understand it.
I don't know enough to know why I should be interested.
>So you need to decide whether a vague conceptual overview is enough for you, or whether you want to really understand it.
That sounds like a much better way to start than by going back to calculating polynomial equations. How do I find materials geared for self consumption at a beginner level that teach concept and application first?
> I don't know enough to know why I should be interested.
Are you interested in finding out more, or not? :-)
> How do I find materials geared for self consumption at a beginner level that teach concept and application first?
I have no specific sources to recommend, but I would think that "academic" courses are not where you should be looking for something like this. You should be looking at books for the general reader by people who enjoyed trying to explain math to the general reader. Someone like Raymond Smullyan or Martin Gardner or John Allen Paulos.
> Given my situation, how would you try to convince me that I should learn math and how would I teach myself the actually interesting parts without getting bogged down by doing lengthy calculations that a computer could do.
I don't think I have enough information about you to answer this, but I'll make a suggestion anyway. Since you did 30 years in tech, try Donald Knuth's Art of Computer Programming. Despite the name, it really is a book for the math-oriented. He has thousands of exercises with complete solutions for each, and every exercise has a "rating" (estimated number of minutes to complete), and exercises that require more math are marked as such.
The first volume covers fundamental stuff, the second numerical analysis (with a nice discussion of random number generators), the third sorting algorithms, and the fourth combinatorics problems. You can jump into any volume without a strong background in math.
You can get them used and in great condition for a good price. Lots of people just buy them and let them sit on their shelf for years.
> Given my situation, how would you try to convince me that I should learn math
Learning math has been the only time that I have ever been truly humbled by the aesthetic beauty of an idea. I didn't intend on studying math, I wanted to be an english major, but the woman I was dating at the time was somewhat of a math prodigy and I wanted to understand her world more // impress her. This may seem silly to some of the more mathematically mature people here, but the moment I fully understood Cantor's theorem it felt like my mind was dunked into this sublime understanding that left me in a daze for a week. Russell sums this up pretty well,
"""
Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.
"""
> how would I teach myself the actually interesting parts without getting bogged down by doing lengthy calculations that a computer could do. The standard curriculum is so heavy on the latter and mostly absent of the former.
This wont be much of a problem if you're interested in pure math as numbers bigger than 10 are rare in that domain. I would recommend picking up an intro to proofs type book like [1]. The reviews are mixed but I would take that with a grain of salt as I suspect many of them were written by bitter students.
This isn't about convincing you to like math or anything like that. Just a bit of an exploratory thing. Check out some of the math and geometry videos that Vsauce has made. One of my favorites is A Proof That The Square Root of Two Is Irrational: https://youtu.be/LmpAntNjPj0
A common trick to get someone interested is to present something surprising. That surprise gets you attention that can be turned into understanding by explaining the mystery.
The hard part is guessing what would get you surprised enough.
Over my years (probably more than most here), I have found no need for math beyond some simple algebra and statistics. This includes 30 years in a tech career. I'm now semi-retired and working in an even less mathy field. That said, I have always felt like I might have missed out on something important in my auto-didactic intellectual development by skipping math.
Given my situation, how would you try to convince me that I should learn math and how would I teach myself the actually interesting parts without getting bogged down by doing lengthy calculations that a computer could do. The standard curriculum is so heavy on the latter and mostly absent of the former.