Because proofs are interesting. They're the "under the hood" of larger chunks of math knowledge. If you understand how to follow a proof, you'll have a much better understanding of the strengths and limitations of various mathematical statements. If you can work a proof youself (which is a lot harder actually), then you can participate in the global conversation among mathematicians and maybe even contribute.
For most people, dealing with mathematical proofs is a kind of parroting.
They learn a path and can follow it all right, but they never deviate from the said path because there's no point.
Which might be insightful but is inherently boring, because there's no way you'll make anything that didn't exist before. You only make some mind ways in your brain which will perhaps help you one day dealing with some real problem with real output.
Might as well flash a firmware over your brain.
Given the current state of math, very few people would ever be able to contribute anything.
Others can skip to the plan B immediately.
For most people, dealing with any math is parroting, which is the problem. Creating proofs of simple things is well within the grasp of bright high school students, and is a wonderful experience -- I feel sorry for anyone who misses out on it. Really, very little traditional mathematics is required to enjoy proving that there is no solution to the bridges of Konigsberg problem, no way to cover a chess board with dominoes leaving only opposite corners exposed, or no largest prime.
Most people don't learn proofs. If you're going to learn about proofs beyond mere knowledge that they exist, then you have to be forced to do proofs from scratch.
Doing a proof from scratch is akin to being given a compass and told that somewhere past the wilderness is the promised land where others have blazed trails to but otherwise given no other help.
You know you can create the proof (since its a book problem) but how to is entirely up to you.
guard-of-terra said You either know what you're proving is already proved, then what's the point? Or you know it probably is false, then there's even less reason to. Well I guess that's true of every kind of math a 12-year-old does. Why bother doing any of it? Well, mainly because it's a useful skill to have when you want to do something interesting.
Learning "useful skills" preemptively while doing no actual work is counterproductive. It would probably work if you could motivate yourself all along, but in the current world with all the distractions, you probably would not.
It's like learning to swim in an empty pool while being reassured that it would be filled once you're able to swim.
Programming is instantly addictive because you create from the day two. Math isn't.
Programming is instantly addictive because you create from the day two. Math isn't.
It isn't, because students aren't given problems to be solved. They're given the solutions first.
The profound feeling of figuring out a solution to a problem (a real one, unlike the ones given at school) is hard to explain to someone who did not experience it. That's why, having choice to do Masters degree in Math or CS, I choose Math.
Students are sad losers unless they practice programming before and even instead of college.
Programming is addictive, learned long before you decide to specialize in it, and you make up problems for yourself creating unique software products from day one.
With math, you only reiterate the same thing over and over.
That's why, having choice, I choose to work as a programmed early and do as little as possible without being kicked off at my higher education facility.
Oh no, wait - I did as little as possible even before I began working. I just amn't good at that learning thing perhaps.
With math, you only reiterate the same thing over and over.
If you do that, yes, it's dull and pointless. The thing is, you don't need to do it. It's like complaining that programming sucks because writing hello world over and over again is boring.
At this point I have to say we are just different people, I get those feelings from programming and not math for you it is vice verse. Even when the Math is programming related it still doesn't hit those cues. For me, my friend, happiness is a warm compiler.
