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Consider mathematics. If you already know enough math to derive the quadratic equation, you might make a small change, like adding X^3 or X^4. See where your

Consider mathematics. If you already know enough math to derive the quadratic equation, you might make a small change, like adding X^3 or X^4. See where your own techniques take you before looking up the answer. With just a few pen strokes, you will be playing with an equation for which there is no general solution, or no known solution. In mathematics it will take you very little time to start playing at the boundaries of human knowledge, and it's relatively easy to memorize a few starting points that many hours of passenger travel fly by.

jolt42 6mo ago
I like this. I like crossword puzzles but don't like I'm just solving pre-made puzzles rather than exploring new territory. Math seems the best candidate but are there other fields with similar challenges?
codazoda 6mo ago
Since I was a kid I was fascinated by computer math, such as a projectile in Scorched Earth (wind, angle, velocity, gravity). I turned 50 this week and I STILL haven’t dug into how even the basics work.
- elric 6mo ago
  Can still remember the sound of the Funky Bomb firing in Scorched Earth. Thanks fot reminding me of that. If you're interested in this sort of stuff, the book Nature Of Code is great for exploring this topic by creating simulations. There's a Javascript version and Java based version (using the Processing framework). It isn't actually all that difficult, and I found it very satisfying to work through.
ivanjermakov 6mo ago
There is a lot of less popular math problems in spatial and high dimentional geometry, packing, topology. Nice example of something many of us could try: https://news.ycombinator.com/item?id=45694856 https://news.ycombinator.com/item?id=45694856
futune 6mo ago
It might be interesting to try your idea, to see for yourself where the difficulty lies, but be warned that finding general solution formulas for degree 3 and 4 equations is kind of brutally difficult. I'd link to the historical developments but it would spoil it for those that nevertheless want to give it a shot. Degree 5 requires some serious far out of the box ideas, if you want to understand what's going on. But in general the idea of making small changes to solved problems and seeing if you can tackle them is an excellent approach to recreational mathematics! I think I'd start somewhere other than higher degree equations though, that would be a rough start.

jolt42 6mo ago

I like this. I like crossword puzzles but don't like I'm just solving pre-made puzzles rather than exploring new territory. Math seems the best candidate but are there other fields with similar challenges?

codazoda 6mo ago

Since I was a kid I was fascinated by computer math, such as a projectile in Scorched Earth (wind, angle, velocity, gravity). I turned 50 this week and I STILL haven’t dug into how even the basics work.

elric 6mo ago
Can still remember the sound of the Funky Bomb firing in Scorched Earth. Thanks fot reminding me of that. If you're interested in this sort of stuff, the book Nature Of Code is great for exploring this topic by creating simulations. There's a Javascript version and Java based version (using the Processing framework). It isn't actually all that difficult, and I found it very satisfying to work through.

ivanjermakov 6mo ago

There is a lot of less popular math problems in spatial and high dimentional geometry, packing, topology. Nice example of something many of us could try: https://news.ycombinator.com/item?id=45694856 https://news.ycombinator.com/item?id=45694856

futune 6mo ago

It might be interesting to try your idea, to see for yourself where the difficulty lies, but be warned that finding general solution formulas for degree 3 and 4 equations is kind of brutally difficult. I'd link to the historical developments but it would spoil it for those that nevertheless want to give it a shot. Degree 5 requires some serious far out of the box ideas, if you want to understand what's going on. But in general the idea of making small changes to solved problems and seeing if you can tackle them is an excellent approach to recreational mathematics! I think I'd start somewhere other than higher degree equations though, that would be a rough start.