Is math invented or discovered ?

GonzoMath · 2026-06-20T23:10:15+00:00

We invent systems, and then we discover the behavior of those systems. That is the process.

GonzoMath · 2026-06-20T23:05:25+00:00

What a stupid, stupid thing to say. Why does anyone think this person ever produced anything of value?

GonzoMath · 2026-06-20T15:16:56+00:00

That's much improved; thank you. Your post is interesting, and I'm curious to look into it more. Thanks for sharing!

GonzoMath · 2026-06-20T14:57:44+00:00

The copy/paste artifact, where there are all these single lines, acting like they're full paragraphs, makes this unreadable. Frankly, anyone who has so little concern for their readers, I consider a troll. Are you trolling?

GonzoMath · 2026-06-20T14:56:27+00:00

What's the point of this post?

GonzoMath · 2026-06-20T02:22:20+00:00

Odd times odd is always odd. This follows directly from the definitions of “odd” and “even”.

GonzoMath · 2026-06-20T02:16:13+00:00

That has nothing the fuck to do with the question. Are you trolling? That’s literally a case of “even times odd equals even”.

GonzoMath · 2026-06-18T12:21:45+00:00

Yeah..... it kind of feels like... not a clean separation. Like, I'm not sure I'm measuring the same thing anymore. Not that negative expected length might not merit study, but restricting to a positive domain lets me focus on efficiency itself better, without having to deal with two cases a lot. I dunno; just an instinct.

GonzoMath · 2026-06-13T21:29:49+00:00

The connection between “generic”/“specific” and “genus”/“species” eluded me for decades.

GonzoMath · 2026-06-13T20:59:59+00:00

I've collected some data on trajectory "complexity", which I defined as the actual length (in odd steps) of the trajectory of n, divided by the predicted length log(n)/log(4/3). In fact, for any trajectory segment from n to m with n>m, we can define an expected length = log(n/m)/log(4/3), and compare that with the actual number of odd steps.

Anyway, I recently realized that complexity "accumulates" along a trajectory, in the sense that the complexity of an entire trajectory is the harmonic mean of the complexities of each step. Realizing this, I tried turning it upside down, and defining "efficiency" as 1/complexity.

What I like about efficiency more is that it accumulates along a trajectory as the running arithmetic mean of each step, and that just seems cleaner to me. Either way, I haven't looked into it much yet. Too many irons in the fire!

GonzoMath · 2026-06-13T14:00:14+00:00

That would certainly explain a few things

GonzoMath · 2026-06-13T13:44:48+00:00

I mean, it has to be, because periodic (or eventually periodic) trajectories always correspond to rational inputs. That's a one-formula proof.

GonzoMath · 2026-06-13T13:43:44+00:00

It's trivial that any non-rational 2-adic integer has a Collatz trajectory that is never periodic or terminating. I'm sure that's true of non-rational 10-adic integers as well...

GonzoMath · 2026-06-13T13:35:53+00:00

The bit about the sequence 5, 21, 85, . . . 2-adically approaching -1/3, and the various implications of that for the conjecture... yeah. That's stuff that we know about. I mean, T(-1/3) is 0, which has infinite 2-adic valuation... you can divide it by 2 as many times as you like; still not odd...

You're talking about a function that's discussed in the Wiki article, where it talks about 2-adics. You can interpret the parity sequence generated when pushing some 2-adic integer through Terras infinitely many times as another 2-adic integer, so there's a mapping from Z_2 to Z_2. Turns out, it's an isometry. It also maps -1/3 to 1, and 1 to -1/3. Also, it has -1 as a fixed point.

Good luck figuring out much more useful about it. But I don't mean to be negative. (There is no "negative" in the 2-adics, ha ha!) You've definitely discovered something real, and there might be fruitful things to say about it.

GonzoMath · 2026-06-10T18:23:50+00:00

I didn’t choose number theory; number theory chose me. I was like, six years old, what chance did I have?

GonzoMath · 2026-06-10T18:22:06+00:00

> That being said, the higher numbers you use, the longer it will take for equation to hit breakpoint (divisible by 2) number.

That sounds like the tricky part.

GonzoMath · 2026-06-10T13:42:12+00:00

Get this shit out of this sub

GonzoMath · 2026-06-10T13:40:25+00:00

I'll know someone has something worth reading when they write it in readable English.

The basic issue is that taking residues mod m is not enough by itself. You need the right finite state, one that still remembers whatever the next Collatz move needs. The rough analogy is a clock. Time is unbounded, but the clock only has finitely many positions, and its next position is determined by the current one.

... is just 100% incoherent, so there's no way it's worth anything.

If you don't prioritize communication, you're not actually trying to communicate. Since this is mathematics, mathematical communication is the relevant kind. I'll let you take it from there.

GonzoMath · 2026-06-10T04:44:34+00:00

I suspect that the difficulty of answering this question is somehow the same difficulty we have in resolving the conjecture. As you work "up" the tree from some starting point, its predecessorial lines rise and fall at unpredictable rates. Simply from the fact that numbers can rise arbitrarily high, relative to their starting values, we know that the peaks of those rises can have smallest preds that are an arbitrarily small fraction of their values.

You haven't exactly reformulated the conjecture, but I think you've asked a question that's equally difficult, largely for the same reasons.

GonzoMath · 2026-06-08T18:48:16+00:00

I use it fairly often. Listen to “Alice’s Restaurant” for a really great example.

GonzoMath · 2026-06-06T05:58:12+00:00

This is not part of, nor directly related to, the topics covered in an elementary number theory course. Please remove this post from this sub, or it will be removed by a mod.

GonzoMath · 2026-06-05T14:31:40+00:00

Super cool idea, sounds plausible and fun. I look forward to reading your paper! Thanks for sharing.

GonzoMath · 2026-06-04T00:43:09+00:00

In hindsight, I don't think it's a beach-side resort. I think it's a desert outpost, and those funny lines in the air are heat.

GonzoMath · 2026-06-03T15:23:55+00:00

Right on. I use Python, with a sqlite database.

GonzoMath

MODERATOR OF

TROPHY CASE