[koheripbal]

I would like $100k to work on the Collatz conjecture for 6 months.

I have an idea that will probably fail, but if I had that money I would quit my job work my ass off for six months to flesh it out.

But I have no credentials, no way to write a grant proposal, and even I wouldn't invest in myself.

....and yet if we did this sort of experiment 10000 times over, humanity might make some big breakthroughs because some of this people would be legitimately smart (unlike me).

of course 10000 x one billion dollars, so maybe we should just fund legit grant seeking PhDs.

[ok_dad]

For something like this, if you have a good idea, why not explain it and make the idea public so someone with more time can research it? You'll only lose the chance to make a big name for yourself, and if it pans out you'll still get some credit, and the human race will have advanced in knowledge. It's not like you're giving away a possible formula to nuclear fusion. What's the downside I'm not seeing?

[koheripbal]

I have tried that, but people online don't really have an open mind.

I'll tell you right now... I feel like there is a way to model the 3n+1 system of equations (or really any such generalized system) using Godel numbering as a representation of each operation, as a prime number based programming language of nature, and then try to glean something from the output primes to see if there is something that predicts the single 4->2->1 outcome we always see. e.g. if it is a certain form of Fermat prime or something.

It would require me to put my computers to work because these numbers get very big, but the real limitation is my time because I have three kids and cannot afford to quit my job.

[axelsvensson]

I feel like that would fail. The reason is that Gödel numbers are rather arbitrary, and will therefore be rather far from a form that insights can be gleaned from. They are a representation of a representation, using the fundamental theorem of arithmetic only as a trick to encode any string of symbols into one integer.

As an example of just how arbitrary Gödel numbers are, consider the expressions `((3*n)+1)` and `((n*3)+1)`. Those expressions are clearly equivalent, yet the Gödel numbers for those two expressions are wildly different, with a relation that is rather complex.

IIUC Gödel himself never "used" or analyzed Gödel numbers as such, only the idea that they could be constructed.

[koheripbal]

In your example, the Godel number works out to be the same when you multiply them out - but your underlying point is valid that the assignment of primes to variables and operators cannot be as arbitrary as Godel used them as.

...a better example is just "x 1". You could add that ad infinitum to any equation and it cannot change the meaning of the outputted Godel number. ...but remember that getting a different result does not mean the interpretation of the Godel number is different. For example, multiples of ten are also even. 64 and 9 are different numbers, but they are both perfect squares. ...and the goal is to find something descriptive of the resultant number - not the number itself.

...but that's one of the main areas to explore. There are different types of primes to experiment with to see if anything meaningful can be discovered.

[sdwr]

If you multiply it out, then it's just a regular number?

Your idea smells like wishful thinking.

[q1w2]

I tried to Google Collatz and Gödel to see if anyone's done any work like this, and all I found was a now-private Youtube video with the description "Reframing the Collatz Conjecture using Gödel numbering..."

https://www.youtube.com/watch?v=VPQx1q9cfkU

...so maybe there's something to this line of research. I don't think this is a bad idea at all.

[physicsgraph]

I'm not sure I follow what you're proposing, but in case it is tangentially related to a project I work on, I'll describe what I did.

Write down every quantitative expression in Mathematical Physics. Assign a unique numerical ID to each expression. Identify the relations between each of the expressions to create a graph. Does that graph feature any patterns? Is there a path from any expression to every other expression?

[koheripbal]

Rather than a numeric ID, the variables as well as the operations are represented by primes, as Godel described.

The resulting number's geometric properties might provide some insight into the properties of the original system.

The trick is figuring out which primes to use initially, and how to interpret the resulting number.

....but my gut tells me there is something there.

[webmaven]

The only reason to use primes is to ensure that compound expressions are implicitly and uniquely related to their components. But with the magic of modern computers, this is unnecessary, as we have plenty of data storage and information representation implementations that simply store the relations explicitly (not to mention indexing them, enforcing uniqueness constraints, etc.).

In any case, the geometric (or perhaps you meant topological) properties of the objects are independent of the specific primes used, so "figuring out which primes to use initially" is a bit of a non sequitur.

[jonathanstrange]

And, did you find something?

[smusamashah]

What platform would be the most suitable one to publish ideas in a way that a future researcher can pick it up and work on it. A blog post on internet? That will just get lost in the internet noise. What you are suggesting is probably writing a white paper on it.

[kenferry]

Maybe I’m misreading, but it SEEMS like this site is reverse kickstarter: I would like to FUND people to work on the Collatz conjecture, please apply.

[koheripbal]

The site isn't active yet

[burntoutfire]

Unfortunately, availability of money for an speculative work results in emergence of entire industry of scammers, whose only competence is getting grants to do that speculative work. For example, various European Union programmes are overtaken by such people.

Also, this is the reason why VCs, after funding a startup, generallly prefer to be breathing down the CEO's neck (instead of a hands-off approach) - they know that the temptation do just burn through someone else's money while doing a half-assed attempt is too strong for many. In other words, people in general are took weak morally for your idea to produce good results.

[ok_dad]

My wife says a similar thing, and I agree that it's a hard problem to solve to prevent all that cash going to someone who will just play video games for the length of the grant. I guess you still need some signal that a person will work somewhat diligently on the grant work. I still think that it's important to fund that sort of work because there are so many examples of famous mathematicians in history who were just bored rich folks, or folks who had a benefactor and an idea, or maybe just a poor hermit from nowhere.

[burntoutfire]

Well, we were getting pretty nice results pre-XX century, before any of the taxpayers' money got (forcibly) involved. Why not just continue relying on that proven model (i.e. the rich bored folks, the benefactors and the crazy hermits)? Esp. in math, where there's no need for any equipment or materials, it seemed to work well.

[ok_dad]

I can see that, but I don't want to get into the implications for taxes and such, that's a polarizing topic. Wherever it comes from, it's necessary to support people with good ideas (and even some bad ones).

[barrenko]

I'll send you 10 bucks. I really believe Naval x Joe Rogan outlined the whole future of work, together with the movie "Her".

[yosito]

> I would like $100k to work on the Collatz conjecture for 6 months

> I have no credentials

Then why would you need $100k to work on mathematics?

[chii]

> why would you need $100k to work on mathematics?

it's to live off, and support dependents while doing something that would not bring in traditional forms of profit.

That's why it's usually called a grant, rather than an investment - because the granter isn't going to see a direct financial return (but would want to see a societal return such as knowledge or something cultural etc).

[jaredklewis]

100k for 6 months __living expenses__ would be without question the most generous grant I have ever seen or heard of.

[mirker]

Yeah, PhD income is $40k or less a year. So 5x above market rate for high-risk research. On top of that, PhD students are well-aligned for the research and have other non-monetary reasons to pursue the research (their PhD requirements).

[chii]

as mentioned in the other thread - the grant needs to compete with existing salary, or the OP would need to sacrifice potential income.

I dont think 100k for 6 months is ridiculous, because this is basically the starting salary for a grad engineer at a FAANG tech company. More, if they have experience.

What's actually ridiculous is "PhD income is $40k or less a year" - i think people (such as yourself) is so desensitized to low income as to feel normalized about it!

[koheripbal]

I'm saying I have no formal credentials in Math specifically, not no professional credentials in any field.

100k for six months would be a pay cut for me, but maybe you're right... Maybe I'm being greedy at the opportunity to make a real contribution.

At the end of the day I still need to feed/house a family of five so the 100k is still ballpark, but maybe I can set aside a few more than 6 months. 10?

Not that it matters because who would fund someone with no formal credentials in Math? Even I wouldn't fund me.

[nathancahill]

> Even I wouldn't fund me.

I mean, that's the heart of it right there. You're netting $200k+ but you wouldn't set aside six months expenses and take a sabbatical to work on your idea. So why would someone else?

[greyface-]

> So why would someone else?

Because different people have different marginal utilities of money. It's not implausible that there is someone (or a group of people) out there who is interested in seeing the Collatz conjecture proven, who places less value on the $100k than koheripbal does.

[pjerem]

What you fail to understand is that when you net 200k$, you are rich. There's a moral issue to ask other to fund your rich lifestyle to allow you work on something and on top of that, taking all the fame in case of success.

It's ok to be on the top 1% by the benefits of you work. However, it's hard to justify asking others to finance your stay on the top 1% for charity.

[greyface-]

I don't disagree with you -- $200k is a lot, especially by global standards. But I encourage you to check the Form 990s filed with the IRS by your favorite 501 charity, and see how much is spent on e.g. executive salaries. This kind of compensation is not uncommon.

[quickthrower2]

This is the problem of lifestyle creep. I have the same problem too, though I earn less than that. If everyone could live off next to nothing maybe we’d all have time to solve stuff sans-grants.

Sadly if you decide to have a family in an expensive COL then you are kinda out of the race for bang-for-buck grants unless you are genius level talented.

[yosito]

> If everyone could live off next to nothing maybe we’d all have time to solve stuff sans-grants.

I think this is, theoretically, one of the promises of communism. When I was in Cuba, I went to a local theater production of Don Quixote. It was free, and no one got any money from it, yet it was professional-level quality. In good times at least, under comminism, people have the freedom to explore their passions, because the state takes care of all their essential needs. Sadly, communism rarely leads to good times, and I can tell you for certian that none of my Cuban friends would say that the state adequately provides for their needs most of the time. It's a nice idea, at least.

[R0b0t1]

In your case I think you would be better served by being able to discuss with a mathematics faculty in a way similar to what happens naturally in academia.

I think it's not just money but the ability to more freely go back to school. It is difficult-ish to get the funding for, essentially, self-directed research during the best years of your life, and basically impossible if you don't already have an undergraduate degree.

[q1w2]

Asking someone with a mature career to formally return to academia seems like a non-starter.

In such a case he'd need to pay more money and spend even more time - when all he wants to do is work on this one particular problem.

[R0b0t1]

I know, that's why I'm not asking him to do that. It's just instead of giving him money what he really needs is an opportunity to speak with professionals. The issue is a typical academic career path is usually the only way to speak to those people.

[techbio]

If you don't then solve it, you burned $100,000 in good will and a year of your life. Better not to even suggest it, there's little enough going around as is.

[robotresearcher]

> maybe we should just fund legit grant seeking PhDs.

We already do, through the NSF, DARPA, DOJ, NSA, NASA, etc.

[q1w2]

Parent commenter doesn't seem like he'd qualify for any of those since he has no math credentials.

To be honest, it's a tough question. He's clearly a successful senior IT professional (assuming everything he said is true), and so he's probably intelligent. Even if we assume he's mature enough to stay well focused for that period and work hard, it's sort of a toss-up as to whether it's worth us funding it over another candidate.

Then again, there is no other platform like this, so if I had the option between contributing $50 to this person vs doing nothing - I'd rather give $50 to him on the off-chance that he solves (or materially advances) the Collatz Conjecture.

...but also, this speaks to a dysfunction in the Math community, in general. There should be a more constructive online forum for people like him to participate in.

[bsedlm]

sounds a lot like what VCs are already doing, except they're interested in business, not big breakthroughs

[varelse]

As someone just barely past past the affluence event horizon, VCs are now actively courting me to lead startups to develop their ideas or to invest in their funds. Previously, they just dismissed me as hella smart but clearly not leadership material (apparently net worth is an equivalent virtue signal to academic pedigree, who knew?). I am instead investing in myself and building skills orthogonal to what got me here so as to push senility off into the far off future.

I like the concept here in principle. But I would love to see it expand to also attracting tribes both in terms of time and money to build concepts. These days, I tell startups that want my money that it is off the table, but I offer my time and opinions in exchange for free dinners. It's up to them whether they consider that a good deal or not. Or it's easy to get money if you're willing to search for someone who's already pursuing something similar and you just need to express your concept as if it is their concept. What's hard is finding people who can execute all the way to production. Thank you for attending my TED Talk(tm).

[_jal]

I've had a similar experience. It is kinda satisfying to tell those folks thanks, but you simply don't have time for their call.

Valley VCs shop for very particular people, and behaviorally, are perfectly fine ignoring good ideas if the body in front of them (when young) didn't go to Stanford or (when older) doesn't care about some of the same things.

Just ignore them, they're increasingly unnecessary.