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.
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.
...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.
Your idea smells like wishful thinking.
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.
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?
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.
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.
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.
> I have no credentials
Then 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).
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!
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.
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?
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.
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.
He's an expensive grant, but he's probably got more potential to solve a problem than the average PhD student.
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.
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.
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.
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.
We already do, through the NSF, DARPA, DOJ, NSA, NASA, etc.
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.
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).
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.
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.