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Unsolved Problems

First Edition. Items with Dust Jacket. But you are not proposing a treatment to some disease or an improvement to internet technology or a stock market trading advantage. If there was any significant money to be made by publishing mathematical results, I would not be sitting here reading Reddit all day. That goes doubly for results made by a single person, especially by an amateur. If there are any errors in your results, the community will be more than glad to help you realize them, and again, educate you if you are willing to listen.

If there are not, and you have actually proven something novel I won't say that this is unlikely; I will just say that in the years of my mathematical career I have never seen this happen, even once , then people will point you towards the right avenues for getting the result published and properly attributed to you. It's like most things in life! Your expectations should not be: "Hundreds of mathematicians spent thousands of hours working on this, and I have solved it in a week - they must be doing something wrong, and I'm about to become famous! Let me give you one more analogy: If you think that there is something wrong with the government in your area, you will be advised to go contact your representative let's pretend we're in the US for a moment.

And indeed - this is the right thing to do! If employees are being abused, or roads are in disrepair, or you want more public funding to be spent on building local parks, this is the best way to get your ideas out there.

Unsolved Problems -- from Wolfram MathWorld

However, imagine someone writes a letter to their representative that goes something like:. I am an amateur lawyer have had one US history class in high school. I have spent several nights thinking about this whole "world peace" problem, and I don't really see what's so hard about it. All the world's politicians must be so stupid not to see this. I have an elegant solution that will guarantee universal world peace for everyone. It uses sharks with laser beams on their heads. However, I will not be able to give you any details whatsoever, because I am afraid you will steal it and use it yourself.

Just trust me, it definitely works. Please let me know how to bring it up to the UN to implement immediately. I'm sure you can see why that guy gets laughed at. Nobody likes that guy. Don't be that guy. Actually, yes: I have had a paper published in a moderately important journal while in my undergrad giving some complexity results on a variant of a graph coloring problem. But that was after taking many undergrad and several grad courses on the topic, and collaborating with actual mathematicians and professors.

I'm not saying it can't happen - but the likelihood of one being able to produce a novel mathematical result increases drastically with exposure and with contacts. An university student, familiar with some of the literature, with professors advising them where to look and which approaches work and which don't? Sure, I can easily see that.

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Someone straight out of high school working completely from scratch? Extremely unlikely. I would also not consider someone with a degree in math a "non-mathematician", as per the title of your post, however. If you already have a degree, you should know pretty well how all of this stuff works. But that's just semantics. I see.

Math Puzzles and Unsolved Problems: Prime Numbers and Factorization

Personally I'm not really at a point I think I could call myself a mathematician, but I think I could get to that stage. I did a minor in math as an undergraduate and have taken graduate level courses in math one on machine learning algorithms and another on complex variables. I'm currently thinking I might part-time an online master's program in math after I finish with my current program in physical chemistry. I enjoy learning it so the idea that after graduation I'd split ways with taking courses and learning new things bothers me, plus there are plenty of courses I never got the chance to take that I'd find interesting.

Does anyone ever get this thing where you think "I'll write a one-sentence reply to this guy really quick", and you end up with two pages of text? Because I do this all the time. Send help? It's just so hard for amateur mathematicians without an academic logon or the cash to pay for access to papers to be knowledgeable about everything in the literature, and the current state of the art. A lot of professional mathematicians would be quite willing to collaborate on a paper with someone enthusiastic if all they had to do was lend their expertise about the context and relevant literature, and they'd know who to sanity check the work by before risking their reputation.

I understand your main point but do you seriously think that someone who has a PhD in maths is incapable of knowing if they have made progress on an old problem, just because they only continued doing maths as a hobby? Just start small with normal math instead of problems that have remained a mystery to every single paid mathematician, formally trained, as well as every single hobbiest. When you do the normal stuff, you can stop in the middle of any chapter in and prove a theorem before viewing the proof or even try to come up with and proof your prediction of theorems to come.

Try looking at the final proofs and attempt to synthesize the next needed theorems with only THAT final theorem, a nice fake unsolved problem for you to fine-tune your intuition -- you even got partial and complete answers if you get stuck! You're going to find this about as impossible as the unsolved problems out there since they started that way as well, but you'll have a nice guide, the author of your choice try Rudin and Halmos, apostle calculus before them.

Try to pick up math topics related to the unsolved question you're feinding for, though a good baseline of the classics, i. You'll find as you learn different branches in math that they link in unintuitive ways, so before studying it in that fashion, you'll basically have more uncertainty of where to start than good choices made.

So randomly choose the bread and butter here, it's the standard curriculum for a reason. A good balance between breadth and depth.

If you must use an open problem as a way to start engaging in the math world, try Collatz Conjecture. I have some background in math, like a minor in math as an undergrad and some graduate courses, and am in grad school for chemistry. I was playing around with the collatz conjecture a lot in the last year. It seemed to totally not impress anyone in this subreddit so I guess it's all already known and is unimportant. Without learning more about ergodic theory I don't think there's any chance I could solve that one. Also I recently read about supertasks and I find those interesting, I might read more about those.

I'll probably look into now.

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