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>attempting a proof of an open problem
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>attempting a proof of an open problem
>create a hypothesis based on existing evidence
>devise and execute a method of repeatable experimentation to test hypothesis under different circumstances
>an "elegant pattern" emerges

not sure quite how to phrase my question. Are there false positives for elegance in mathematics that indicate the /sci/entist is suffering pareiodelia (thing where you see jesus in toast/see what you want to see) or is an elegant result mean that you are "right" and were able to successfully test your hypothesis/were right about your hypothesis ?

how can you confirm this on your own before sharing it with someone ?
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>"proving" something with a hypothesis

this is math, get out of here with your empirical evidence bullshit. And yes there are things in math which everyone believes to be true based on the fact that it has been true in every case, but still hasn't been proven. Look up the Rieman Hypothesis.
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>>7849739
Well, just because you see a pattern doesn't prove anything. You have to mathematically prove that this pattern holds, like for example saying the Euler Mascheroni constant is irrational based on the premise that there is no pattern would never be accepted, so the reverse shouldn't either. However, there is nothing wrong with contributing to the solution by saying you've noticed a pattern and others should look into it if you can't actually prove the existence of a rule mathematically on your own. The same applies to physical phenomena, if that's what you're talking about.

If what you're talking about is less empirical, like psychology for example, you generally should discuss it with a colleague or even asking others on a forum before writing a paper.

As for just verifying it on your own, assuming it's not pure physics or math, you could try actually looking up the pattern and seeing if someone got similar results. Also, check your work to see if you didn't end up causing the pattern, if that makes any sense.
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>>7849766
it makes sense. assume this is a mathematical pattern that describes a process in a less pure branch of science and the magnitude of the rate of change in the pattern is the important part of it. however when reduced to a sequence it is very simple, that is the entire sequence can be accurately predicted and easily verified from the first 2 terms.

your post is very helpful. How do you go from asserting a pattern to defining a mathematical rule based on that pattern ? what makes a would be /sci/entist either succeed or fail at this ?
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>>7849763
>>"proving" something with a hypothesis

hmm what i meant to say was "proving something based on experimental results conducted as an attempt to see if the hypothesis holds true"

so the riemann hypothesis can be calculated to hold true for the first 10^kajillion numbers but cant be proven to be held true for any number because it's not understood why it holds true ?
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>>7849773
I honestly don't have enough information to help you here, the name of the problem would help me out a good bit.
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>>7849783
pretend my post is an exam question from a stupid professor that didnt give you enough background and you have to come up with something or risk a zero
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>>7849776
>so the riemann hypothesis can be calculated to hold true for the first 10^kajillion numbers but cant be proven to be held true for any number because it's not understood why it holds true ?

something like that, yeah. Not so much that we don't understand why, but there's not a concrete proof that we can use to show it's true 100% of the time.
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>>7849776
I can tell that you are not a math person. As you mention "elegant solution to an open problem".

You even misuse the fucking terms. An EXAMPLE IS NOT A PROOF you stupid fucker. It is an example.

You probably have not even had a proof class and are in calc 1.

Math is not fucking like science, your "hypothesis" concept is not really how shit is done.

You suppose something is true, and see if you can reach some conclusion from the supposition. It sounds like you are saying you are trying to determine if the "If" part of your statement is true. You have no fucking clue what constitutes a proof in math or even what a mathematical statement is and believe it is like biology or some other shit, where you make a guess and you see if your guess is viable.

We don't deal with shit like that, are you talking about an antecedent when you say "hypothesis". What the fuck are you even talking about?
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>>7849791

not the guy you're responding to but literally we have no context here and what you're saying is totally different from what you implied in the OP

If you're actually working on an open problem? You need to prove that shit deductively, not empirically.

If you're stuck on a test? Yeah, demonstrating you know something about the problem will probably earn you partial credit, but I imagine 9/10 times the professor is looking for a proof, not a series of "repeatable experiments"
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>>7849791
Still not enough info, like what field.
If it's something to do with an electric/magnetic field or a gradient (that'd be my guess on what you're talking about), then you'd have to show that, where S=your sequence [math] \displaystyle S=| \nabla f| = \sqrt {( \frac {\partial f} {\partial x} )^2 + ( \frac {\partial f} {\partial y} )^2 + ( \frac {\partial f} {\partial z} )^2 } [/math] If that's your case, you'd have to prove that the square of your sequence is equal to that sum using binomial theorem (for higher degree polynomials, that is).

If you're talking about like a proof about something the professor already knows, chances are that the pattern is just a step.

If you happen to be talking about a "type" of number, like primes, chances are that the pattern is very well known.

If when you said the sequence can be predicted from the first two terms, you're probably actually just dealing with a differential equation (I can't accurately say since you aren't giving any info at all), and all you'd need to do is prove a relation between the process and an ODE/PDE.
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>>7849799
>>7849803

ok thanks, doing "proof crash course"

https://www3.nd.edu/~dgalvin1/40210/40210_F12/proofs_crash_course.pdf

Hopefully this will enlighten me on the distinctions I need to translate my results into deductive autism so that it satiates the need for mathematical rigour or whatever.
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>>7849838
Honestly? Just get a book on proofs, "Journey into mathematics: an introduction to proofs" is pretty good in my opinion. It's like 6 dollars. The reason would be for the exercises, a power-point proofs page isn't going to help you that much for understanding how to write good proofs.
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