Why Do People Misunderstand Mathematical Proofs of Nonexistence?

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The discussion centers on the assertion that there is no algebraic formula for the roots of a general quintic polynomial, with participants debating the implications of this statement. One participant argues that the lack of a formula is based on current knowledge, while another insists that it has been proven that no such formula exists. This leads to a broader conversation about the nature of mathematical proof and existence. Key points include the distinction between mathematical axioms, which are not subject to change based on empirical evidence, and the general public's misunderstanding of mathematical nonexistence as merely a lack of discovery. The conversation also touches on the philosophical implications of existence in mathematics, with some participants asserting that without proof, something cannot be considered to exist, while others argue that this perspective oversimplifies the complexities of mathematical inquiry.The discussion highlights the challenges of communicating mathematical concepts to those without a deep understanding of the field and emphasizes the importance of precise definitions and logical reasoning in mathematics compared to informal reasoning in everyday life.
  • #31
lendav_rott said:
If I am to assume lack of proof of existence leads to limbo (uncertainty whether something does or does not exist) then it very quickly becomes a philosophical topic. The only certainty is existence and proof of the latter.

It doesn't have to be material, even - how do we know emotions exist? Hate, anger, happiness, love? Billions of people have no reason to lie to me or anyone else and put on an act - the only logical conclusion is that these emotions do exist, we can all feel them.

What I've been saying is: "lack of proof means non-existence" in math exclusively - we are welcome to philosophize about what you or I or they hold true or theologize about the existence of god all we want, until there is solid proof, it stays out of the math field.

You don't go to work because you MAY be paid for your work - the only certainty you accept is you WILL get paid and you have proof of it from many other co-workers who also get paid - the money does exist regardless, however your salary will only exist once you get paid.

Should you not get paid, therefore you can't prove your salary exists - so you can't convince the bank to give you a house loan or all purpose loan either. If there is no proof, it does not exist.

Or maybe you like to deal a lot with maybes and I am the crazy one, works for me either way.

Might also be necessary - I don't think of math as punching numbers and theories together - to me, math is logic. So to answer the original question of the topic (not worded as a yes-or-no question, but essentially comes down to it) - No - I don't care for "none-that-we-know-of"s - Either 1 or 0. If you can't prove it, it's a 0, if you prove it's a 0, it's a 0 and naturally, if you prove it's a 1, it's a 1.

To be blunt: you're wrong. And your post has just proven that you don't know enough about mathematics to discuss this matter properly. I can't convince you of the way math really is since your opinion is just so illogical and since you are so badly informed about math. So I'm not going to try.

I wish to leave this topic open for other discussions. So please do not respond to this thread anymore. I will consider it a thread hijack.
 
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  • #32
lendav_rott said:
These are examples from dear life outside the 4 walls. It makes no difference, I like to take examples from life - the logic behind it is all the same as if it were a math assignment.

In mathematics, terms are defined precisely enough for the logic to prove things with absolute certainty. We do not have this luxury in "life."

In real life examples you can use formal logic, but terms are not precisely defined and so argumentation is much sloppier. That's where informal logic is helpful (fallacies and other "thinking tools" to use Daniel Dennett's term).

Using real life examples to treat mathematical topics is like...is like... somebody help me out here. It's bad. Really bad.

Edit: Sorry to provoke lendav_rott any further as I do not wish to participate in thread hijacking.

My first sentence above I think is a pretty good contribution to the original post.

-Dave K
 
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