Why Do People Misunderstand Mathematical Proofs of Nonexistence?

  • Context: Graduate 
  • Thread starter Thread starter 1MileCrash
  • Start date Start date
Click For Summary
SUMMARY

The discussion centers on the misunderstanding of mathematical proofs of nonexistence, particularly in relation to quintic polynomials and prime numbers. Participants assert that mathematical statements of nonexistence are often misconstrued by the general public as mere indications of unproven possibilities. The conversation emphasizes that mathematical truths are derived from axioms and are not subject to empirical validation, contrasting mathematics with other disciplines that rely on observational evidence. The conclusion drawn is that without proof of existence, a mathematical entity is considered nonexistent.

PREREQUISITES
  • Understanding of mathematical axioms and theorems
  • Familiarity with the concept of nonexistence in mathematics
  • Knowledge of quintic polynomials and their properties
  • Basic principles of mathematical proof and logic
NEXT STEPS
  • Research the implications of Galois theory on quintic polynomials
  • Study the concept of mathematical proof and its philosophical underpinnings
  • Explore the relationship between axioms and theorems in mathematics
  • Investigate common misconceptions about mathematical existence proofs
USEFUL FOR

Mathematicians, educators, philosophy students, and anyone interested in the foundational principles of mathematics and the nature of mathematical truths.

  • #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.
 
Mathematics news on Phys.org
  • #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
 
  • Like
Likes   Reactions: 1 person

Similar threads

  • · Replies 33 ·
2
Replies
33
Views
8K
  • · Replies 2 ·
Replies
2
Views
669
  • · Replies 0 ·
Replies
0
Views
2K
  • · Replies 70 ·
3
Replies
70
Views
18K
  • · Replies 333 ·
12
Replies
333
Views
19K
  • · Replies 22 ·
Replies
22
Views
5K
  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 26 ·
Replies
26
Views
3K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K