(Math) How would you respond?

1. Jun 11, 2014

1MileCrash

"There is no algebraic formula for the roots of a general quintic polynomial."

R: "That we KNOW of."

"No, we can confirm that one does not exist."

R: "But that's according to our current knowledge."

I just changed the topic since the quintic thing was an analogy, but this misunderstanding troubled me.

What would be a fitting response? I suppose a response is that all of our "current knowledge" is also developed through mathematical proof, and thus any result derived from our "current knowledge" cannot be nullified by "further knowledge" as this would require that our axioms have an underlying inconsistency. But I suspect this response would not satisfy someone who did not study mathematics.

Statements of nonexistence in math seem to be taken as "we haven't found it yet" by the general populace. Why is that?

2. Jun 11, 2014

micromass

Staff Emeritus

"Are there any prime >2 that are even?"

If he says "No", then proceed telling him that that's due to our current knowledge and maybe later knowledge will reveal one. If he protests, then use this protest against him and tell him it's exactly the same with the quintic polynomial case.

Now, if he does agree that we might someday find a prime >2 that is even, then I would just stop arguing with him as it's useless.

(Or go for something simpler: are there any squares that are circles or are there any even numbers that are odd)

3. Jun 11, 2014

ModusPwnd

Math is unlike most or all other intellectual endeavors. Math is built upon axioms that are assumed for the sake of the math. Theorems derived under these axioms are (if derived correctly) air tight since the logic follows and the axiom is assumed or taken for granted. There is no empirical requirement to substantiate the axioms. In other endeavors the axioms (or postulates) are always subject to change or refinement since there is a requirement of empirical substantiation. If new observational evidence is found the postulates themselves change which is what "we haven't found it yet" assumes can or will happen. This will never happen in math since observational evidence doesn't change the axioms a theorem has been derived under. (Though it might inspire new axioms under which new theorems could be derived.) The general population doesn't, in general , make this distinction.

Last edited: Jun 11, 2014
4. Jun 11, 2014

Staff: Mentor

Making a mistake doesn't stop those making it from reproduce.

As opposed to eating cyanide or jumping from the roof.

5. Jun 11, 2014

Staff: Mentor

Because for every other field this is a perfectly normal thing to hear and the majority of people aren't educated in mathematics. Sure they may have gone through a bit at school but that just covers the basics, none of the theory and for many was a long time ago.

6. Jun 11, 2014

AlephZero

Even eating cyanide or jumping from the roof doesn't stop you reproducing, if you do things in the correct order

7. Jun 11, 2014

leroyjenkens

I used to jump off the roof all the time when I was a kid. Jackie Chan was a bad influence on me. But that didn't stop me from reproducing. Other things have stopped me from reproducing, such as being the kind of loser who jumps off roofs.

8. Jun 11, 2014

DennisN

9. Jun 12, 2014

disregardthat

Just explain that it's logically impossible. If we were to find one, then we would have a logical contradiction on our hands.

10. Jun 17, 2014

jmeps

If it is understood that the world of mathematics is:
1. Purely a product of the mind.
2. Coupled with the observational power of "man".
3. And used as a tool for predicting and explaining.
Then no response is required. Other than the person does not understand 1,2,or 3.

11. Jun 18, 2014

lendav_rott

Statement
"There is no formula to generate primes indefinitely."

Counterargument
"Oh you are just saying that cuz it's not been discovered yet"

Defense
"It's been proven many times over that it can't be done"

Ignorance
"Ohhh, you are so shortsighted, I'll soon have my own spaceship that goes faster than the speed of light"

Irritability
"GRRRRRRRRRRRRR XXXXXX SSSPPFFFFF!!!@!@!@!@ %%$^$&&*\$*I"

If there is a statement of existence - then prove it DOES exist. Do not defend the argument with something like "oh? Prove it doesn't exist, then"

If there is no proof of existence - then it does not exist.
If there is proof of non-existence, then it does not exist.

Simple math

Last edited: Jun 18, 2014
12. Jun 18, 2014

micromass

Staff Emeritus
Not sure if that's the best example since there are formulas to generate primes indefinitely. They're just not practical and simple. Who knows, maybe there is such a formula? I really doubt it has been proven that it can't be done.

Last edited: Jun 18, 2014
13. Jun 18, 2014

Staff: Mentor

What does it mean "formula"?

I mean, I guess P(i) - function that returns ith prime - doesn't count. But why it doesn't count, and what does?

14. Jun 18, 2014

1MileCrash

Going to have to disagree entirely on that one.

15. Jun 18, 2014

micromass

Staff Emeritus
Agreed. I completely missed that sentence. It's very very very wrong.

16. Jun 19, 2014

lendav_rott

Let's avoid a philosophical debate. I claim that without proof, something does not exist. The basis of that claim is that if something really did exist, well then it shouldn't be a problem to prove it.

Let's say we Claim that there is a civilization in another galaxy, millions of light years away from us and that there is a pack of oreos in someone's hand at this very moment. Doesn't have to be oreos even, cookies of some sort - similar to the composition of ours. Now, we can't prove it is the case, but we Could claim such a thing - mainly because we Know we can't prove this to be correct or incorrect for some time now. Until it is proven, such a thing does not exist, which would, of course, make this "If no proof, doesn't exist" a false one, but so far it's working for me, unless you can bend my faith - I understand why you say it's wrong, well, should have your hands full then.

17. Jun 19, 2014

Staff: Mentor

No. Without a proof we simply don't know if it exists or not.

18. Jun 19, 2014

lendav_rott

In that case we have the extremists on our case with the existence of god and whatnot.

19. Jun 19, 2014

micromass

Staff Emeritus
How could you possibly think that? I don't even know how to respond to that, it's just so illogical.

20. Jun 19, 2014

micromass

Staff Emeritus