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/sci/ - Science & Math

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9957272 No.9957272 [Reply] [Original]

Why do mathematicians insist on having proofs of all results? A case in point is Cleo on math stackexchange. Cleo regularly is able to come up with values of complicated integrals faster than any one else, but because she does not post a proof, people say that her results are useless or disrespectful. In fact all proofs depend on axioms, so if a result is known to be true, one should just work in an axiomatic system that accepts it as an axiom. I prefer this approach when I know the result. Therefore, Cleo in fact gave full proofs. It is like Bertrand Russell says about the First Cause argument:
" If everything must have a cause, then God must have a cause. If there can be anything without a cause, it may just as well be the world as God, so that there cannot be any validity in that argument. There is no reason why the world could not have come into being without a cause; nor, on the other hand, is there any reason why it should not have always existed. There is no reason to suppose that the world had a beginning at all. The idea that things must have a beginning is really due to the poverty of our imagination. Therefore, perhaps, I need not waste any more time upon the argument about the First Cause. "

>> No.9957283

Math Stackexchange exists to help people who are trying to educate themselves and improve their own math skills. Just giving them an answer and not showing the method completely defeats the purpose a lot of the time.

>> No.9957289

>>9957272
i wish it was for this reason: because the proof is evidence of the reasoning, it literally paves new paths of reasoning in a persons brain. they are thirsty for the idea and jealous that others know a good path that is secret to them.

realistically it is because people are jealous and spiteful and if they can't prove they're better than someone by actually outperforming they will diminish their greatness by nitpicking their work and thoughts for their form.

cleo sounds based a.f. giving fruits from their great table but only inviting the worthy to dine with them. are you sure its a she? i'm seriously smitten by your description from them.

>> No.9957314

If that's black to move then A5 wins on the spot, if it's white to move then a stalemate by moving the king is the best he can do

>> No.9957467

>>9957272
>t. never heard of ramanujan

>> No.9957710

>>9957314
Nope, white to move and win.

>> No.9957737

>>9957272
Ok, so now you have new axioms that may or may not be consistent and are basing new proofs off those, and the problem repeats itself with anything new you want to prove. Are you going to prove other things or just assume what makes the most sense is true?
Now what is true or false mathematically is completely arbitrary, and there is no reason to even bother.
Go ahead and make your own system of mathematics and axioms, but don't expect anyone to take it seriously.

>> No.9957749
File: 178 KB, 1190x906, least intelligent comment of all time.png [View same] [iqdb] [saucenao] [google]
9957749

>>9957272
>In fact all proofs depend on axioms, so if a result is known to be true, one should just work in an axiomatic system that accepts it as an axiom. I prefer this approach when I know the result. Therefore, Cleo in fact gave full proofs. It is like Bertrand Russell says about the First Cause argument:
Funniest thing I've read all day. The Xtian shit at the end doesn't help.

>> No.9957774
File: 405 KB, 700x700, whince.jpg [View same] [iqdb] [saucenao] [google]
9957774

>>9957272
What a retarded post.

>> No.9957793

>>9957710
White can't win there

>> No.9957803

You'll understand when you find something you """think""" is true but turns out you were wrong. Only by careful proof construction can you be sure a statement is true.

>Cleo
the stack exchangers are butthurt, Cleo has a proof but doesn't supply it due to autism.

>>9957710
King to A3

>> No.9957815

>>9957793
chesslet

>> No.9957823

>>9957803
I mean B3

>> No.9957830

>>9957289
>Have great new way to reason.
>Don't share it with the world even if you could be compensated for it and given the fame for coming up with it.
>Don't help others reason better with your new algorithm and help improve the world.
>Call other people selfish and spiteful.
Okay, anon.

>> No.9957842

>>9957793
While indisputably wins you dipshit.

>> No.9957847

>>9957272
Either OP is Cleo trolling or OP is a genuine retard who misinterpreted Cleo's next level bants as a legit argument against proof. Cleo just want to take the time to write out a proof and she's not the only person to do that (google Sonnhard Graubner).
>There are many ways to prove this result. The easiest one is to work in an axiomatic system that accepts it as an axiom. I prefer this approach when I know the result. Therefore, the full proof is given here. I understand and accept that some people who are not willing to work in this axiomatic system may find my proof not useful for their purposes. In such a case it is perfectly okay to downvote my answers (downvote means "not useful"). I also invite them to post their proofs then. I would prefer not to go into this discussion anymore. My apologies to anyone who feels irritated by my answers. – Cleo
>Remember, you are not locked into a single axiom system. You may invent your own, whenever you wish — just use your intuition and imagination. - Cleo

>> No.9957885

>>9957823
>I mean B3

>Kb3, a5
Now what, nigga. White can't block both pawns

>> No.9957901

>>9957272
>result is known to be true, one should just work in an axiomatic system that accepts it as an axiom. I prefer this approach when I know the result.
It's like you don't even know what consistency is.
Can woman finally fuck off from Math? She clearly has no idea what math is about. It has never been about results.

>> No.9957907

>>9957885
>Kb3 a5
>Kc4 a4
>Kc5 a3
>Kb6 a2
>c7++
That doesn't work.
If black king moves away you gain tempo to move instead to Kd6 and Kc7 and promote with check for another tempo.

>> No.9957911

>she

What's more likely?
>Cleo is an autistic woman that got into and sticks with solving integrals.
>Cleo is a lonesome male larper that got into and sticks with solving integrals.

There aren't even many autistic women - autism is biologically speaking a condition that affects men. And while there are naturally ugly women who go into math and don't socialize, there are much more basement dwellers. Just comparing the odds, I'd assume the latter is more of a common thing than the latter. I might be wrong.

>> No.9957926

>>9957272
>durr what is the cause of god then? Checkmate natural theologians!
Jesus, the whole point of the argument is that an entity that could be described as the first cause is called god exactly because it has those unique properties. If """god""" has a cause, then it's not really god and you could just use the same reasoning to find the actual first cause, the real god. Eternal universe doesn't make sense because, by simple logic, the universe couldn't have made it to "the current state" because priorly existing eternal time makes it impossible for anything to "escape" that prior eternality.

>> No.9957930

>>9957272
>>9957926
Quoting russell is an embarrassment that should be avoided.

Also, he was an insufferable cunt:

https://www.google.com/url?sa=t&source=web&rct=j&url=http://www-groups.dcs.st-and.ac.uk/history/Extras/Russell_Euclid.html&ved=2ahUKEwjNs5mUjIjdAhXlx4MKHfSUDRsQFjAAegQIAhAB&usg=AOvVaw2ATZ0Fmt3P3L8daVyVbyhR

>> No.9957952

>>9957907
>Kb3 a5
>Kc4 a4
>Kc5 Kc7
White can stop only one pawn

>> No.9958009

>>9957930
Russel isn't wrong. Euclid's work has a lot of shortcomings from a modern perspective (including more serious issues pointed out by other mathematicians). I don't think Russel is punching down at Euclid, I think he is merely responding to the fact that Euclid was used as the standard geometry text for almost 2000 years when it shouldn't have been.
Mindlessly worshiping Euclid is an embarrassment.

>> No.9958045

>>9957952
not Kc5, but Kb5 with threat to sneak around via a6-a7 to promote. It's a clever composition.

>> No.9958062 [DELETED] 

>>9957314
>>9957710
>>9957793

this is a tablebase position. if it's white's move, white wins:
1. Ka5 Kc7 2. Ka6 Kb8 3. c7+ Kxc7 4. Kxa7 Kd7 5. Kb6 Kd6 6. b8=Q+ Kd5 7. Kb5 Kd4
8. Kc6 Ke4 9. Qb4+ Ke3 10. Kd5 Kd3 11. Qb3+ Kd2 12. Ke4 Ke2 13. Qb2+ Kf1 14.
Qh2 Ke1 15. Ke3 Kd1 16. Qd2#

if it's black's move then it's a draw:
[Event ""]
[Site ""]
[Date ""]
[Round ""]
[White ""]
[Black ""]
[Result ""]
[FEN "1k6/pP6/2P5/4p3/K7/8/8/8 b - - 20 16"]
[Setup "1"]

16... e4 17. Ka5 e3 18. Ka6 e2 19. c7+ Kxc7 20. Kxa7 e1=Q 21. b8=Q+ Kd7 22. Kb7
Qd1 23. Ka7 Qc1 24. Kb7 Qb1+ 25. Ka7 Qa1+ 26. Kb7 Qb1+ 27. Ka7 Qa1+ 28. Kb7
Qb1+ 29. Ka7 Qa1+ 30. Kb7 Qb1+ (draw by repetition)

>> No.9958063 [DELETED] 

>>9957793
>>9957815
>>9957842

Stockfish says otherwise faggot.

>> No.9958064

I just drew against Stockfish 9, holy shit.......

>> No.9958065

>>9957314
>>9957710
>>9957793

this is a tablebase position. if it's white's move, white wins:
1. Ka5 Kc7 2. Ka6 Kb8 3. c7+ Kxc7 4. Kxa7 Kd7 5. Kb6 Kd6 6. b8=Q+ Kd5 7. Kb5 Kd4
8. Kc6 Ke4 9. Qb4+ Ke3 10. Kd5 Kd3 11. Qb3+ Kd2 12. Ke4 Ke2 13. Qb2+ Kf1 14.
Qh2 Ke1 15. Ke3 Kd1 16. Qd2#

if it's black's move then it's a draw:

1... e4 2. Ka5 e3 3. Ka6 e2 4. c7+ Kxc75. Kxa7 e1=Q 6. b8=Q+ Kd7 7. Kb7
Qd1 8. Ka7 Qc1 9. Kb7 Qb1+ 10. Ka7 Qa1+ 11. Kb7 Qb1+ 12. Ka7 Qa1+ 13. Kb7
Qb1+ 14. Ka7 Qa1+ 15. Kb7 Qb1+ (draw by repetition)

>> No.9958081

>>9958065
>Ka5
Nigger are you fucking retarded?

>> No.9958087

>>9957289
the proof is oftentimes more important than the result. that's why we're so interested in the proof of collatz, but the actual yes/no answer to the conjecture is largely useless

>> No.9958089

>>9957930
>t. Guy who unironically recommends Euclid on forums.

>> No.9958152

>>9958045
>sneak around via a6-a7
That IS clever

>> No.9958166

>>9958089
I don't recommend euclid but Russell's criticisms are shallow, unfounded an unnecessarily toxic

>> No.9958184

>>9957272
>In fact all proofs depend on axioms, so if a result is known to be true, one should just work in an axiomatic system that accepts it as an axiom
But how do you know it's true without proof?

>> No.9958192

>>9957847
Kinda sounds like someone who just understands the solution intuitively and doesn't get why people keep demanding a proof for something so obvious. I mean, pretend that first quote is in response to someone asking for a proof that 1 + 1 = 2, which would take an incredibly involved answer.

>> No.9958194
File: 321 KB, 2000x1000, 12zx1g.jpg [View same] [iqdb] [saucenao] [google]
9958194

>>9958184
>But how do you know it's true without proof?
he doesn't know what an axiom is

>> No.9958204

>>9957926
>an entity that could be described as the first cause is called god exactly because it has those unique properties.
All you've really done there is make a definition, "we call 'god' whatever objects do not need causes." You still need to demonstrate existence and uniqueness, and moreover that this condition is equivalent to being whichever of the thousands of gods you are actually trying to show exists. Russell was saying there is no plausible basis for the former

>> No.9958592

>>9958204
You both missed the point and also tried to pull a strawman on me. Then you just straight out pulled some bullshit out of your ass. I'm not sure what you're trying to accomplish here, I don't think you're trying to bait me. I'm legitimately confused here. Am I dealing with an actually retarded person here?

>> No.9959168

>>9957272
>Why do mathematicians insist on having proofs of all results?

Because that's literally a mathematician's job. Without proofs it wouldn't be math.

Nobody gives a fuck about Stack Exchange.

>> No.9959411

>>9957272
The entire concept of proofs is foreign to me.

At what point is a proof required? Is a formal proof of the results of addition required or is it axiomatic?

>> No.9959436

>>9959411
different people have different requirements for rigour. Poincare has a pretty funny essay on this.

http://www-history.mcs.st-andrews.ac.uk/Extras/Poincare_Intuition.html

and really, mathematicians do things because they're fun. would you enjoy "proving" that 2+2=4? maybe, maybe not. But with the right definitions, it flows naturally:

define a successor function S such that S(x) is the number after x along with an identity zero. From here, the positive integers flow naturally, with S(0)=1, S(S(0)) = 2, etc. Define addition function A(x,y) = a + y = S(S(.(x times)...S(0))) + y = (S( ... (x times )... S(y))

From here, it is clear that 2 + 2 = S(S(0)) + 2 = S(S(2)) = 4

>> No.9959440

>>9959411
You can prove the results of addition.

There's this kind of weird thing where mathematicians talk about structures satisfying certain axioms but then also show that there is actually a way to construct that structure. So for example the real numbers are defined as the set of things satisfying certain axioms (for example commutativity of addition). There are somewhat involved constructions (Dedekind cuts, equivalence classes of Cauchy sequences, etc) including definitions of addition/multiplication on these which you can show satisfy the real number axioms. In everyday use though no one actually thinks of the real numbers like this. We just take the real numbers as the things satisfying the real number axioms.

>> No.9959447

Idgaf about a namefag from the masturbatory treehouse society that is stackexch, thanks.

>> No.9959459

>>9957911
>autism is biologically speaking a condition that affects men.
Shame to see a take like this with no reply. Here (You) go

>> No.9959484

>>9959459
I ignored that post because its basically saying "people say there's a solar eclipse today but statistically there's more days without solar eclipses than days with solar eclipses so therefore there is not a solar eclipse today and any evidence to the contrary is a lie QED"

>> No.9959531

Guys. Guys. Guys, listen. Guys. Listen, guys. I just proved the Riemann Hypothesis, guys. Ok, here it goes:
Assume the Riemann hypothesis as an axiom. Write down the statement of the hypothesis. QED. Where's my fields medal?

>> No.9959555

>>9959459
It was low tier b8.
This is too >>9959484

>> No.9959566

>>9958087
of course the proof is more important than the result, just like a bridge is more important than its towers. but its pretty disingenuous to ask a question and resent the correct answer, and to stretch the bridge metaphor, they found the right place to start the opposite span and you're mad they didn't build the whole bridge for you.

>>9957830
some people are so smart and reason so hard their reasoning exceeds their ability to explain it to lesser people. it is a gift from god and only a fool resents it.

>> No.9961118

>>9957272
The results are useless because proofs give hints on how to tackle similar problems. Also, without proofs, you can't know you're right. There's always the possibility that there's an exception to any rule that you believe to be true, but haven't proven. For example, people tried for hundreds of years to find the quintic formula. But it was later proven that no such formula exists. If morons like you were in charge, we'd just assume there was a formula and add it as an axiom and completely fuck up math.

>> No.9961141

>>9957272
>In fact all proofs depend on axioms, so if a result is known to be true, one should just work in an axiomatic system that accepts it as an axiom
This is a risky and unreliable way of going about constructing formal systems. If you "guess" a result to be true and then blindly add it as an axiom, you run the risk of creating a inconsistent system or simply creating unnecessary axioms which can be logically deduced from other established postulates. Remember, intuition =/= proof, so it is imperative that crucial statements which can have a profound meaning or use must have a reliable logical base on which it is deduced. Of course, some results can be obvious, but when it come to critical reasoning and rigorous formulation, you should be able to prove such a result in a critical and rigorous manner.

>> No.9962120

>>9957272
Most of Cleo's replies are to people asking if there's a closed form for the equations they're working on since they can't find one, or if there are cleaner ones. She provides. They're already working on finding the path there so I believe only the answer is needed and acceptable.
If you're not a complete retard you can make better guesses as to the paths to the correct or better answer.

>> No.9963870

>>9957815
>>9957842
Black promotes his pawn on his next turn, ...h2-h1(Q), and it is all over.
Did you just assume the board's orientation, you shitlord?

>> No.9963895

>>9957272
Alright you cunts, let's play it out
if Black moves first, Kc3
if White moves first, Kb3

>> No.9965435

>>9963895
E5 for black

>> No.9965486
File: 148 KB, 641x481, file.png [View same] [iqdb] [saucenao] [google]
9965486

>>9958065
>Ka7 to Ka5