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June 26th, 2014, 12:37 AM   #1
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How much bluffing is there in mathematics?

I am new to mathematics in the sense that I'm only starting to independently read books on higher maths, mostly mathematical logic and set theory. I came to math from philosophy, usually it's the other way around. I wanted to prove my philosophical arguments and I discovered that I had better find out how mathematicians prove their arguments. To my astonishment I found that many mathematical arguments are enormously slipshod. I have now become a very radical logician and reject many of the axioms that most logicians accept. Consequently, I have come to be quite skeptical of many mathematical arguments. The discussion I want to generate here is in your opinion how much bluffing goes on in the mathematics community? Let's describe what bluffing is:

x bluffs about y means x knows that x does not understand y and x says something so that z will believe that x understands y.

E.g. Jim bluffs about Godel's theorem means Jim knows that he does not understand Godel's theorem and Jim says something so that Ryan will believe that Jim understands GT.

Let's contrast bluffing with another form of intellectual fallacy: self-deception. Self-deception is like bluffing but not exactly.

x deceives themself about y means x believes x understands y but x never tests x to determine if x really understands y and x does not understand y.

E.g. I deceived myself that I proved the Continuum Hypothesis means I believe I understand the Continuum Hypothesis but I never tested myself to determine if I really understood the Continuum Hypothesis and I do not understand the Continuum Hypothesis.

I think self-deception is much more widespread than people are willing to admit. I have personal experience with self-deception because there have been numerous times when I wrote up all these logical symbols on paper and thought I had proven something and didn't bother to test them for months but then when I tried to get a computer to process the symbols it turns out that I had just built a house of cards.

I think there is a lot of self-deception in the mathematics community mostly because mathematicians are not forced to use their symbols to solve real world problems.
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June 26th, 2014, 04:06 AM   #2
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SELF-DECEPTION

Self-deception in maths could arguably fall into more than 1 category.


If you look at my first post on this thread :-

prove*

... you would see that I decieved myself into thinking I'd solved the problem HOWEVER I didn't mean to so I became decieved not by solely by intention but by my complacency and/or my own inadequacies. I don't feel I did anything morally wrong.


To decieve oneself deliberately I think is a different kind of self-deception.

BLUFFING

I've done that. Can't speak for other people.

Mathematician B says to Mathematician A, "I'll teach you about the Riemann Hypothesis, if you tell me that you understand Godel's Thereom".

Mathematician A knows he doesn't understand GT but knows that he doesn't need to to understand the Riemann Hypothesis and he really wants nothing more than to do so.

He replies (bluffs) :-

I do understand Godel's Theorem.

Mathematician B explains the Riemann Hypothesis.

30 years later Mathematician A solves it.

It seems to me that also worth asking is :

Is a mathemtician bluffing necessarily a bad thing ?
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June 26th, 2014, 05:46 AM   #3
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I think this is very common in some fields but quite rare in mathematics. Or rather, rare by actual practitioners of mathematics: there are plenty of cranks who can do nothing but bluff (in your terminology).
Thanks from Evgeny.Makarov
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June 26th, 2014, 07:57 AM   #4
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Yes, we are talking about science here, not complementary medicine, paranormal activity or religion. So as a result I'd expect bluffing to be relatively rare. It's not unknown though. But with scientific results being open to peer review, it quickly becomes obvious when someone is truly bluffing. And that would be highly damaging to their credibility as a scientist. Bluffing actually goes against the scientific method. In less professional circles, there is probably more bluffing, but to what extent that necessarily matters I couldn't say. Certainly, your example is about social morale rather than scientific morales, so one could suggest that it's not important to mathematics.

True self-deception where one believe that one has an answer to a problem (or understands a theory) is much more common. We see some of it on here (FLT recently, Goldbach Conjecture before that, geometrical constructions, etc...). I don;'t think it's about testing oneself. I think most people that are self-deceived are so precisely because they have looked hard at the problem and can't see how their solution might be wrong. The problem comes with a reluctance to accept and fully consider other people's views and weigh them honestly against their own convictions.

I've read in the past that older scientists are more prone to this, than younger ones. SO old discredited theories only usually die with the scientists that cling to them.
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June 26th, 2014, 11:02 AM   #5
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$10,000 USD, NOT bluffing

I think this is the perfect time for me to introduce this.

What IF, I am NOT bluffing?

Quote:
Originally Posted by CRGreathouse View Post
Actually they [origami] can give exact trisections -- though not exact quinquesections.
This is my Flickr page.

https://www.flickr.com/photos/859374...7636438514124/

I will wager 10,000 USD against anybody who can prove that origami can trisect an angle, and that origami "bested" Euclid.

If you win you win 10,000 USD.
If you lose, you lose 10,000 USD.



Who are you gonna believe? Me or Koshiro Hatori, of the so called Huzita–Hatori axioms.


Last edited by long_quach; June 26th, 2014 at 11:28 AM.
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June 26th, 2014, 12:55 PM   #6
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I don't think that I could prove that at this moment, but with a reward of $10,000 eminent I could probably learn the proof in an hour or two. But who would judge the outcome?
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June 26th, 2014, 12:56 PM   #7
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Quote:
Originally Posted by bobsmith76 View Post
To my astonishment I found that many mathematical arguments are enormously slipshod.
In actual mathematical articles and even monographs, proof are often substantially abbreviated. These proofs become audience-dependent: they aim to convince people who have a lot of experience in a certain field and can "feel" what is right. Further, there are some areas of mathematics where writing detailed proofs is practically impossible (for example, Hilbert-Bernays derivability conditions in the proof of the second Gödel's incompleteness theorem). In such situations a mathematician usually writes an outline and does some hand-waving hoping to convince other mathematicians who have a lot of intuitions about how things work. To an outsider, such level of details may seem completely insufficient.

I believe that referees of conference papers seldom check all calculations, and it comes down to authors' responsibilities for their results. If mistakes are discovered in several published results, the credibility of such researcher would be damaged.

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Originally Posted by bobsmith76 View Post
I have now become a very radical logician and reject many of the axioms that most logicians accept.
Many? May I ask which axioms?

Quote:
Originally Posted by bobsmith76 View Post
I have personal experience with self-deception because there have been numerous times when I wrote up all these logical symbols on paper and thought I had proven something and didn't bother to test them for months but then when I tried to get a computer to process the symbols it turns out that I had just built a house of cards.
What do you mean by processing the symbols on a computer: numerical calculations? In my experience, writing a proof on paper is a good method of finding mistakes, but it depends on the level of detail. Sometimes it is necessary to take a deep breath and to start writing at a more detailed level that I'd like.
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June 26th, 2014, 01:02 PM   #8
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Quote:
Originally Posted by Evgeny.Makarov View Post
I believe that referees of conference papers seldom check all calculations
Yes. Papers submitted for publication in journals are checked pretty carefully, but conference proceedings are given little more than a sanity check.
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June 26th, 2014, 01:07 PM   #9
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But who would judge the outcome?
If possible, somebody should sponsor this contest. The Bill and Melinda Gates foundation or something.

I nominate the makers of GeoGebra to be the judges. I cannot think of anyone more qualified.

Last edited by long_quach; June 26th, 2014 at 01:18 PM.
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June 26th, 2014, 01:11 PM   #10
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Quote:
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I don't think that I could prove that at this moment . . .
This is the so called proof.

https://www.math.lsu.edu/~verrill/origami/trisect/
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