493:. Namely, "to prove" something in the common mathematical sense is to establish its truth, but in another sense "to prove" something is to test its truth or quality (as in "a proving ground" or "proven reserves of oil"). More often than not, the adage is taken to mean "the rule is true despite the counter-example"--or absurdly, "the rule is true because of the counter-example". But in fact it means "the counter-example puts the rule to the test". Thus I agree that the use of the adage is inappropriate here--but it would make for a nice ...(idiom) page!
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a statement, believed to be true, that has amassed a reasonable amount of compelling theoretical and experimental (yes, mathematical experimental) evidence to support it. You just don't go spouting off anything you want in number theory, "I think this sequence satisfies...blah, blah, blah" You better have a lot of evidence or no one is going to take you seriously. For a better explanation of this, you can see Daniel Shanks number theory book, he has a long discussion of this topic.
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In the article, it says, "Until recently, the most famous conjecture was Fermat's Last
Theorem." Really? I would have thought that the Riemann Hypothesis was much more famous, at least amongst mathematicians. Furthermore, a proof of the Riemann Hypothesis would lead to a lot of light shed on a lot
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Even more ironically, this correction is also incorrect. The meaning of "the exception proves the rule" is probably best seen in an example: a traffic sign that says "Only emergency vehicles may park here" is equivalent to a rule "No parking here - except by emergency vehicles". The exception - which
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Some comments on "hypothesis"...I tend to blaze in and make changes without thinking through the best way to present or justify them to people. "Hypothesis", strictly speaking, refers to one of the assumptions in a logical argument or mathematical proof. ("Are the hypotheses sufficient?", "One of the
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This article gives the impression that (forgive the expression) "anything goes", i.e. anything can be a conjecture, because if we don't know if it's true or not, why not?? This is really not accurate. One cannot go around saying anything and everything under the sun is a "conjecture". A conjecture is
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would ever be is a redirect here. That doesn't make sense. Another thing is that redirects are not obvious and having the article at a parenthetical title will mean that new contributors will be typing the unnecessary . Isn't one of the founding principles of our naming conventions the preservation
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true or false. In other words, RH is either true or false (unless it ends up depending on GCH or something, heaven forbid), the twin prime conjecture is either true or false, Poincare conjecture is either true or false. The statement "R is an integral domain" is not like this. It's conditional,
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is an integral domain", "Without the hypothesis that the space is compact, the conclusion may be false", etc., etc.) This isn't really the same thing as "conjecture". Conjectures aren't necessarily assumptions in a logical argument or proof; they're simply statements which we don't know whether
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I know I've heard something at least similar many times. The only way I can make sense out of it is if the exceptions are are made explicit in the rule (and proved to be the only exceptions). This -is- legitimate in mathematics, at least to my understanding. I'm always forgetting to sign my
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All mathematicians have heard of both Fermat's last theorem and the
Riemann hypothesis, so there's nothing to choose between them in terms of fame in mathematics, and importance to mathematics has nothing to do with fame. In any case, the article doesn't say it was the most famous among
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What is there to say about these conjectures? Would the alternate articles be anything other than dictionary definitions? How are these other conjectures substantially different from "a proposition that is unproven but appears correct and has not been disproven"?
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of other theorems, whilst at least to me it seems that Fermat's Last
Theorem has much less applications. Riemann Hypothesis seems to be more 'mainstream mathematics', whereas FLT seems to be a bit less important in regards to the progress of mathematics.
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I just spoke to Larry and he says there isn't a term in philosophy called conjecture that could be made into an encylcopedia article. I will move the entry back to the simple title. There is no need to disambiguate when there isn't a valid ambiguity.
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The problem with that expression is I think it is too vague and non-mathematical to start with. I am not sure it is worth thinking that much about it. I would actually not mind removing it from the article altogether. What do you think?
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depending on what R is. "Suppose f is entire" is not a true/false statement, it depends on f. This is why calling conjectures "hypotheses" rings false for me. One reason, say, CH is called as it is, is because it is exactly that -- a
423:, i.e. in the world of set theory, you can take it to be true or false; it's your choice. In this sense, it's not "true" or "false" in the sense that we consider a conjecture to be true or false (but don't know yet).
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But how does one decide what is the most famous theorem? It changes over time as well. Clearly FLT's fame has decreased since it has been solved, but the
Riemann Hypothesis still retains that 'mysticism'.
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Would this be anything other than a dictionary definition. How is a scientific conjecture substantially different from "a proposition that is unproven but appears correct and has not been disproven"? —
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372:. So just because there is a dictionary definition doesn't mean that we must pre-emptively disambiguate from that term. Now that is just silly. If this article is at a parenthetical title then all
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For this reason soon I am going to move the whole page about mathematical "Conjecture" to entry "Conjecture (mathematics)" and change the "Conjecture" entry into a disambiguation page.
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333:.Also a conjecture means that a guess that is maybe ture. Like for example if a odd number minus an even numer is the answer even or odd?the answer is odd. See this is what it means.
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I'm not a mathematician and have heard of Fermat's theorem and not of
Riemann's hypothesis. However, any statement about "most famous" needs a reference, so I put a tag there.
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Hm. The term "Jesus Christ" has an alternate dictionary definition in slang usage that differs from the meaning in this article. I propose we move the article on the person to
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Knowledge. If you would like to support the project, please visit the project page, where you can get more details on how you can help, and where you can join the
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IF there is no proff then we can conclude that the funtion in question is indeed a
Logarithm function, meaning the funtion takes the form of a Logarithm.
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is the real
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Unlike the empirical sciences, mathematics is based on provable truth; one cannot apply the adage about "the exception that proves the rule".
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The adage does exist, but ironically it is almost universally misunderstood. The problem is the ambiguity of the
English verb "to prove"
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I do tend to think too much about trivial things. I would say either leave it as it is or remove it. I wouldn't try to "fix" it. --
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where it is used in terms of scientific conjecture, but only covers mathematics. Could someone please add the meaning in science. ..
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is the collatz conjecture verified up to 2.88 Ă— 10^18 like indicated in its own article or up to 10^12 like said here?
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Why does this need to be renamed? Other than dictionary definitions I'm not aware of any other use of the term. --
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Hm. Perhaps. But what more than a simple definition can be written on this subject? Maybe we should ask Larry. --
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Again, I hate this type of pre-emptive disambiguation. This is an encyclopedia and in that content we
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I heard this saying about the exception that proves the rule many times before. I think it is real.
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mathematicians, but in general, and (though I have no source) I'm pretty sure this is correct.
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There is a need for disambiguation here (rhetorical conjecture, textual conjecture etc.)
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is explicit - proves the existence of the general rule ("no parking") - which is not.
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is not there at all. Maybe speculated considering Numbers. But Ordinal by right
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they're true or false. Even worse, conjectures tend to be statements that are
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I am not familiar with this adage. Is it real? (user did not sign)
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comments. I made the original question sometime earlier today. --
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of free-linking where ambiguities do not exist (such as here)? --
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need concern ourselfs with disambiguating encyclopedic terms.--
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This Article lacks, coz' for the reason that referencing for
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I disagree with mav's conclusion. See my user talk page. --
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What part of the article (if any) are you talking about? -
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I may see this as Time Function, that's where I felt this
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Philosophers would certianly want a different article...
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