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331:) 19:52, 2 February 2012 (UTC) Hardy lived 1877-1947 (not 1977-1947 as mentioned by you). Hardy & Wright published their observations actually in 1938 itself only (which is certainly prior to 1947). Their publication was reviewed by another author in 1939 and this can be checked in the Knowledge articles on both Hardy as well as Wright.--
426:. For benefit of people as obtuse as me it might (anyone want to second this?) also be cute to say that, now that we have Wiles's proof, Fermat's Last Theorem guarantees that the sum of two cubic positive integers is not cubic. (And actually I see the claim that Euler much earlier resolved the case n=3 of Fermat's Last Theorem.) --
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Currently the article states that, "J. A. Dardis found Ta(5) in 1994 and it was confirmed by David W. Wilson in 1999." This is my wording. Some sources seem to state that Dardis proved the number was Ta(5). I have yet to see the original source in
Personal Computer World magazine. It is possible that
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The statement "" makes little sense, since a probability is always based on a state of knowledge! Thus there is no such concept as "the real probability". (If we knew every detail of a throw of a die (position, velocity, exact shape of die, every detail of its air resistance, etc.), we could say with
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Ta(5) but was unproved until Wilson. Wilson's article cites works by Dardis so there are two likely situations, Wilson didn't know the result had already been proven by Dardis in PCW magazine or that Dardis only found the number but didn't prove it. The wording is currently such that the sentence
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Hardy thinks a number is boring and
Ramanujan explains to him that it is the smallest number that can be expressed as the sum of two cubes in two different ways. So why does it get called the Hardy-Ramanujan number rather than the Ramanujan number? The property was not discovered by Hardy.
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Ta(5) is not displaying properly. This looks as if it might be due to a bug in the underlying math display software. Swapping over the last two cubes of Ta(5), ie: changing "231518^3 + 331954^3" to "331954^3 + 231518^3", seems to re-enable the display and could be used as a temporary fix.
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The number Ta(3) does not match the exact definition of a taxicab number, since it is the second smallest number satisfying the definition of Ta(2). Maybe it can be endowed with a different identifier, e. g. Ta(2)*.
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347:) 18:38, 28 August 2012 (UTC) I have corrected this now, changed the year 1954 to 1938, based on the Knowledge article on Taxicab Numbers and the literature references cited therein.--
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339:) 18:23, 28 August 2012 (UTC) E. M. Wright's biographical article in Knowledge and the references cited therein may be referred for the needed information.--
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It would be helpful to know the origin of the name "taxicab number". I see no connection between a taxicab and this particular type of number.
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Would be nice to explain the relevance of being cubefree. Here's one ref that does:
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Consequently, the identifiers of all the following taxicab numbers Ta(k) for k : -->
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I found the answer. Apparently Dardis did prove Ta(5) in PCW. This is based on an
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Since Hardy lived 1977-1947, he can hardly have proved anything in 1954.
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Why is Hardy given credit in the naming of this number?
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