Crab: Well, it was this way. This fellow Najunamar had apparently never
had any formal training in mathematics, but had instead worked out
some of his own methods for deriving new truths of mathematics.
Some of his discoveries defeated me completely; I had never seen
anything in the least like them before. For instance, he exhibited a map
of India that he had managed to color using no fewer than 1729
distinct colors.
Achilles: 1729! Did you say 1729?
Crab: Yes-why do you ask?
Achilles: Well, 1729 is a very interesting number, you know.
Crab: Indeed. I wasn't aware of it.
Achilles: In particular, it so happens that 1729 is the number of the taxicab
which I took to Mr. Tortoise's this morning!
Crab: How fascinating! Could you possibly tell me the number of the
trolley car which you'll take to Mr. Tortoise's tomorrow morning?
Achilles (after a moment's thought): It's not obvious to me; however, I should
think it would be very large.
Tortoise: Achilles has a wonderful intuition for these things.
Crab: Yes. Well, as I was saying, Najunamar in his letter also proved that
every even prime is the sum of two odd numbers, and that there are no
solutions in positive integers to the equation
for n = O.
Achilles: What? All these old classics of mathematics resolved in one fell
swoop? He must be a genius of the first rank!
Tortoise: But Achilles-aren't you even in the slightest skeptical?
Achilles: What? Oh, yes-skeptical. Well, of course I am. You don't think I
believe that Mr. Crab got such a letter, do you? I don't fall for just
anything, you know. So it must have been YOU, Mr. T, who received
the letter!
Tortoise: Oh, no, Achilles, the part about Mr. C receiving the letter is quite
true. What I meant was, aren't you skeptical about the content of the
letter-its extravagant claims?
Achilles: Why should I be? Hmm ... Well, of course I am. I'm a very
skeptical person, as both of you should well know by now. It's very
hard to convince me of anything, no matter how true or false it is.
Tortoise: Very well put, Achilles. You certainly have a first-class awareness
of your own mental workings.
Achilles: Did it ever occur to you, my friends, that these claims of
Najunamar might be incorrect?
Crub: Frankly, Achilles, being rather conservative and orthodox myself, I
was a bit concerned about that very point on first receiving the letter.
In fact, I suspected at first that here was an out-and-out fraud. But on
second thought, it occurred to me that not many types of people could
manufacture such strange-sounding and complex results purely from
their imagination. In fact, what it boiled down to was this question:The Magnificrab, Indeed^551