Sum of Two Cubes Activity Sheet

Ken Keeler has a PhD in applied math from Harvard.
When he was finishing up, there were very
few jobs, so he applied to both academic and TV writing jobs. After a
year at Bell Labs, he decided to try TV writing. In a gotfuturama.com (CGEF)
interview, when he was asked about his many years at school, Ken Keeler
joked that a
*Futurama* reference to 1729 was worth six years of grad
school:

Keeler refers to the episode *Xmas Story*
[2ACV04] written by David X. Cohen
in which Bender the robot receives a card from the machine that
built him wishing "Son #1729" a Merry Christmas.
**Answer the following questions on a separate sheet of paper.**

**Question 1** Use an effective
web search to find out what Ken Keeler means when he says that
1729 is "a historically significant integer to mathematicians everywhere."
Your answer should include information about the mathematicians
Ramanujan and Hardy and a calculation statement about the
number 1729.

**Question 2**
Verify that the related computation statement holds, but do not
prove that it is the smallest
such number. Show work. Next discuss a general proof method or
technique one could use to
show that 1729 is the *smallest* such number
but do not prove the statement.

Ken Keeler says that, "We didn't have the agenda of putting a
mathematical reference in there, other than that we needed a number for plot
reasons. We could have picked one at random, but there was no reason not
to make it an interesting one, and that's how many of these references found
their way in."
The number 1729 also appears in many episodes of
*Futurama*
on the hull of the space ship called the Nimbus
and as the reference number of the universe populated by "bobble head"
characters in the episode *The Farnsworth Parabox*
[4ACV15].

**Question 3**
Search the web to find
recent results about the sum of two cubes
(within the last five years)
and summarize what you found.

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