36. [20] Order any subset of the following twentieth century mathematical achievements chronologically, from earliest to most recent. If you correctly place at least six of the events in order, your score will be $2(n-5)$, where $n$ is the number of events in your sequence; otherwise, your score will be zero. Note: if you order any number of events with one error, your score will be zero.
A). Axioms for Set Theory published by Zermelo
B). Category Theory introduced by Mac Lane and Eilenberg
C). Collatz Conjecture proposed
D). Erdos number defined by Goffman
E). First United States delegation sent to International Mathematical Olympiad
F). Four Color Theorem proven with computer assistance by Appel and Haken
G). Harvard-MIT Math Tournament founded
H). Hierarchy of grammars described by Chomsky
I). Hilbert Problems stated
J). Incompleteness Theorems published by Godel
K). Million dollar prize for Millennium Problems offered by Clay Mathematics Institute
L). Minimum number of shuffles needed to randomize a deck of cards established by Diaconis
M). Nash Equilibrium introduced in doctoral dissertation
N). Proof of Fermat's Last Theorem completed by Wiles
O). Quicksort algorithm invented by Hoare
Write your answer as a list of letters, without any commas or parentheses.
Answer: IAJCBMHODEFLNGK The dates are as follows:
A). Axioms for Set Theory published by Zermelo 1908
B). Category Theory introduced by Mac Lane and Eilenberg 1942-1945
C). Collatz Conjecture proposed 1937
D). Erdos number defined by Goffman 1969
E). First United States delegation sent to International Mathematical Olympiad 1974
F). Four Color Theorem proven with computer assistance by Appel and Haken 1976
G). Harvard-MIT Math Tournament founded 1998
H). Hierarchy of grammars described by Chomsky 1956
I). Hilbert Problems stated 1900
J). Incompleteness Theorems published by Godel 1931
K). Million dollar prize for Millennium Problems offered by Clay Mathematics Institute 2000
L). Minimum number of shuffles needed to randomize a deck of cards established by Diaconis 1992
M). Nash Equilibrium introduced in doctoral dissertation 1950
N). Proof of Fermat's Last Theorem completed by Wiles 1994
O). Quicksort algorithm invented by Hoare 1960
so the answer is IAJCBMHODEFLNGK.