What is so special about Arnold's Trivium? I have read from Experimental Mathematics by V. I. Arnold that if someone wants to study with Vladimir Arnold, they must solve Arnold's Trivium first in order to "understand mathematics". Arnold himself had said that solving the Trivium was a way to truly understand mathematics.
Why? What does Arnold mean with "truly understand mathematics"? 

(Too long for a comment.)  Quoting author's motivation from the source (page 2 of the linked pdf):

In  Feynman's  words,  these students  understand  nothing,  but  never  ask  questions, so  that  they
  appear  to understand  everything. [...] The  students  reach  a  state of  "self-propagating  pseudo-education"  and  can teach  future
  generations in  the same way.  But  all  this  activity  is completely  senseless,  and  in  fact  our  output  of
  specialists is to  a  significant  extent a fraud,  an  illusion  and  a sham:  these so-called specialists are not
  in  a position  to  solve  the  simplest  problems,  and  do  not  possess the  rudiments  of  their  trade.
Thus, to put  an end to  this spurious enhancement of  the results, we  must  specify  not  a  list  of
  theorems, but  a collection of problems  which students should be able to solve.  [...] The  compilation  of  model  problems  is  a laborious job,  but  I think  it  must  be  done.  As  an  attempt
  I  give  below  a list  of  one hundred  problems  forming  a mathematical  minimum  for  a physics  student.

