This view of curriculum runs far less risk of becoming obsolete before it is even
implemented. Difference equations may fall out of fashion,but the algorithmic
thinking behind their study certainly won’t. Even if the language of linear algebra
becomes less useful in the next century than it is now,the habit of using geometric
language to describe algebraic phenomena (and vice-versa) will be a big idea
decades from now. At the turn of the 20th century,the ideas and thought experiments
behind number theory (the decomposition of ideals into prime factors in
number fields,for example) was smiled upon as the pastime of a dedicated collection
of intellectuals looking for the elusive solution to the Fermat conjecture; at the
turn of the 21st century,even after it appears that Fermat is settled,these same
habits of mind that led to class field theory are at the forefront of applied research
in cryptography