Why Does Natural Rubber Harden/Crystallize?

Doing some rewiring in our 84-year old house, I notice that the old wiring is insulated with cloth and rubber. the old insulation is quite brittle-if you bend the wire, the insulation will crack and break off. Why does natural rubber harden like this? is it a chemical reaction with oxygen. or is it a crystallization process?

It is a reaction with oxygen.