Their importance first of all is that they lead to interesting deep problems of a completely new type; they have quite unexpectedly surprising consequences in many branches of mathematics - differential equations, numerical algebra, and various branches of function theory.
Ang kanilang kahalagahan unang ng lahat na sila ay humahantong sa mga kagiliw-giliw na malalim problema ng isang lubos na bagong uri; sila ay may hindi inaasahan kamangha-mangha kahihinatnan sa maraming mga sangay ng matematika - kaugalian equation, de-numerong algebra, at iba't-ibang sangay ng function theory.