Hello, evolutionary biologists!
We do know that elephants have very long memory but probably they do not themselves remember how they evolved those ears and for what purpose. Neither do we.
So let us study and work towards a scientific theory that would explain to our satisfaction how elephant ears have evolved and for what purpose..
The more brave ones among the evolutionists will even use the active expression "Elephants have evolved their ears for the purpose of..."
Less brave scientists do not think that animal species actively evolved anything. It is generally assumed that all the features of an elephant are the product of many natural processes and have a given logic that operates on random genetic mutations as the living raw material in a specific natural environment.
The evolution of elephant and its ears, trunk, tooth and all the rest of this amazing animal has taken millions of years.
"The earliest known ancestors of modern-day elephants evolved about 60 million years ago. The ancestor of the elephants from 37 million years ago was aquatic and had a similar lifestyle to a hippopotamus." (wikipedia)
The evolutionary explanation of elephant ears should be something that can reasonably be assumed to have helped the species in nature's ongoing fight for survival. For this it is necessary to figure out what could be the practical advantage of having such nice big ears.
The theory explaining the evolution of elephant ears should help us understand the differences in the ear sizes of modern Indian (Elephas maximus) and African (Loxodonta) elephant species.
Of course, it would be very important also to define what changing environmental factors have been at play in elephant ear evolution. What would be the best angle to explain in a systematic and rational way the strange growth of elephant ears? They are (according to my limited knowledge) quite unique among the known animal species that have ever been living on this planet.
Dwarf elephant skull
The theory would be crowned by the discovery of fossil evidence demonstrating many ear size and shape variations to show from what kind of ear(s) the evolution started and to prove the existence of mutant variations from which natural laws gradually selected the most fitting ear model for the animal.
Unfortunately to science, softer parts of organisms do not survive well when buried underground or at the bottom of lakes so much of the study must be based on bony skulls of elephants and their ancestors - perhaps the skull features can tell something about the changes in the ears?
Luckily for science some of those enormous mammoths were buried swamps and deep muds and frozen under Siberia's extreme climate. Perhaps study of mammoth ears can suggest something about the evolution of elephant ears?
Take the role of God of Israel, the Creator of the world, and design the head of a woodpecker so that it does not get head injury when looking for wood. Its head moves about 6m/s (20ft/s) at each peck enduring a deceleration more than 1,000 times that of gravity.
(For one recently suggested solution to this difficult task you may take a look at the work of Ming Zhang of the Hong Kong Polytechnic University here)
Take the role of God of Israel, the Creator of the world, and describe how to use the lathe of environmental change and natural selection to create such a head for the woodpecker.
(If you figure out a reasonable solution, you can send it for review to Science or Evolutionary Biology as a pioneer researcher of the subject.)