What actually is the so called "Electromagnetic field"? Is it just a mathematical construct or Is it something more than that. i read something about Maxwell trying to explain the EM field by giving a physical mechanism as to how the ether might actually work but once the idea of ether was disregarded after michelson and morley experiment, this idea went down with it too. I am about to complete my graduation. Do i assume that i will learn about the nature of this "field" and how the EM force actually works "at a distance" or is it just mathematical abstractions, to explain what's going on more and more efficiently, all the way down?
PS: Am i asking a naive question? i mean, just like the fact that we cant imagine or percieve a fourth spatial dimension doesnt prove that it doesnt exist, is me trying to find what it would be like to hold or see some amount of field just wrong. Is this question just a result of me being human, trying to compare the kind of interactions that i have in my daily life like touching, holding and seeing and hearing stuff with the things nature has in store.
 A: The EM four potential is a physical field, not just a mathematical construct. Physics is built from mathematics but models what I like to call objective reality.
A: This is a really good question. What we really do know is that "forces exist". 
But, do fields exist? We don't really know if a single charge in the universe would actually create a vector in all points in space, with its corresponding potential. If we wanted to measure it, we would be introducing a measurement apparatus, made of matter, so forces would appear. We measure forces, not potentials.
So we can't know wether fields do exist or not, but... should we care? It's not relevant, they just work, and make sense, so they are a really useful mathematical tool.
A: EM waves exist around us. Starting from a fundamental charge, we can visualise the flow lines made by body hairs near charged body, also the flow lines made by iron filings and magnet experiment. Further by varying the charges, so the  electric field, we can induce the magnetic field in space and vis-versa. 
You may also refer original works of Maxwell for clearer understanding of how he has developed EM theory by basic scientific experiments.
