Why would there be a huge field of corn and have 3 trees in a row right down the middle? ?

In addition to all of the answers already provided, all of which are totally viable, they could have been set out as a memorial to some person or event.  There may be a cemetery around them.  They could be used as a marker of some sort for air traffic.

My favorite answer, aside from my own, is the one about being a rest area for the farmer working the field.

the trees were probably there long before the owner wanted a corn field. why not let them grow?? probably a nice place to take a break from plowing, planting and harvesting.

Because this was where they just tried to legalise stealing police vehicles.

It wasn't always a corn field.Something else stood there or its a visual marker on the property.Sounds neat.

Maybe the land owner didn't want to see the trees destroyed. 

Two fields have been combined to make a bigger field at some point in the past 80 years or so.  Like a previous answerer has stated mature trees are a lot of work to remove so they often get left behind.  It's a fairly common sight in areas with old crop land as changes in technology have changed the size and shape of the ideal field.

I went to a boarding school in the 70's. It was surounded by corn fields.  And WE know that every 18 corn plants had a Pot plant in that spot. All you needed to do was to count. 

I suppose the trees were there before the corn was.  Trees are difficult and expensive to remove, and their roots make it impossible to plow the ground unless you get those roots out (which go deep and wide).

It is possible they were associated with bottom land.  A low spot which was holding water.  Leaving the trees provide a habitat for animals depending on the bottom-land.  The boggy soil is unsuitable for corn.