How can I stop Downloading Messages on iMac Mail?

Has anyone had the problem of nonstop Downloading Messages on the iMac Mail program? When I open the Mail program, I see at the lower left corner a running count of Downloading Messages. The top number is in the thousands; invariably the number is never reached. Sometimes the count stops and a new count begins with a higher or lower top number. The count begins anew every time I open the program, either from a minimum or closed state.

I found numerous complaints of this type on the Internet, both on Apple and Window systems, and for different account types. It wasn’t clear if this was a problem or not. Can one simply ignore the Downloading Messages? Are any messages really being downloaded? Where do they reside?

In my case, the problem arose with an AOL account after I uninstalled and reinstalled to try to remedy another matter. I have a 2013 iMac running El Capitan 10.11.6.

Appreciate any thoughts,

Ed