We moved into our hundred-year-old (somewhat neglected) house about 8 years ago. The first two years, during the hot humid days of summer, here came the black ants. They were huge! Curious that they were in no other room of the house than the second-floor bathroom and seemed to be coming from a storage area we hadn't yet got to for remodel, etc.
Because we had dogs, we wanted to poisons, etc., so did the cornmeal thing. Within a couple days, we saw no more. Next year, there they were again, but not quite as many as the year before. Repeated the process. Had nothing for the next several years after that. Then, I saw one or two this year and went right at it. NO MORE ANTS!
Hope this clean, safe way works for you.
I don't know if baking soda would work. A friend of mine moved into a new apartment with roaches (yuck!), and quickly got them under control with lines of baking soda around all walls, counters, etc., and her youngsters were safe as well. Might be worth a try for the ants if the cornmeal doesn't turn them off. I think they won't crawl through the baking soda.