It’s very difficult to date the invention of the bra. Does the mastodeton–the chest-binding worn by ancient Greek women while they were exercising–count as a bra? Maybe, maybe not. It depends on who you ask.
Most will agree the evolution of modern shapewear got going in the 19th century. However before the Victorian masterminds who applied their brainpower to this engineering challenge came up with the bra, there were a few false starts. Maybe they should have asked a woman?
Here’s an interesting infographic about the evolution of the brassiere from Herroom.