Who was the first person to cross the Brooklyn Bridge?

The first person to cross the Brooklyn Bridge was Emily Warren Roebling, the wife of the Chief Engineer, Washington Roebling. She was also critical to its construction.

Her father-in-law, Washington Roebling's father John Roebling, was originally the Chief Engineer, but he died not long after groundbreaking, when a collapse on the site crushed his toes, requiring amputation, which led to a deadly tetanus infection. So Washington Roebling inherited his father's job.

The younger Roebling also inherited some of his father's bad luck: he got a bad case of decompression sickness (also known as "cassion disease," or, more commonly, "the bends") while surveying the underwater cassions. Since he was bedridden during most of the bridge's construction, his wife Emily was required to speak to the workman on his behalf, and run messages between them. She had studied engineering and higher math, and so was able to provide crucial assistance over the 11 years until the bridge's completion.