[1][2][3] He was born to Edward Birmingham and Elly Bell[2] and grew up on the Millbrook Estate outside Milltown, County Galway and was educated at St Jarlath's College in Tuam.

He first attracted attention with his articles on sedimentary rocks in the west of Ireland which he contributed to the Journal of the Geological Society of Dublin.

At Millbrook he built what The Tuam Herald called a large wooden house with a sliding roof, which formed his first observatory.

[4] In 1866, he wrote an essay about the disappearance of a crater on the surface of the Moon and the subsequent appearance of a vast luminous cloud in its place.

In its review of the essay, The Irish Times commented: “We know of no paper which contains an equal amount of learning in so brief a space, in so charming a style and manner, and stamps him as a man of learning, eloquence and refined taste combined with genius.” In 1883, the Royal Irish Academy presented Birmingham with a gold medal for his valuable contributions to the society's transactions.

Birmingham Lunar Crater is located near the northern limb of the Moon, and so is viewed from the Earth at a low angle.

All that survives of the original formation is an irregular perimeter of low, indented ridges surrounding the lava-resurfaced interior.