His father, Jules de Polignac (1780-1847) was prime minister of Charles X until the Bourbon dynasty was overthrown in the July Revolution of 1830.
Alphonse was born in London during his father's time as ambassador to the United Kingdom.
In 1849 he was admitted to Polytechnique and went onto serve in the Crimean War as an artillery officer, achieving the rank of Captain.
He was also a historian, a poet, a musician, and authored a translation of the play Faust by Goethe.
In his first year at Polytechnique Polignac formulated his eponymous conjecture, which states that: For every positive integer k, there are infinitely many prime gaps of size 2k.