Talbot was born in Melbury House in Dorset and was the only child of William Davenport Talbot, of Lacock Abbey, near Chippenham, Wiltshire, and his wife Lady Elisabeth Fox Strangways, daughter of the 2nd Earl of Ilchester. His governess was Agnes Porter who had also educated his mother. Talbot was educated at Rottingdean, Harrow School and at Trinity College, Cambridge, where he was awarded the Porson Prize in Classics in 1820, and graduated as twelfth wrangler in 1821. From 1822 to 1872, he communicated papers to the Royal Society, many of them on mathematical subjects. At an early period, he began optical research, which later bore fruit in connection with photography. To the Edinburgh Philosophical Journal in 1826 he contributed a paper on "Some Experiments on Coloured Flame"; to the Quarterly Journal of Science in 1827 a paper on "Monochromatic Light"; and to the Philosophical Magazine papers on chemical subjects, including one on "Chemical Changes of Colour".