Arthur Eddington's father, Arthur Henry Eddington, taught at a Quaker training college in Lancashire before moving to Kendal to become headmaster of Stramongate School. He died of typhoid in an epidemic which swept the country in 1884 before his son was two years old. Arthur Eddington's mother, Sarah Ann Shout, came from Darlington and, like her husband, was also from a Quaker family. On Arthur Henry Eddington's death she was left to bring up Arthur and his older sister with relatively little income. The family moved to Weston-super-Mare where at first Arthur was educated at home before spending three years at a preparatory school.
In 1893 Arthur entered Brymelyn School in Weston-super-Mare which was mainly for boarders but he did not board at the school, being one of a small number of day pupils. The school provided a good education within the limited resources available to it and allowed Arthur to excel in mathematics and English literature. His progress through the school was rapid and he earned high distinction in mathematics. The level to which the school was able to take Arthur was, however, not very advanced and his good grounding in mathematics stopped short of reaching the differential and integral calculus.
In 1898 he was awarded a scholarship of £60 a year for three years by Somerset County (Weston-super-Mare is now in Avon but it was at that time in Somerset). Eddington had not reached sixteen years of age at the time, and so officially he was too young to enter university. It was a problem which was solved quickly, however, and did not cause him to delay his entry to Owens College, Manchester which he attended from 1898 to 1902. In his first year of study Eddington took general subjects before spending the next three years studying mainly physics. Although on a physics course, Eddington attended the mathematics lectures, being greatly influenced by one of his mathematics teachers, Horace Lamb. Of course the financial position of his family meant that they were not able to provide him with financial support but his outstanding academic work allowed him to win a number of highly competitive scholarships to provide enough money to let him complete his B.Sc. course with First Class Honours in 1902.
He was awarded a Natural Science scholarship of £75 a year to study at Trinity College, Cambridge, near the end of 1901. Entering Trinity in 1902 he received, in March 1903, a Mathematics Scholarship of £100 a year instead of the Natural Science scholarship. At Trinity he was taught by E T Whittaker, A N Whitehead and E W Barnes. He became Senior Royal Society.
Shortly after taking up his role of leading astronomy research at Cambridge, World War I broke out. As we noted above Eddington came from a Quaker tradition and, as a conscientious objector, he avoided active war service and was able to continue his research at Cambridge during the war years of 1914-18. This was, however, not an easy time for him giving him a highly stressful period right at the beginning of his tenure of the Cambridge chair.
Eddington made important contributions to the theory of general relativity. His interest in this topic started in 1915 when he received papers by Einstein and by de Sitter which came to him via the Royal Astronomical Society (1924), The National Academy of Washington (1924), the French Astronomical Society (1928), and the Royal Society, he was elected to the Royal Irish Academy, the Russian Academy of Sciences, the Royal Society of London in 1926 when he lectured on Diffuse matter in interstellar space.
Plummer writes in :-
To his splendid equipment as a mathematical physicist he owed much ... A bold imagination was coupled with an exceptional knowledge of those features which are accessible to observation. ... To launch out into unknown seas, to be venturesome even at the risk of error, Eddington felt himself called, and the reward of the pioneer came to him. ... Simplicity and modesty were his outstanding characteristics ...
Eddington's achievements are summed up in  as follows:-
He was a gifted astronomer whose original theories and powers of mathematical analysis took his science a long way forward; he was a brilliant expositor of physics and astronomy, able to communicate the most difficult conceptions in the simplest and most fascinating language; and he was an able interpreter to philosophers of the significance of the latest scientific discoveries.