The Arya Samaj was founded in the year

A socio-religious reform society is dated by the year in which its founder formally constituted it as an organised body — the act of establishment itself. The year his preaching, travels or writings began is a different thing and is not what such a date records. Every major nineteenth-century Indian reform society therefore fixes on one founding year, one named place and one named founder.

Applying that to this society: the Arya Samaj was the organised expression of Swami Dayananda Saraswati’s call of “Back to the Vedas”. Trained at Mathura by the blind ascetic Swami Virjanand, Dayananda formally established the Samaj at Bombay (now Mumbai) in April 1875 — 10 April 1875 is the date usually given. Its programme rejected idol worship, hereditary caste and child marriage, and promoted the shuddhi (reconversion) movement, Vedic education and education for women.

Placing it beside the other major reform societies fixes the position of that year in the sequence:

The movement’s own internal chronology cross-checks the same year:

• The first edition of Dayananda’s Satyarth Prakash appeared in 1875.

• The Lahore branch, which later became the Samaj’s principal centre, was set up in 1877.

• The first Dayanand Anglo-Vedic (DAV) school opened at Lahore in 1886.

Every one of these dates sits at or after 1875 and is consistent with an establishment in that year. The Arya Samaj was therefore founded in 1875.