John Greaves (1602 – 8 October 1652) was an English mathematician, astronomer and antiquarian.

Educated at Balliol College, Oxford, he was elected a Fellow of Merton College in 1624. He studied Persian and Arabic, acquired a number of old books and manuscripts for archbishop William Laud (some still in Merton College Library), and wrote a treatise (in Latin) on the Persian language. He travelled in Italy and the Levant from 1636 to 1640 and made a survey of the Great Pyramid of Giza.

He was Gresham Professor of Geometry at Gresham College, London, and Savilian professor of astronomy at Oxford University, and collected astrolabes and astronomical measuring devices (now in the Museum of the History of Science, Oxford). He was particularly interested in the study of weights and measures, and wrote a treatise on the Roman foot and denarius, and was a keen numismatist. In 1645 he attempted a reform of the Julian calendar, which was not adopted.

During the English Civil War he supported Charles I, who stayed at Merton College while in Oxford, but lost his academic positions at Oxford in 1647 through the animosity of Nathaniel Brent, Warden of Merton College and a Parliamentarian.

He was born in Colemore, near Alresford, Hampshire. He was the eldest son of John Greaves, rector of Colemore, and Sarah Greaves. His brothers were Nicholas Greaves, Thomas Greaves and Sir Edward Greaves, physician to Charles II.

His father ran a school for sons of the neighbouring gentry, where Greaves began his education. Aged 15, he went to Balliol College, Oxford between 1617–1621, gaining a B.A. degree. In 1624 he was the first of five newly elected Fellows of Merton College, becoming M.A. in 1628. He began to study astronomy and oriental languages, and especially the works of the ancient eastern astronomers. In 1630 Greaves was chosen Gresham Professor of Geometry at Gresham College, London. Through his predecessor, Peter Turner, he later met archbishop William Laud, the chancellor of Oxford University and Visitor (patron) of Merton College. Laud was keen to make English editions of Greek and Arabic authors, and Greaves' later travels abroad involved collecting manuscripts and books for presentation to his new patron.

Greaves enrolled at University of Leyden in 1633, where he became friends with Jacob Golius, professor of Arabic at Leyden. He enrolled at the University of Padua in 1635 along with George Ent, meeting the Dane Johan Rode (John Rhodius), an expert on ancient weights and measures, who also made a commentary on Celsus. A brief return to England was followed by a second European journey; in 1636 he sailed via Livorno (Leghorn) to Rome, dining with Ent on 5 October at the English College, Rome; he also met William Harvey, who was entertained at the college on the 12th, Gasparo Berti, Lucas Holstenius and Athanasius Kircher.

Probably in the same month he met and consulted with the Earl of Arundel's art-collecting agent, William Petty (who dined at the college on 14 October), on the Earl's attempted acquisition of the Obelisk of Domitian, then still lying broken in the Circus of Maxentius. Though "now it is broken into 5 stones", he measured these and including a sketch of the obelisk as hypothetically repaired in his almanac-notebook (Bodleian Library Savile MS 49,1). Though Arundel paid a 60 crown deposit for the obelisk, pope Urban VIII vetoed its export and it was erected by his successor Innocent X above Bernini's Fountain of the Four Rivers in the Piazza Navona.