* 1721 – Grinling Gibbons, English sculptor and woodcarver ( b. 1648 )

* 1667 – Louise of Mecklenburg-Güstrow ( d. 1721 )

Alexander Selkirk ( 1676 – 13 December 1721 ) was a Scottish sailor who spent four years as a castaway after being marooned on an uninhabited island.

* 1721 – Michel Chamillart, French statesman ( b. 1652 )

* 1665 – Jacques Lelong, French bibliographer ( d. 1721 )

* 1721 – Roger Sherman, American statesman and signer of the U. S. Declaration of Independence ( d. 1793 )

* 1721 – Granville Leveson-Gower, 1st Marquess of Stafford, English politician ( d. 1803 )

* 1648 – John Sheffield, 1st Duke of Buckingham and Normanby, English statesman and poet ( d. 1721 )

* Pierre Coustant ( 1654 – 1721 )

* Catherine of Siena ( 1707 – 1721 ) Opere, ed.

* 1721 – Richard Lumley, 1st Earl of Scarbrough, English statesman ( b. 1640 )

* 1721 – James Elphinston, British philologist ( d. 1809 )

* 1721 – Guillaume-Chrétien de Lamoignon de Malesherbes, French statesman ( d. 1794 )

* 1721 – François Hemsterhuis, Dutch philosopher ( d. 1790 )

* 1721 – Peter Pelham, English-born American musician and composer ( d. 1805 )

* 1721 – Alexander Selkirk, Scottish sailor and castaway ( b. 1676 )

Elihu Yale ( April 5, 1649 – July 8, 1721 ) was an American merchant and philanthropist, governor of the East India Company settlement at Madras and a benefactor of the Collegiate School of Connecticut, which in 1718 was named Yale College in his honor.

* 1721 – Christian Friedrich Heinecken, German child prodigy ( d. 1725 )

* 1721 – John Reid, British army general and composer ( d. 1807 )

Rabbi Yedidiah Tiah Weil ( 1721 – 1805 ), a Prague resident, who described the creation of golems, including those created by Rabbi Avigdor Kara of Prague, did not mention the Maharal, and Rabbi Meir Perels ' biography of the Maharal published in 1718 does not mention a golem.

* 1721 March – Philip V of Spain requested the restitution of Gibraltar to proceed to the renewal of the trade licences of Great Britain with the Spanish possessions in America.

* 1721 1 June – George I sent a letter to Philip V promising " to make use of the first favourable Opportunity to regulate this Article ( the Demand touching the Restitution of Gibraltar ), with the Consent of my Parliament ".

Their purpose was defense from attacks from water and their construction was urged by the Great Northern War of 1700 – 1721.

* 1790 – François Hemsterhuis, Dutch philosopher ( b. 1721 )

Public discourse ranged in tone from organized arguments by tobacconist and medical practitioner John Williams, who posited that " several arguments proving that inoculating the smallpox is not contained in the law of Physick, either natural or divine, and therefore unlawful ," to more slanderous attacks, such as those put forth in a pamphlet by Dr. William Douglass of Boston entitled The Abuses and Scandals of Some Late Pamphlets in Favour of Inoculation of the Small Pox ( 1721 ), on the qualifications of inoculation's proponents.

Arguably the first was John Lombe's water-powered silk mill at Derby, operational by 1721.

* April 7 – John Sheffield, 1st Duke of Buckingham and Normanby, English statesman and poet ( d. 1721 )

* May 18 – John Douglas, Scottish Anglican bishop and man of letters ( b. 1721 )

* August 21 – John McKinly, American physician and President of Delaware ( b. 1721 )

* March 26 – John Mudge, English physician and inventor ( b. 1721 )

* September 4 – John Fielding, English magistrate and social reformer ( b. 1721 )

The play was revived again in 1718 and 1719 ( with John Bickerstaff as Aaron ) and 1721 ( with Thomas Walker in the role ).

* John Anderson ( theologian and controversialist ) ( 1668 ?– 1721 ), Scottish theologian and controversialist

In July 1721 John Vanbrugh made Hawksmoor his deputy as Comptroller of the Works.

* John Douglas ( bishop of Salisbury ) ( 1721 – 1807 ), Scottish man of letters and Anglican bishop

On her death in 1721, the house passed to her husband's nephew ( and her son-in-law ) Sir John Brownlow III ( later Viscount Tyrconnel ).

* John McKinly ( 1721 – 1796 ), President of Delaware

( Other claims might be made for John Lombe's silk mill in Derby ( 1721 ), or Richard Arkwright's Cromford Mill ( 1772 )— purpose built to fit the equipment it held and taking the material through the various manufacturing processes.

John Douglas ( 14 July 1721 – 18 May 1807 ) was a Scottish scholar and Anglican bishop.

Middleton's supporters ( 14 December 1721 ), passed a vote through the university Senate making him a librarian — a salaried " Protobibliothecarius " of the university library — a new post, on the pretext of the king's recent donation of Bishop John Moore's library.

John Cleland entered Westminster School in 1721, but he left or was expelled in 1723.

Important developments in reflecting telescopes were John Hadley's production of larger paraboloidal mirrors in 1721 ; the process of silvering glass mirrors introduced by Léon Foucault in 1857 ; and the adoption of long lasting aluminized coatings on reflector mirrors in 1932.

* John Carteret, 2nd Baron Carteret: 5 February 1721 – 21 February 1721

The most notable Marquess of Granby was John Manners ( 1721 – 1770 ), son of the third Duke.

* John Manners, 2nd Duke of Rutland ( 1676 – 1721 ), son of the 1st Duke