* 1638 – Tokugawa shogunate forces put down the Shimabara Rebellion when they retake Hara Castle from the rebels.

* 1638 – Nicolas Malebranche, French philosopher ( d. 1715 )

* Adrian von Mynsicht ( 1603 – 1638 ), German alchemist

* 1638 – Shimazu Tadatsune, Japanese ruler of Satsuma ( b. 1576 )

However, this statement for integers can be found already in the work of another French mathematician, Claude Gaspard Bachet de Méziriac ( 1581 – 1638 ).

James Gregory ( 1638 – 1675 ) observed the diffraction patterns caused by a bird feather, which was effectively the first diffraction grating to be discovered.

* 1638 – The Scottish National Covenant is signed in Edinburgh.

Nicolas Steno ( 1638 – 1686 ) is credited with the law of superposition, the principle of original horizontality, and the principle of lateral continuity: three defining principles of stratigraphy.

* John Harvard ( clergyman ) ( 1607 – 1638 ), a clergyman after whom Harvard University is named

* 1638 – David Teniers III, Flemish painter ( d. 1685 )

* 1706 – Charles Sackville, 6th Earl of Dorset, English poet and courtier ( b. 1638 )

* 1638 – Nicolas Steno, Danish scientist ( d. 1686 )

* 1552 – Gabriello Chiabrera, Italian poet ( d. 1638 )

Johann Heinrich Alsted ( March 1588 – November 9, 1638 ) was a German Calvinist minister and academic, known for his varied interests: in Ramism and Lullism, pedagogy and encyclopedias, theology and millennarianism.

* 1638 – Giovanni Buonaventura Viviani, Italian composer and violinist ( d. 1693 )

* Claud Hamilton, 2nd Baron Hamilton of Strabane ( c. 1606 – 1638 )

The second half of the century saw no composers equal in stature, but in the early 17th century Johannes Hieronymus Kapsberger ( c. 1580 – 1651 ) and Alessandro Piccinini ( 1566 – 1638 ) revolutionized the instrument's technique and Kapsberger, possibly, influenced the keyboard music of Frescobaldi.

* 1638 – Henry Capell, 1st Baron Capell, English first Lord of the British Admiralty ( d. 1696 )

* 1638 – Richard Simon, French critic ( d. 1712 )

* 1638 – Anne Hutchinson is expelled from Massachusetts Bay Colony for religious dissent.

* 1685 – Emperor Go-Sai of Japan ( b. 1638 )

* 1638 – Swedish colonists establish the first European settlement in Delaware, naming it New Sweden.

* 1638 – Queen Catherine of Braganza, consort of Charles II of England ( d. 1705 )

* Marie Touchet ( 1549 – 1638 ): the only mistress of King Charles IX of France

* January 29 – Charles Sackville, 6th Earl of Dorset, English poet and courtier ( b. 1638 )

* November 30 – Catherine of Braganza, queen of Charles II of England ( b. 1638 )

Charles Emmanuel II () ( 20 June 1634 – 12 June 1675 ) was the Duke of Savoy from 1638 to 1675 and under regency of his mother Christine of France until 1663.

In 1638 at the death of his older brother Francis Hyacinth, Duke of Savoy, Charles Emmanuel succeeded to the duchy of Savoy at the age of 4.

* 20 June 1634 – 4 October 1638 His Highness Prince Charles Emmanuel of Savoy

* Charles Emmanuel II: 1638 – 1675

* Catherine ( 1584 – 1638 ), married a prince of the Palatinate Zweibrücken, becoming mother of Charles X Gustav.

The Cecil family retained the manor for fifty years before it was bought by Charles I in 1638 for his Queen, Henrietta Maria.

However, in 1638, that decision was reversed, and King Charles I became the undertaker to ensure the work was completed.

Also around this time, circa 1638, Jones devised drawings completely redesigning the Palace of Whitehall, but the execution of these designs was frustrated by Charles I ’ s financial and political difficulties.

The work of translating the Old Testament was undertaken by William Bedel ( 1571 – 1642 ), Bishop of Kilmore, who completed his translation within the reign of Charles I, although it was not published until 1680 in a revised version by Narcissus Marsh ( 1638 – 1713 ), Archbishop of Dublin.

* Catherine of Braganza ( 1638 – 1705 ), wife of Charles II of England

In attempting to force the Scots to accept a new Prayer Book in 1637, Charles sparked a crisis that led to the compilation and subscription of the National Covenant in early 1638, a document which rejected all innovations in worship that had not been subject to the approval of both the Scottish Parliament and the General Assembly of the church.

In 1638 he became governor of Charles, Prince of Wales, and in 1639 a Privy Counsellor.

Charles I repealed Canon Law in 1638 after uprisings of Covenanters confronting the Bishops of Aberdeen following the convention at Muchalls Castle and other revolts across Scotland earlier that year.

Catherine of Braganza (; 25 November 1638 – 31 December 1705 ) was the wife of King Charles II of England.

A veteran of 18 years ' experience, Captain Skippon returned to England in 1638, and on 23 October 1639 was recommended by Charles I of England for a command in the Honourable Artillery Company and he moved to London to take up this command.

By far the most common Charles I threepences were produced at the Aberystwyth mint between 1638 and 1642.

Navigation on the first from Burrowbridge to Ham Mill was much easier than on the final stretch to Taunton, and in 1638, John Mallett, the Sheriff of Somerset and Member of Parliament for Bath, obtained a Commission under the Great Seal from King Charles II.

* Charles de Créquy, Prince of Poix, Duke of Lesdiguières ( 1580 – 1638 ), Marshal of France in 1621.

Maghull Manor House was built in 1638 and local tradition has it that Charles II slept there during a visit to the area but by 1780 a new manor house had been built near the site of the original and it still stands in the grounds of Maghull Homes with part of the original moat.