Isaac Newton was born on December 25, 1642, according to the Julian calendar. However, since his birth predates the adoption of the Gregorian calendar in many countries, including England, there isn't an official "Gregorian date" for his birth. The Gregorian calendar was introduced in England in 1752, after Newton's death.
The confusion arises because the Julian and Gregorian calendars diverged over time, leading to different dates being used in different parts of the world during the period between their introduction and universal adoption. Newton's works were influential across Europe, and scholars who refer to his works in different countries might use different calendar systems when citing his birth date.
If you were to convert Newton's Julian birth date to the Gregorian calendar, considering the ten-day difference that would have been adjusted in 1582 if England had adopted the Gregorian calendar at that time, his birth date would have been January 4, 1643, in the Gregorian calendar.
It's important to note that this conversion is a retrospective adjustment and does not reflect the calendar system in use in England during Newton's lifetime. During his lifetime, Newton and his contemporaries would have referred to his birth date as December 25, 1642.