why there are two different versions of isaac newton's birth date

The discrepancy in Isaac Newton's reported birth dates stems from the difference between the Julian calendar, which was used in England before 1752, and the Gregorian calendar, which is the commonly accepted civil calendar today. Isaac Newton was born on January 4, 1643, according to the Julian calendar, which was in use in England at that time. However, the Gregorian calendar, which had been introduced by Pope Gregory XIII in 1582 and had replaced the Julian calendar in most Catholic countries, was 10 days ahead of the Julian calendar. England was slow to adopt the Gregorian reformation and only did so on September 14, 1752, with the Calendar Act of 1750. As part of this adoption, September 3rd was followed directly by September 14th in 1752, effectively dropping 11 days. Prior to this change in calendar systems, New Year's Day was considered to be on March 25, rather than January 1. To reconcile Newton's birth date with modern calendar use, one would add 10 days, giving you January 14, 1643; however, because England also moved the start of the year from March 25th to January 1st as part of the adoption of the Gregorian calendar, his birth date could also be stated as December 25, 1642 (Julian calendar) or then convert that to our current calendar by adding 10 days. Hence, some accounts might say Isaac Newton was born on December 25, 1642 (Julian calendar), while others express it as January 4, 1643 (also the Julian calendar). To align this with the Gregorian calendar, you'd use January 14 or 15, 1643. The exact conversion can depend on whether the intent is to correct for the full 10 days shift or also for the change in the start of the year from March 25th to January 1st.