Atem’s birthday is supposed to be June 2nd (and not July 26th)
I've been seeing posts for years saying Atem’s birthday is July 26th so I decided to speak up because it's wrong xD. Obviously there was a huge misunderstanding about which calendar Kazuki Takahashi used to establish Atem's birthday.
First, note that Kazuki Takahashi only gave egyptian dates for his egyptian characters and no modern date. According to KT, Atem is born on the 19th day of the 3rd month of Shemu.
I. Which calendar was used for Atem’s birthday?
The Egyptians had several calendars throughout their history. The one Kazuki Takahashi used is the Ancient Egyptian civil calendar whereas the fans that tried to convert Atem’s birthday into a gregorian date used the Coptic calendar hence getting the wrong date.
The Coptic calendar was used in the Middle Ages by Christian Egyptians. Atem died milleniums before this calendar was even put to use...
The Ancient Egyptian civil calendar was slightly different from the Coptic one. http://www.lavia.org/english/archivo/EgyptianCalendarEN.html
It had no names for the months. Months were referred to by their number within the season. The seasons followed the Nile’s Flood Cycle: Akhet (flood) - Peret (germination) - Shemu (it literally means 'dry' or 'low water', it's also harvest time).
If you check the Nile's flooding cycle, you'll see that the flood comes about at the end of July (which means the end of July was during Akhet season whereas Atem was born during Shemu when there was no water).
II. How do we convert Atem’s birthday into a gregorian date?
Egyptologists have established the equivalences between our two calendars long ago. Of course, this is all very theoritical because the Ancient Egyptian civil calendar doesn’t have a leap year. So the exact equivalences made by Egyptologists are only real if we pretend that February 29th doesn’t exist xD.
Anyway, the important part is that Kazuki Takahashi used these equivalences. I’m sure of it because if we use the Ancient Egyptian civil calendar instead of the Coptic one, all the Egyptian characters have the same birthdays as their modern counterparts. Seth and Seto are both born on October 25th, for example.
If you check the link up above, you'll find that it says that the 1st month of Akhet is from July 19th to August 17th. It means that the 1st day of the 1st month of Akhet is July 19th, the 2nd day of the 1st month of Akhet is then July 20th, etc.
Go to Shemu season, check the 3rd month and count for yourself the 19th day. It falls on June 2nd. Interestingly enough, Yuugi's birthday is June 4th and you'll see below that all the Egyptian characters are linked to their modern counterpart.
July 14th, 15th, 16th, 17th and 18th were five extra days added in between the last day of the year and the first day of the new year.
Atem - June 2nd (Yuugi is June 4th) 19th day, 3rd month, Harvest
Shimon - Oct 5th (Sugoroku is October 4th) 19th day, 3rd month, Flood
Mahad - October 31st 15th day, 4th month, Flood
Isis - April 4th (Isis Ishtar is April 5th) 20th day, 1st month, Harvest
Karim - August 18th 1st day, 2nd month, Flood
Shadah - July 21st 3rd day, 1st month, Flood
Aknadin - February 12th 29th day, 3rd month, Germination
Seto - October 25th (Kaiba is October 25th) 9th day, 4th month, Flood
Mana - September 20th 4th day, 3rd month, Flood
Bakura - September 1st (Ryou is September 2nd) 15th day, 2nd month, Flood