See this post for a fuller treatment of the subject.
Articles about the birth date of Christ sometimes state that it was an ancient teaching or understanding that the rabbis and other believed that the righteous died on their birth dates.
While the claim is often made, I have rarely come across an article which gives a reference to a text that actually states this.
So here is one reference for the claim. It is from the Babylonian Talmud, Tractate Kidushin, folio 38a. I have arranged the text to make it easier to read and provided a fairly literal translation and references for the quotations:
תַּנְיָא אִידַּךְ:
בְּשִׁבְעָה בַּאֲדָר מֵת מֹשֶׁה,
וּבְשִׁבְעָה בַּאֲדָר נוֹלַד.
מִנַּיִן שֶׁבְּשִׁבְעָה בַּאֲדָר מֵת –
שֶׁנֶּאֱמַר: ״וַיָּמׇת שָׁם מֹשֶׁה עֶבֶד ה׳״,
וּכְתִיב: ״וַיִּבְכּוּ בְנֵי יִשְׂרָאֵל אֶת מֹשֶׁה בְּעַרְבֹת מוֹאָב שְׁלֹשִׁים יוֹם״,
וּכְתִיב: ״וַיְהִי אַחֲרֵי מוֹת מֹשֶׁה עֶבֶד ה׳״,
וּכְתִיב: ״מֹשֶׁה עַבְדִּי מֵת וְעַתָּה קוּם עֲבֹר״
וּכְתִיב: ״עִבְרוּ בְּקֶרֶב הַמַּחֲנֶה וְצַוּוּ אֶת הָעָם
לֵאמֹר הָכִינוּ לָכֶם צֵדָה
כִּי בְּעוֹד שְׁלֹשֶׁת יָמִים תַּעַבְרוּ אֶת הַיַּרְדֵּן״
וּכְתִיב: ״וְהָעָם עָלוּ מִן הַיַּרְדֵּן בֶּעָשׂוֹר לַחֹדֶשׁ הָרִאשׁוֹן״,
צֵא מֵהֶן שְׁלֹשִׁים וּשְׁלֹשָׁה יָמִים לְמַפְרֵעַ,
הָא לָמַדְתָּ שֶׁבְּשִׁבְעָה בַּאֲדָר מֵת מֹשֶׁה.
It is taught again
Moses died on the seventh of Adar,
and he was born on the seventh of Adar.
From where is this that on the seventh of Adar he died?
As it is stated:
“And Moses the servant of the Lord died there…” (Dt 34:5)
And as it is written:
“And the children of Israel mourned Moses in the plains of Moab for thirty days.” (Dt 34:8)
And as it is written:
“And so it was after the death of Moses, the servant of the Lord…” (Jos 1:1)
And as it is written:
“Moses my servant is dead. Now you arise and cross over…” (Jos 1:2)
And as it is written:
“Pass through the middle of the camp and command the people
saying: ‘Prepare your provisions for in yet three days you will cross the Jordan…’” (Jos 1:11)
And as it is written:
“And the people went up from the Jordan on the tenth day of the first month…” (Jos 4:19)
Go
back from them thirty three days
[30 for the mourning of Moses
and 3 for the preparation to cross the Jordan]
thus you learn that it was on the seventh of Adar that Moses died.
וּמִנַּיִן
שֶׁבְּשִׁבְעָה בַּאֲדָר נוֹלַד מֹשֶׁה –
שֶׁנֶּאֱמַר:
״וַיֹּאמֶר אֲלֵהֶם
בֶּן מֵאָה וְעֶשְׂרִים שָׁנָה אָנֹכִי הַיּוֹם
לֹא אוּכַל עוֹד לָצֵאת וְלָבוֹא״,
שֶׁאֵין תַּלְמוּד לוֹמַר ״הַיּוֹם״,
מָה תַּלְמוּד לוֹמַר ״הַיּוֹם״?
מְלַמֵּד שֶׁהַקָּדוֹשׁ בָּרוּךְ הוּא
יוֹשֵׁב וּמְמַלֵּא שְׁנוֹתֵיהֶם שֶׁל צַדִּיקִים מִיּוֹם לְיוֹם וּמֵחֹדֶשׁ לְחֹדֶשׁ,
שֶׁנֶּאֱמַר: ״אֶת מִסְפַּר יָמֶיךָ אֲמַלֵּא״.
And
where does is come from
that Moses was born on the seventh of
Adar?
As
it is stated:
“And he said to them:
‘I am one
hundred and twenty years old today.
I am not able again to go
out or to come in…” (Dt 31:2)
Since there is no need for the verse to say “today”
what [reason does] the verse say “today”?
This teaches that the Holy One, Blessed be He,
sits and fills up the years of the righteous from day to day and from month to month.
As it is stated: “The number of your days, I will make full.” (Ex 23:26)
Some rabbis in the Babylonian Talmud interpreted Exodus 23:26 as teaching that a righteous man would die on his birthday. Moses was given as evidence. Indeed, this fulfillment of days is interpreted as the specific reason Moses used the word "today" at the end of his life in Deuteronomy 31.
You can find the text of Kidushin 38a in the
following two references. The Sefaria website reference has a more
expansive translation.
Mechon Mamre מסכת קידושין פרק דף לח,א גמרא
https://mechon-mamre.org/b/l/l3701.htm
Kiddushin
38a The William Davidson Talmud (Koren –
Steinsaltz)
https://www.sefaria.org/Kiddushin.38a.5-6?lang=bi&with=all&lang2=en
Click the image below to view the text, then right click, select open in a new tab and you will be able to enlarge the image for easier reading.