Moshe the servant of Hashem died there, by the mouth of Hashem.
“When the lots that Haman had cast landed on the month of Adar, he rejoiced and said, ‘My lots fell on the month in which Moshe died.’ But Haman did not know that while Moshe died on the seventh of Adar, he was also born on the seventh of Adar,” teaches the Gemara.
While it is clear that Haman did not know that Moshe was born on the seventh of Adar, it is evident from the beginning of this gemara that he did know the date of his death. The Gemara’s statement that he “did not know that while Moshe died on the seventh of Adar, he was also born on the seventh of Adar” implies that there was something that he did not know about the death of Moshe as well.
It also behooves us to discover why it was that a man who was so obsessed with the Jewish people and so knowledgeable of their ways missed the birth date of Moshe, and only knew the day of his death. Midrashim are replete with accounts of Haman quoting verses from the Torah. Like most of our enemies, he knew much about our Torah (even though he combated it viciously, nevertheless). So why, then, did he never learn of the birth of Moshe?
Rav Tzadok Hakohen of Lublin writes that “the day that a man is born is when his mazel is at its most powerful point. On that day, every year, he need not fear that any misfortune will befall him. When our Sages taught us that the righteous die on their birthdays – that is because for those so righteous, death is an elevation of their mazel, and the next step in their spiritual climb.”
“Ki lo yirani ha’adam v’chai” is normally translated as, “No man can see Me and survive.” But Abudraham offers an alternative translation. “‘Neither can man see me, nor can the chai,’ referring to the angels.” Even the angels cannot see Hashem! But Chazal have taught us that while no man can see G-d in his lifetime, he sees him in his death! In fact, the Chida offers a number of reasons that the righteous must die – and his fifth reason is “Ki lo yirani ha’adam v’chai!” At a righteous human’s death, he reaches a higher level of appreciation of G-d than even the highest angel can ever reach!
Thus, Haman did not know that not only did Moshe die on the seventh of Adar, but that death was really a birth as well, just as was his original birth. He may have even known the dry information about the day that Moshe was born from an entry in the Encyclopedia Persian-ica. But Haman did not truly understand the Jewish purpose in this world – why Moshe was really born. He therefore could not truly understand why Moshe died, and how that death was a birth to another world. He did not know that Moshe’s death was just another rung in a ladder that begins here on Earth, and reaches into the Heavens.
The Tzaddik, even in death, is considered alive.
It was only some time after this suggestion was written that I found this very interpretation of this gemara in the sefer Chomas Anach on Koheles 3:2. The Chida there quotes his father’s Rav, R. Avraham Itzchaki, who offers a remarkably similar pshat.
 Megillah 13b
 Divrei Chalomos, 20. This idea originates in the Talmud Yerushalmi (Rosh Hashanah 3:5): “R. Yehoshua ben Levi said the nation of Amalek were great sorcerers; they would send people out to battle when it was their exact birthday, for a person does not fall easily on his birthday…” See also Ben Yehoyada to Brachos 28a, s.v. hahu, where he explains that “since on one’s birthday, his mazel is strongest and most successful, we have the custom that every person makes a party for himself on his birthday.” See also Mahari Shteiff Al Hatorah (“Amaros,” Vayeshev, 106), where he says that although we do not find a Jewish custom to celebrate one’s birthday, it is nevertheless told about the Chasam Sofer that on his birthday, he would thank Hashem, prostrated totally to the ground, and would complete a section of the Talmud as well. He therefore suggests that on one’s birthday, one should thank Hashem for the past, and request from Him that he merit ripe, old age.
 Shemos 33:20
 Mussaf of Shabbos, in Kedusha. In fact, a nearly identical interpretation is found in the Sifra to Vayikra, 2, as the opinion of R. Akiva.
 Pirkei Dirabbi Eliezer, 31. See, in fact, Reishis Chochmah (R. Eliahu de Vidas) in “Shaar HaYirah,” 12:43 (also called “Meseches Chibut HaKever”), where he explains that, in fact, the way that man dies is that he sees Hashem, and thus, expires.
 Dvash Lifi, mem, 24
 Brachos 18b
 See also Lechem Lifi Hataf (R. Yitzchak Buchavzeh of Libya), dalet, 3, where he quotes R. Moshe Hakohen’s slightly different, but very relevant, approach to this gemara.