Hillel famously accepted converts who came with seemingly outlandish conditions — one wishing to become High Priest, one wishing to learn the entire Torah on one foot — because he perceived that they would ultimately become sincere, complete converts, as indeed they did.
שׁוּב מַעֲשֶׂה בְּגוֹי אֶחָד שֶׁבָּא לִפְנֵי שַׁמַּאי. אָמַר לוֹ: גַּיְּירֵנִי עַל מְנָת שֶׁתְּלַמְּדֵנִי כׇּל הַתּוֹרָה כּוּלָּהּ כְּשֶׁאֲנִי עוֹמֵד עַל רֶגֶל אַחַת! דְּחָפוֹ בְּאַמַּת הַבִּנְיָן שֶׁבְּיָדוֹ. בָּא לִפְנֵי הִלֵּל, גַּיְירֵיהּ. אָמַר לוֹ: דַּעֲלָךְ סְנֵי לְחַבְרָךְ לָא תַּעֲבֵיד — זוֹ הִיא כׇּל הַתּוֹרָה כּוּלָּהּ, וְאִידַּךְ פֵּירוּשָׁהּ הוּא, זִיל גְּמוֹר. שׁוּב מַעֲשֶׂה בְּגוֹי אֶחָד שֶׁהָיָה עוֹבֵר אֲחוֹרֵי בֵּית הַמִּדְרָשׁ, וְשָׁמַע קוֹל סוֹפֵר שֶׁהָיָה אוֹמֵר: ״וְאֵלֶּה הַבְּגָדִים אֲשֶׁר יַעֲשׂוּ חוֹשֶׁן וְאֵפוֹד״. אָמַר: הַלָּלוּ לְמִי? אָמְרוּ לוֹ: לְכֹהֵן גָּדוֹל. אָמַר אוֹתוֹ גּוֹי בְּעַצְמוֹ: אֵלֵךְ וְאֶתְגַּיֵּיר בִּשְׁבִיל שֶׁיְּשִׂימוּנִי כֹּהֵן גָּדוֹל. בָּא לִפְנֵי שַׁמַּאי, אָמַר לוֹ: גַּיְּירֵנִי עַל מְנָת שֶׁתְּשִׂימֵנִי כֹּהֵן גָּדוֹל. דְּחָפוֹ בְּאַמַּת הַבִּנְיָן שֶׁבְּיָדוֹ. בָּא לִפְנֵי הִלֵּל, גַּיְירֵיהּ. אָמַר לוֹ: כְּלוּם מַעֲמִידִין מֶלֶךְ אֶלָּא מִי שֶׁיּוֹדֵעַ טַכְסִיסֵי מַלְכוּת, לֵךְ לְמוֹד טַכְסִיסֵי מַלְכוּת. הָלַךְ וְקָרָא. כֵּיוָן שֶׁהִגִּיעַ ״וְהַזָּר הַקָּרֵב יוּמָת״, אָמַר לֵיהּ: מִקְרָא זֶה עַל מִי נֶאֱמַר? אָמַר לוֹ: אֲפִילּוּ עַל דָּוִד מֶלֶךְ יִשְׂרָאֵל. נָשָׂא אוֹתוֹ גֵּר קַל וָחוֹמֶר בְּעַצְמוֹ: וּמַה יִּשְׂרָאֵל שֶׁנִּקְרְאוּ בָּנִים לַמָּקוֹם וּמִתּוֹךְ אַהֲבָה שֶׁאֲהָבָם קְרָא לָהֶם: ״בְּנִי בְּכוֹרִי יִשְׂרָאֵל״, כְּתִיב עֲלֵיהֶם ״וְהַזָּר הַקָּרֵב יוּמָת״ — גֵּר הַקַּל שֶׁבָּא בְּמַקְלוֹ וּבְתַרְמִילוֹ, עַל אַחַת כַּמָּה וְכַמָּה. בָּא לִפְנֵי שַׁמַּאי, אָמַר לוֹ: כְּלוּם רָאוּי אֲנִי לִהְיוֹת כֹּהֵן גָּדוֹל? וַהֲלֹא כְּתִיב בַּתּוֹרָה: ״וְהַזָּר הַקָּרֵב יוּמָת״. בָּא לִפְנֵי הִלֵּל, אָמַר לוֹ: עַנְוְותָן הִלֵּל, יָנוּחוּ לְךָ בְּרָכוֹת עַל רֹאשְׁךָ, שֶׁקֵּרַבְתַּנִי תַּחַת כַּנְפֵי הַשְּׁכִינָה. לְיָמִים נִזְדַּוְּוגוּ שְׁלָשְׁתָּן לִמְקוֹם אֶחָד, אָמְרוּ: קַפְּדָנוּתוֹ שֶׁל שַׁמַּאי בִּקְּשָׁה לְטוֹרְדֵנוּ מִן הָעוֹלָם, עִנְוְותָנוּתוֹ שֶׁל הִלֵּל קֵרְבַתְנוּ תַּחַת כַּנְפֵי הַשְּׁכִינָה.
There was another incident involving one gentile who came before Shammai and said to Shammai: Convert me on condition that you teach me the entire Torah while I am standing on one foot. Shammai pushed him away with the builder’s cubit in his hand. This was a common measuring stick and Shammai was a builder by trade. The same gentile came before Hillel. He converted him and said to him: That which is hateful to you do not do to another; that is the entire Torah, and the rest is its interpretation. Go study. There was another incident involving one gentile who was passing behind the study hall and heard the voice of a teacher who was teaching Torah to his students and saying the verse: “And these are the garments which they shall make: A breastplate, and an efod, and a robe, and a tunic of checkered work, a mitre, and a girdle” (Exodus 28:4). The gentile said: These garments, for whom are they designated? The students said to him: For the High Priest. The gentile said to himself: I will go and convert so that they will install me as High Priest. He came before Shammai and said to him: Convert me on condition that you install me as High Priest. Shammai pushed him with the builder’s cubit in his hand. He came before Hillel; he converted him. Hillel said to him, to the convert: Is it not the way of the world that only one who knows the protocols [takhsisei] of royalty is appointed king? Go and learn the royal protocols by engaging in Torah study. He went and read the Bible. When he reached the verse which says: “And the common man that draws near shall be put to death” (Numbers 1:51), the convert said to Hillel: With regard to whom is the verse speaking? Hillel said to him: Even with regard to David, king of Israel. The convert reasoned an a fortiori inference himself: If the Jewish people are called God’s children, and due to the love that God loved them he called them: “Israel is My son, My firstborn” (Exodus 4:22), and nevertheless it is written about them: And the common man that draws near shall be put to death; a mere convert who came without merit, with nothing more than his staff and traveling bag, all the more so that this applies to him, as well. The convert came before Shammai and told him that he retracts his demand to appoint him High Priest, saying: Am I at all worthy to be High Priest? Is it not written in the Torah: And the common man that draws near shall be put to death? He came before Hillel and said to him: Hillel the patient, may blessings rest upon your head as you brought me under the wings of the Divine Presence. The Gemara relates: Eventually, the three converts gathered together in one place, and they said: Shammai’s impatience sought to drive us from the world; Hillel’s patience brought us beneath the wings of the Divine Presence.