Hillel and Shammai
תנו רבנן מצות חנוכה נר איש וביתו והמהדרין נר לכל אחד ואחד והמהדרין מן המהדרין בית שמאי אומרים יום ראשון מדליק שמנה מכאן ואילך פוחת והולך ובית הלל אומרים יום ראשון מדליק אחת מכאן ואילך מוסיף והולך

The Sages taught in a baraita: The basic mitzva of Hanukkah is each day to have a light kindled by a person, the head of the household, for himself and his household. And the mehadrin, i.e., those who are meticulous in the performance of mitzvot, kindle a light for each and every one in the household. And the mehadrin min hamehadrin, who are even more meticulous, adjust the number of lights daily. Beit Shammai and Beit Hillel disagree as to the nature of that adjustment. Beit Shammai say: On the first day one kindles eight lights and, from there on, gradually decreases the number of lights until, on the last day of Hanukkah, he kindles one light. And Beit Hillel say: On the first day one kindles one light, and from there on, gradually increases the number of lights until, on the last day, he kindles eight lights.

כָּל מַחֲלֹקֶת שֶׁהִיא לְשֵׁם שָׁמַיִם, סוֹפָהּ לְהִתְקַיֵּם. וְשֶׁאֵינָהּ לְשֵׁם שָׁמַיִם, אֵין סוֹפָהּ לְהִתְקַיֵּם. אֵיזוֹ הִיא מַחֲלֹקֶת שֶׁהִיא לְשֵׁם שָׁמַיִם, זוֹ מַחֲלֹקֶת הִלֵּל וְשַׁמַּאי. וְשֶׁאֵינָהּ לְשֵׁם שָׁמַיִם, זוֹ מַחֲלֹקֶת קֹרַח וְכָל עֲדָתוֹ:

Every argument which is for the sake of Heaven — the end is [for the parties to that argument] to endure, [as in the argument between Beth Hillel and Beth Shammai, where none of the parties to the argument (the disciples) were lost (as opposed to Korach and his congregation, who were lost). Or: "the end" — the desired end of the argument. In an argument for the sake of Heaven, the desired end is to attain the truth. And this was attained in the argument between Beth Hillel and Beth Shammai — that the halachah is in accordance with Beth Hillel.] And an argument which is not for the sake of Heaven — the [desired] end, [power and love of conquest,] does not endure. [And so we find in the argument of Korach and his congregation. Their end was the attainment of glory and power — and the opposite was what transpired.] What is an argument for the sake of Heaven? The argument between Hillel and Shammai. And (what is an argument) that is not for the sake of Heaven? The argument of Korach and his whole congregation.

תנו רבנן שתי שנים ומחצה נחלקו בית שמאי ובית הלל הללו אומרים נוח לו לאדם שלא נברא יותר משנברא והללו אומרים נוח לו לאדם שנברא יותר משלא נברא נמנו וגמרו נוח לו לאדם שלא נברא יותר משנברא עכשיו שנברא יפשפש במעשיו ואמרי לה ימשמש במעשיו

The Sages taught the following baraita: For two and a half years, Beit Shammai and Beit Hillel disagreed. These say: It would have been preferable had man not been created than to have been created. And those said: It is preferable for man to have been created than had he not been created. Ultimately, they were counted and concluded: It would have been preferable had man not been created than to have been created. However, now that he has been created, he should examine his actions that he has performed and seek to correct them. And some say: He should scrutinize his planned actions and evaluate whether or not and in what manner those actions should be performed, so that he will not sin.

כלה כמות שהיא ובית הלל אומרים כלה נאה וחסודה אמרו להן ב"ש לב"ה הרי שהיתה חיגרת או סומא אומרי' לה כלה נאה וחסודה והתורה אמרה (שמות כג, ז) מדבר שקר תרחק אמרו להם ב"ה לב"ש לדבריכם מי שלקח מקח רע מן השוק ישבחנו בעיניו או יגננו בעיניו הוי אומר ישבחנו בעיניו מכאן אמרו חכמים לעולם תהא דעתו של אדם מעורבת עם הבריות

The bride as she is. And Bet Hillel say: “A beautiful and graceful bride”! Bet Shammai said to Bet Hillel: If she was lame or blind, does one say of her, “Beautiful and graceful bride”? Whereas the Torah said, “Keep away from a lie” (Exodus 23:7). Bet Hillel said to Bet Shammai: According to your words, if one has made a bad purchase in the market, should one praise it in front of him or denigrate it? Surely, one should praise it in front of him. Therefore, the sages said: One should always have a pleasing disposition in front of other people.

כָּל הַבָּשָׂר אָסוּר לְבַשֵּׁל בְּחָלָב, חוּץ מִבְּשַׂר דָּגִים וַחֲגָבִים. וְאָסוּר לְהַעֲלוֹתוֹ עִם הַגְּבִינָה עַל הַשֻּׁלְחָן, חוּץ מִבְּשַׂר דָּגִים וַחֲגָבִים. הַנּוֹדֵר מִן הַבָּשָׂר, מֻתָּר בִּבְשַׂר דָּגִים וַחֲגָבִים. הָעוֹף עוֹלֶה עִם הַגְּבִינָה עַל הַשֻּׁלְחָן וְאֵינוֹ נֶאֱכָל, דִּבְרֵי בֵית שַׁמַּאי. וּבֵית הִלֵּל אוֹמְרִים, לֹא עוֹלֶה וְלֹא נֶאֱכָל. אָמַר רַבִּי יוֹסֵי, זוֹ מִקֻּלֵּי בֵית שַׁמַּאי וּמֵחֻמְרֵי בֵית הִלֵּל. בְּאֵיזֶה שֻׁלְחָן אָמְרוּ, בַּשֻּׁלְחָן שֶׁאוֹכֵל עָלָיו. אֲבָל בַּשֻּׁלְחָן שֶׁסּוֹדֵר עָלָיו אֶת הַתַּבְשִׁיל, נוֹתֵן זֶה בְצַד זֶה וְאֵינוֹ חוֹשֵׁשׁ:

All meat is forbidden to cook with milk, except for the meat of fish and locusts. And it is forbidden to place it with cheese on the table, except for the meat of fish and locusts. One who vows [to abstain] from meat, is permitted to [eat] fish and locusts. "A bird may go on with cheese on the table, but is not eaten," in the words of Beit Shammai. And Beit Hillel says, "It does not go and it is not eaten." Said Rabbi Yose, "This is [one] of the lenient rulings of Beit Shammai and stringent rulings of Beit Hillel." About which table were they speaking? About a table on which one eats. But for a table where one sets dishes on it, one puts this next to this and does not worry.

סֻכָּה שֶׁהִיא גְבוֹהָה לְמַעְלָה מֵעֶשְׂרִים אַמָּה, פְּסוּלָה. רַבִּי יְהוּדָה מַכְשִׁיר. וְשֶׁאֵינָהּ גְּבוֹהָה עֲשָׂרָה טְפָחִים, וְשֶׁאֵין לָהּ שְׁלֹשָׁה דְּפָנוֹת, וְשֶׁחַמָּתָהּ מְרֻבָּה מִצִּלָּתָהּ, פְּסוּלָה. סֻכָּה יְשָׁנָה, בֵּית שַׁמַּאי פּוֹסְלִין, וּבֵית הִלֵּל מַכְשִׁירִין. וְאֵיזוֹ הִיא סֻכָּה יְשָׁנָה, כָּל שֶׁעֲשָׂאָהּ קֹדֶם לֶחָג שְׁלשִׁים יוֹם. אֲבָל אִם עֲשָׂאָהּ לְשֵׁם חָג, אֲפִלּוּ מִתְּחִלַּת הַשָּׁנָה, כְּשֵׁרָה:

A succah that is higher than twenty cubits is pasul (unfit)... An old succah — Beth Shammai rule it pasul, and Beth Hillel rule it kasher. What is "an old succah"? One which was made thirty days before the festival. But if it were made for the sake of the festival, even from the beginning of the year, it is kasher. [Beth Shammai rule it pasul, for they require a succah lishmah (for the sake of the mitzvah); but this one was made without such intent. But if it were made within thirty days of the festival, since in that period people review the halachoth of the festival, it is assumed that it was made lishmah. Before thirty days, it is assumed otherwise. And Beth Hillel rule it kasher, for they do not require a succah (to be made) for the sake of the festival.]

בֵּיצָה שֶׁנּוֹלְדָה בְיוֹם טוֹב, בֵּית שַׁמַּאי אוֹמְרִים, תֵּאָכֵל. וּבֵית הִלֵּל אוֹמְרִים, לֹא תֵאָכֵל. בֵּית שַׁמַּאי אוֹמְרִים, שְׂאֹר בְּכַזַּיִת וְחָמֵץ בְּכַכּוֹתֶבֶת. וּבֵית הִלֵּל אוֹמְרִים, זֶה וָזֶה בְּכַזָּיִת:

If an egg was hatched on a festival, Beit Shammai say: it may be eaten. And Beit Hillel say: it may not be eaten. Beit Shammai say: [On Pesach, the forbidden measure of] leaven is the equivalent of an olive [in volume], and for leavened food it is the equivalent of a date. Beit Hillel say: for both of them it is the equivalent of an olive.

מתני׳ בית שמאי אומרים בערב כל אדם יטה ויקרא ובבקר יעמוד שנאמר ובשכבך ובקומך

MISHNA: Beit Shammai and Beit Hillel disputed the proper way to recite Shema. Beit Shammai say: One should recite Shema in the manner indicated in the text of Shema itself. Therefore, in the evening every person must recline on his side and recite Shema, in fulfillment of the verse: “When you lie down,” and in the morning he must stand and recite Shema, in fulfillment of the verse: When you rise, as it is stated: “When you lie down, and when you rise.”

זו מחלוקת הלל ושמאי. לפי שתלמידיהם לא שמשו כל צרכן ומהם ואילך רבתה המחלוקת בישראל לפיכך נקטינהו לדוגמא. ומש"ה נמי לא קשיא רישא לסיפא:

THE DISPUTE OF HILLEL AND SHAMMAI. Their students did not fully absorb their ways and teachings, and from that point on disputes became more common among the Torah scholars. This is why the mishna chooses their dispute as an example. Accordingly, the beginning of the mishna does not contradict the end.232Just as in the previous mishna, it would seem that any dispute that is not on the same level as a dispute between Hillel and Shammai is not “for the sake of Heaven”. The end of the mishna, however, makes it clear that only a dispute like that of Korach and his followers is considered “not for the sake of Heaven.” Tosafot Yom Tov clarifies that the dispute of Hillel and Shammai is merely an example, and other disputes that are for the sake of truth and not for personal gain would likewise be called “for the sake of Heaven.”

כִּסֵּא שֶׁל כַּלָּה שֶׁנִּטְּלוּ חִפּוּיָו, בֵּית שַׁמַּאי מְטַמְּאִין, וּבֵית הִלֵּל מְטַהֲרִין. שַׁמַּאי אוֹמֵר, אַף מַלְבֵּן שֶׁל כִּסֵּא, טָמֵא. כִּסֵּא שֶׁקְּבָעוֹ בַעֲרֵבָה, בֵּית שַׁמַּאי מְטַמְּאִין, וּבֵית הִלֵּל מְטַהֲרִין. שַׁמַּאי אוֹמֵר, אַף הֶעָשׂוּי בָּהּ:

A bridal chair whose seat has been removed: Beit Shammai rules that it still susceptible to impurity, and Bet Hillel rules that it is not susceptible. Shammai rules: even the frame of the chair is susceptible to impurity. A stool which was fixed to a kneading-trough - Beit Shammai rules that it susceptible to impurity, and Beit Hillel rules that it is pure. Shammai rules: even one made [in this way originally] is susceptible to impurity.

If Hillel always thinks on the positive side of everything. Shammai is always so serious and strict, and doesn't think on the positive side of the situation. For instance when they are arguing over if an egg hatched on a festival Shammai said: It could be eaten, and Hillel said: It couldn't be eaten. This is showing how Shammai is always thinking on the positive of almost every situation. As for Hillel he is always on the negative side. To draw a conclusion Hillel always thinks at some point there can't be any progression in the argument and for Shammai he always looks for the way to advance or progress.