לזכות א"מ ר' יצחק יונה בן חנה ור' מרדכי דוד בן קריינא בתוך שח"י 

1. The gemara [Rosh Hashana 11a] says that מדלג על ההרים - He skips over the mountains, refers to the זכות אבות, while מקפץ על הגבעות - Jumps over the valleys, refers to the זכות אמהות, the merits of the mothers. What is the nature and difference of these merits?

2.  

בראשית כ"ה:ו'

וְלִבְנֵ֤י הַפִּֽילַגְשִׁים֙ אֲשֶׁ֣ר לְאַבְרָהָ֔ם נָתַ֥ן אַבְרָהָ֖ם מַתָּנֹ֑ת וַֽיְשַׁלְּחֵ֞ם מֵעַ֨ל יִצְחָ֤ק בְּנוֹ֙ בְּעוֹדֶ֣נּוּ חַ֔י קֵ֖דְמָה אֶל⁠־אֶ֥רֶץ קֶֽדֶם׃

And to the sons of Avraham's concubines, Avraham gave gifts. He sent them away from his son Yitzchak, while he was still alive, eastward to the land of Kedem. 

Rashi says that he gave the the שם טומאה. We would like to explain the "sending away from Yitzchak" and the "שם טומאה". Why is Avraham giving over an "impure name"?

3. The pasuk says וְזָכַרְתִּי אֶת בְּרִיתִי יַעֲקוֹב וְאַף אֶת בְּרִיתִי יִצְחָק וְאַף אֶת בְּרִיתִי אַבְרָהָם אֶזְכֹּר וְהָאָרֶץ אֶזְכֹּר - The Gra says that the pasuk is talking not only about the ברית אבות but also the ברית אמהות as alluded to in the three times it says "את" and Rochel and Leah are considered as one, so four [אמהות] all together. The ברית אבות CREATES קדושה while the ברית אמהות preserves קדושה by separating us from evil. Sarah and Rivka expel Yishmael and Esav respectively from the house of the Avos and Rochel and Leah say "הלוא נכריות נחשבנו" - We are like strangers to our father. They separate from Lavan. The pasuk says that Rochel and Leah built the House of Israel [Rus 4-11] which includes separating us from evil. 

4. The [uncensored] Rambam tells us that Esav and Yishmael pave the way to Moshiach. The best of the גויים is פסולת for כלל ישראל. [The source is that at מתן תורה the Torah was offered to Yishmael [פארן] and Esav [שעיר] and to no other nation. So the choicest of the nations are rejected by us]. Specifically THEY pave the way for Moshiach. The בני ישמעאל and בני עשו  stole the name of Moshiach and even though they distorted it, they still have the concept.   

5. Even though they have the concept of משיח from the בית אבות, they have distorted and contaminated and they must be distanced. That is the purpose of the ברית אמהות. 

6. This is all about Esav And Yishmael. What was unique about בני קטורה was that they were born to Avraham after the death of Sarah. Here there was no activation of the ברית אמהות of Sarah and thus emerged that there was no power to separate them from our family. That was why "וישלחם מעל יצחק בנו" - Avraham sent them away. With no mother - the father has to fill her role. So in lieu of Sarah, Avraham sent them away. 

7. Now we can understand the idea of giving them the שם טומאה. The ריב"א [one of the Baalei HaTosfos] says that in contrast to what it says about the generation of אנוש that "אז הוחל לקרוא בשם השם" - that was the beginning of Avoda Zara in the world but with the name of Hashem [בשם השם], Avraham taught the בני קטורה the שם טומאה. This way they would have no connection to us. The ברית אמהות distances Esav and Yishmael who still maintain a connection with us [Christianity and Islam are rooted in Judaism]. What Avraham did distanced the בני קטורה completely. Since it was not Avraham's natural "playing field", he had to work harder to distance them. What Sarah and Rivka accomplished by separating them while they still remained connected on some level, Avraham could only accomplish with complete detachment. 

8. וְלִבְנֵי הַפִּילַגְשִׁים אֲשֶׁר לְאַבְרָהָם נָתַן אַבְרָהָם מַתָּנֹת וַיְשַׁלְּחֵם מֵעַל יִצְחָק בְּנוֹ בְּעוֹדֶנּוּ חַי קֵדְמָה אֶל אֶרֶץ קֶדֶם  - Avraham sent them to the far east [קדמה אל ארץ קדם - to the east of the east], where they have no cultural connection to the Jewish people. 

9. We have to know the Torah relates to all the generations and all the souls. Let us translate the act of ברית אבות ואמהות to our lives. 

10. In the battle between good and evil, evil rejoices at the downfall of the good. There are two versions of this joy. 1] The joy of victory as per the nature of every victor. 2] A MUCH greater joy than a regular victory - as we will explain.  

11. There are some sins that are rooted in the שפלות הנפש - the low state of the human soul. Others are rooted in רוממות הנפש - the elevated state of the human soul. MOST of the sins of the Jewish people are of the second type. "פן אשבע וכחשתי" - lest I be satiated and deny or "וישמן ישורון ויבעט" - Yeshurun [the Jewish people] became fat and rebelled, are more common than "פן אורש וגנבתי" - Lest I become poor and steal. These psukim refer not only to physical comfort and affluence but to the spiritual sort as well. As Rashi says [Bamidbar 11-20] "מאסתם את ה' אשר בקרבכם" - You despised G-d who is in your midst. We became "too holy". So here we have a היכי תצמי - a scenario where spiritual affluence and flourishing opens the door for us to stray. Here, the side of evil is ESPECIALLY happy. This is where the good is transformed as a כלי for evil. That is ממש a yuntiv for the forces of evil! 

12. Here comes the ברית אמהות. Just like in their time they preserved the good by expelling the bad, so for the generations they preserve the good by protecting it from evil. They make sure that all of the great מעלות and spiritual properties we have from the Avos will not be corrupted and used for evil. [Of course, we still maintain our בחירה]. 

13. At יציאת מצרים we merited that Hashem appeared to us "נגלה עליהם מלך מלכי המלכים" thanks to the fulfillment of the promise to the Avos [אני השם - שהבטחתי לאבות בא-ל ש-די - See Rashi at the beginning of Parshas Vaera]. We are assured that those lights will remain with us only. That is the impact of the ברית אבות and ברית אמהות for all the generations to all of the souls. 

14. We go back to where we started. "מדלג על ההרים - בזכות אבות, מקפץ על הגבעות - בזכות אמהות". In the Mishna in Ohalos [8-5] it is explained [see Rambam in Peirush Hamishnayos and Rosh] that דליגה Is skipping with one leg while קפיצה is with two. רליגה is the Avoss. One leg. The creation of Kedusha. קפיצה is the Imahos. Two legs. Not only the edifice of Kedusha [one leg] but it's preservation [second leg]. Creation and separation.   

[עפ"י תורת מרן ראש הישיבה זצ"ל]