Check out The Thinking Jew Podcast episode 4 for the audio that this source sheet accompanies.
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וְהָיָ֗ה אִם־שָׁמֹ֤עַ תִּשְׁמְעוּ֙ אֶל־מִצְוֺתַ֔י אֲשֶׁ֧ר אָנֹכִ֛י מְצַוֶּ֥ה אֶתְכֶ֖ם הַיּ֑וֹם לְאַהֲבָ֞ה אֶת־יְהֹוָ֤ה אֱלֹֽהֵיכֶם֙ וּלְעׇבְד֔וֹ בְּכׇל־לְבַבְכֶ֖ם וּבְכׇל־נַפְשְׁכֶֽם׃
If, then, you obey the commandments that I enjoin upon you this day, loving the LORD your God and serving Him with all your heart and soul,
וּמְנָא לַן דְּבִתְפִלָּה דְּתַנְיָא לְאַהֲבָה אֶת ה׳ אֱלֹהֵיכֶם וּלְעׇבְדוֹ בְּכׇל לְבַבְכֶם אֵיזוֹ הִיא עֲבוֹדָה שֶׁהִיא בַּלֵּב הֱוֵי אוֹמֵר זוֹ תְּפִלָּה וּכְתִיב בָּתְרֵיהּ וְנָתַתִּי מְטַר אַרְצְכֶם בְּעִתּוֹ יוֹרֶה וּמַלְקוֹשׁ
The Gemara asks: And from where do we derive that rain must be mentioned specifically in the Amida prayer? The Gemara answers: As it was taught in a baraita with regard to the verse: “To love the Lord your God and to serve Him with all your heart” (Deuteronomy 11:13). Which is the service of God that is performed in the heart? You must say that this is referring to prayer. And, afterward, it is written: “And I shall give the rain of your land in its due time, the first rain and the last rain” (Deuteronomy 11:14). This juxtaposition teaches that it is appropriate to request rain while engaged in the service of the heart, i.e., prayer.
מִצְוַת עֲשֵׂה לְהִתְפַּלֵּל בְּכָל יוֹם שֶׁנֶּאֱמַר (שמות כג כה) ״וַעֲבַדְתֶּם אֵת ה׳ אֱלֹהֵיכֶם״. מִפִּי הַשְּׁמוּעָה לָמְדוּ שֶׁעֲבוֹדָה זוֹ הִיא תְּפִלָּה שֶׁנֶּאֱמַר (דברים יא יג) ״וּלְעָבְדוֹ בְּכָל לְבַבְכֶם״ אָמְרוּ חֲכָמִים אֵי זוֹ הִיא עֲבוֹדָה שֶׁבַּלֵּב זוֹ תְּפִלָּה. וְאֵין מִנְיַן הַתְּפִלּוֹת מִן הַתּוֹרָה. וְאֵין מִשְׁנֶה הַתְּפִלָּה הַזֹּאת מִן הַתּוֹרָה. וְאֵין לַתְּפִלָּה זְמַן קָבוּעַ מִן הַתּוֹרָה:
To pray daily is an affirmative duty, as it is said, "And ye shall serve the Lord, your God" (Exodus 23:25). The service, here referred to, according to the teaching of tradition, is Prayer, as it is said, "And to serve Him with all your heart" (Deuteronomy 11:13), on which the sages commented, "What may be described as Service of the Heart? Prayer". The number of prayers is not prescribed in the Torah. No form of prayer is prescribed in the Torah. Nor does the Torah prescribe a fixed time for Prayer.
אִיתְּמַר, רַבִּי יוֹסֵי בְּרַבִּי חֲנִינָא אָמַר: תְּפִלּוֹת אָבוֹת תִּקְּנוּם. רַבִּי יְהוֹשֻׁעַ בֶּן לֵוִי אָמַר: תְּפִלּוֹת כְּנֶגֶד תְּמִידִין תִּקְּנוּם. תַּנְיָא כְּווֹתֵיהּ דְּרַבִּי יוֹסֵי בְּרַבִּי חֲנִינָא, וְתַנְיָא כְּווֹתֵיהּ דְּרַבִּי יְהוֹשֻׁעַ בֶּן לֵוִי. תַּנְיָא כְּווֹתֵיהּ דְּרַבִּי יוֹסֵי בְּרַבִּי חֲנִינָא: אַבְרָהָם תִּקֵּן תְּפִלַּת שַׁחֲרִית, שֶׁנֶּאֱמַר: ״וַיַּשְׁכֵּם אַבְרָהָם בַּבֹּקֶר אֶל הַמָּקוֹם אֲשֶׁר עָמַד שָׁם״, וְאֵין ״עֲמִידָה״ אֶלָּא תְּפִלָּה, שֶׁנֶּאֱמַר: ״וַיַּעֲמֹד פִּינְחָס וַיְפַלֵּל״. יִצְחָק תִּקֵּן תְּפִלַּת מִנְחָה, שֶׁנֶּאֱמַר ״וַיֵּצֵא יִצְחָק לָשׂוּחַ בַּשָּׂדֶה לִפְנוֹת עָרֶב״, וְאֵין ״שִׂיחָה״ אֶלָּא תְּפִלָּה, שֶׁנֶּאֱמַר ״תְּפִלָּה לְעָנִי כִי יַעֲטֹף וְלִפְנֵי ה׳ יִשְׁפֹּךְ שִׂיחוֹ״. יַעֲקֹב תִּקֵּן תְּפִלַּת עַרְבִית, שֶׁנֶּאֱמַר: ״וַיִּפְגַּע בַּמָּקוֹם וַיָּלֶן שָׁם״, וְאֵין ״פְּגִיעָה״ אֶלָּא תְּפִלָּה, שֶׁנֶּאֱמַר: ״וְאַתָּה אַל תִּתְפַּלֵּל בְּעַד הָעָם הַזֶּה וְאַל תִּשָּׂא בַעֲדָם רִנָּה וּתְפִלָּה וְאַל תִּפְגַּע בִּי״ וְתַנְיָא כְּווֹתֵיהּ דְּרַבִּי יְהוֹשֻׁעַ בֶּן לֵוִי: מִפְּנֵי מָה אָמְרוּ תְּפִלַּת הַשַּׁחַר עַד חֲצוֹת — שֶׁהֲרֵי תָּמִיד שֶׁל שַׁחַר קָרֵב וְהוֹלֵךְ עַד חֲצוֹת. וְרַבִּי יְהוּדָה אוֹמֵר: עַד אַרְבַּע שָׁעוֹת שֶׁהֲרֵי תָּמִיד שֶׁל שַׁחַר קָרֵב וְהוֹלֵךְ עַד אַרְבַּע שָׁעוֹת. וּמִפְּנֵי מָה אָמְרוּ תְּפִלַּת הַמִּנְחָה עַד הָעֶרֶב — שֶׁהֲרֵי, תָּמִיד שֶׁל בֵּין הָעַרְבַּיִם קָרֵב וְהוֹלֵךְ עַד הָעֶרֶב. רַבִּי יְהוּדָה אוֹמֵר: עַד פְּלַג הַמִּנְחָה, שֶׁהֲרֵי תָּמִיד שֶׁל בֵּין הָעַרְבַּיִם קָרֵב וְהוֹלֵךְ עַד פְּלַג הַמִּנְחָה. וּמִפְּנֵי מָה אָמְרוּ תְּפִלַּת הָעֶרֶב אֵין לָהּ קֶבַע — שֶׁהֲרֵי אֵבָרִים וּפְדָרִים שֶׁלֹּא נִתְעַכְּלוּ מִבָּעֶרֶב, קְרֵבִים וְהוֹלְכִים כׇּל הַלַּיְלָה.
The dispute between the Rabbis and Rabbi Yehuda with regard to the times beyond which the different prayers may not be recited is rooted in a profound disagreement, also manifest in a later amoraic dispute. It was stated: Rabbi Yosei, son of Rabbi Ḥanina, said: The practice of praying three times daily is ancient, albeit not in its present form; prayers were instituted by the Patriarchs. However, Rabbi Yehoshua ben Levi said that the prayers were instituted based on the daily offerings sacrificed in the Holy Temple, and the prayers parallel the offerings, in terms of both time and characteristics. The Gemara comments: It was taught in a baraita in accordance with the opinion of Rabbi Yosei, son of Rabbi Ḥanina, and it was taught in a baraita in accordance with the opinion of Rabbi Yehoshua ben Levi. The Gemara elaborates: It was taught in a baraita in accordance with the opinion of Rabbi Yosei, son of Rabbi Ḥanina: Abraham instituted the morning prayer, as it is stated when Abraham came to look out over Sodom the day after he had prayed on its behalf: “And Abraham rose early in the morning to the place where he had stood before the Lord” (Genesis 19:27), and from the context as well as the language utilized in the verse, the verb standing means nothing other than prayer, as this language is used to describe Pinehas’ prayer after the plague, as it is stated: “And Pinehas stood up and prayed and the plague ended” (Psalms 106:30). Clearly, Abraham was accustomed to stand in prayer in the morning. Isaac instituted the afternoon prayer, as it is stated: “And Isaac went out to converse [lasuaḥ] in the field toward evening” (Genesis 24:63), and conversation means nothing other than prayer, as it is stated: “A prayer of the afflicted when he is faint and pours out his complaint [siḥo] before the Lord” (Psalms 102:1). Obviously, Isaac was the first to pray as evening approached, at the time of the afternoon prayer. Jacob instituted the evening prayer, as it is stated: “And he encountered [vayifga] the place and he slept there for the sun had set” (Genesis 28:11). The word encounter means nothing other than prayer, as it is stated when God spoke to Jeremiah: “And you, do not pray on behalf of this nation and do not raise on their behalf song and prayer, and do not encounter [tifga] Me for I do not hear you” (Jeremiah 7:16). Jacob prayed during the evening, after the sun had set. And it was taught in a baraita in accordance with the opinion of Rabbi Yehoshua ben Levi that the laws of prayer are based on the laws of the daily offerings: Why did the Rabbis say that the morning prayer may be recited until noon? Because, although the daily morning offering is typically brought early in the morning, it may be sacrificed until noon. And Rabbi Yehuda says: My opinion, that the morning prayer may be recited until four hours into the day, is because the daily morning offering is sacrificed until four hours. And why did the Rabbis say that the afternoon prayer may be recited until the evening? Because the daily afternoon offering is sacrificed until the evening. Rabbi Yehuda says that the afternoon prayer may be recited only until the midpoint of the afternoon because, according to his opinion, the daily afternoon offering is sacrificed until the midpoint of the afternoon. And why did they say that the evening prayer is not fixed? Because the burning of the limbs and fats of the offerings that were not consumed by the fire on the altar until the evening. They remained on the altar and were offered continuously throughout the entire night.
אֶת־הַכֶּ֥בֶשׂ אֶחָ֖ד תַּעֲשֶׂ֣ה בַבֹּ֑קֶר וְאֵת֙ הַכֶּ֣בֶשׂ הַשֵּׁנִ֔י תַּעֲשֶׂ֖ה בֵּ֥ין הָֽעַרְבָּֽיִם׃
You shall offer one lamb in the morning, and the other lamb you shall offer at twilight.
Introduction (Hakdama) of Rav Yaakov Ibn-Chaviv to the Sefer Ein Yaakov. Taken from https://beta.hebrewbooks.org/reader/reader.aspx?sfid=47602#p=8&fitMode=fitwidth&hlts=&ocr=