What Exactly Is the Wisdom of the Non-Jews?

(כב) בֶּן בַּג בַּג אוֹמֵר, הֲפֹךְ בָּהּ וַהֲפֹךְ בָּהּ, דְּכֹלָּא בָהּ. וּבָהּ תֶּחֱזֵי, וְסִיב וּבְלֵה בָהּ, וּמִנַּהּ לֹא תָזוּעַ, שֶׁאֵין לְךָ מִדָּה טוֹבָה הֵימֶנָּה:

Pirkei Avot 5:22

(22) Ben Bag Bag says: Search in it and search in it, since everything is in it. And in it should you look, and grow old and be worn in it; and from it do not move, since there is no characteristic greater than it.

רבינו יונה על פרקי אבות ה׳:כ״ב:א׳

(א) הפוך בה וכו'. חזור על דברי תורה שכל חכמת העולם כלולה בה:

Rabbeinu Yonah on Pirkei Avot 5:22:1

(1) Search in it, etc.: Review the words of Torah, as all the wisdom of the world is included in it.

תוספות יום טוב על משנה אבות ה׳:כ״ב:ו׳

(ו) שאין לך מדה טובה הימנה. שלא תאמר שבלמוד חכמת יונית בהכרח אלמד מהם מדיניות והנהגה ומדות טובות. להכי קאמר שאין לך מדה טובה הימנה. כי כל המדות טובות ערוכות בכל ושמורות בה. ועוד יש לפרש דתנא דידן מהדר אכולהו מוסרי החכמים וקאמר שאין בכל המדות טובות שיעצוך שתקנה ותשתלם בהן כמדה הזאת שיעצתיך שזאת היא עולה על גביהן. מד"ש:

Tosafot Yom Tov on Pirkei Avot 5:22:6

(6) FOR THERE IS NO BETTER TRAIT [Heb. middah]²⁴¹Tosafot Yom Tov understands the word as “trait” or “characteristic”, the way it is indeed used in other contexts. The simple understanding of the word here, however, would be something like “way” or “lot”. THAN THIS. You should not think that through learning the wisdom of the Greeks you will certainly learn proper behavior and good character. The mishna says “there is no better trait than this”, for all good character traits are arranged and included in it. Alternatively, our tanna is addressing all of the ethical teachings of the Sages and saying that, from among all of the good character traits that the Sages have advised you to acquire and perfect yourself in, none is like this trait about which I have advised you, for it is the greatest of them all—Midrash Shmuel.

איכה ב׳:ט׳

(ט) טָבְע֤וּ בָאָ֙רֶץ֙ שְׁעָרֶ֔יהָ אִבַּ֥ד וְשִׁבַּ֖ר בְּרִיחֶ֑יהָ מַלְכָּ֨הּ וְשָׂרֶ֤יהָ בַגּוֹיִם֙ אֵ֣ין תּוֹרָ֔ה גַּם־נְבִיאֶ֕יהָ לֹא־מָצְא֥וּ חָז֖וֹן מֵיְהוָֽה׃ (ס)

Lamentations 2:9

(9) Her gates have sunk into the ground, He has smashed her bars to bits; Her king and her leaders are in exile, Instruction is no more; Her prophets, too, receive No vision from the LORD.

רש"י על איכה ב׳:ט׳

(ב) אֵין תּוֹרָה. אֵין בָּהֶם מוֹרֵה הוֹרָאָה:

Rashi on Lamentations 2:9

(2) Without guidance. There is no one among them to give instructions.

עובדיה א׳:ח׳

(ח) הֲל֛וֹא בַּיּ֥וֹם הַה֖וּא נְאֻם־יְהוָ֑ה וְהַאֲבַדְתִּ֤י חֲכָמִים֙ מֵֽאֱד֔וֹם וּתְבוּנָ֖ה מֵהַ֥ר עֵשָֽׂו׃

Obadiah 1:8

(8) In that day —declares the LORD— I will make the wise vanish from Edom, Understanding from Esau’s mount.

מצודת דוד על עובדיה א׳:ח׳

(א) ביום ההוא. ביום בוא הפורעניות: (ב) והאבדתי חכמים. לא יתחכמו בתחבולות המלחמה להציל נפשם:

Metzudat David on Obadiah 1:8

... On that day punishments will come.
They will not use their intellect for tricks of war to save themselves.

איכה רבה ב׳:י״ג

... מַלְכָּהּ וְשָׂרֶיהָ בַגּוֹיִם אֵין תּוֹרָה. אִם יֹאמַר לְךָ אָדָם יֵשׁ חָכְמָה בַּגּוֹיִם, תַּאֲמֵן, הֲדָא הוּא דִכְתִיב (עובדיה א, ח): וְהַאֲבַדְתִּי חֲכָמִים מֵאֱדוֹם וּתְבוּנָה מֵהַר עֵשָׂו. יֵשׁ תּוֹרָה בַּגּוֹיִם, אַל תַּאֲמֵן, דִּכְתִיב: מַלְכָּהּ וְשָׂרֶיהָ בַגּוֹיִם אֵין תּוֹרָה...

Eikhah Rabbah 2:13

Kings and ministers in the Nations, no Torah. If someone will say to you that there is wisdom among the nations, believe him, in that which it is written, "And I will destroy the wise men from Edom and understanding from the Mountain of Seir. (If he says) there is Torah among the nations, don't believe him, as it is written, "Kings and ministers in the Nations, no Torah."

Rabbi Yitzchak Breitowitz
Learning Torah will not teach you rocket science, brain surgery or trigonometry. Torah tells you everything you need to know about life, how to live as a human being, how to understand your purpose in the world, how to understand the WHY of creation though it will not necessarily tell you the WHAT of creation.
Rav Tzadok, Machshavos Charutz 11, described the Torah as the Peirush and Commentary on the Beriah. But you need to read the text to understand the significance of the commentary. You will not get Rashi's explanation of the Chumash unless you also read the Chumash. .

Tzidkos Hatzaddik, Rav Tzadok HaCohen
Gentile wisdom has no reality in the world, and therefore has no ultimate relevance to the True Torah which exists forever. The outer wisdom will develop until the absorption of the good by Israel is completed, and then all their wisdom will cease to exist...
Torah She'Baal Peh in King Solomons time was aided by Gentile wisdom on temporary loan to the Israelites in order thereby to set Divine Wisdom in their hearts... ultimately returned to them as Israel had no further need.

סנהדרין ק״ד ב:י״ג

... אמר רב יהודה אמר רב בקשו עוד למנות אחד, באה דמות דיוקנו של אביו ונשטחה לפניהם ולא השגיחו עליה באה אש מן השמים ולחכה אש בספסליהם ולא השגיחו עליה

Sanhedrin 104b:13

§ The Gemara resumes its discussion of the kings and commoners enumerated in the mishna who have no share in the World-to-Come. The Gemara asks: Who enumerated them? Rav Ashi says: The members of the Great Assembly enumerated them. Rav Yehuda says that Rav says: They sought to enumerate one more, King Solomon, in the list of kings with no share in the World-to-Come. The image of the face of his father, King David, came and prostrated itself before them, pleading to omit Solomon from the list, and they paid it no heed. A fire came from Heaven and the fire scorched their benches [safseleihem], and they paid it no heed.

סנהדרין ק״ד ב:י״ד

יצאה בת קול ואמרה להם (משלי כב, כט) חזית איש מהיר במלאכתו לפני מלכים יתיצב בל יתיצב לפני חשוכים מי שהקדים ביתי לביתו ולא עוד אלא שביתי בנה בשבע שנים וביתו בנה בשלש עשרה שנה לפני מלכים יתיצב [בל יתיצב] לפני חשוכים ולא השגיח עליה יצאה בת קול ואמרה (איוב לד, לג) המעמך ישלמנה כי מאסת כי אתה תבחר ולא אני וגו'

Sanhedrin 104b:14

A Divine Voice emerged and said to the members of the Great Assembly: “Do you see a man diligent in his business? He shall stand before kings; he shall stand not before obscure men” (Proverbs 22:29). See the greatness of Solomon, who preceded construction of My House, the Temple, to the construction of his house. Moreover, My House he built quickly, in just seven years, and his house he constructed in thirteen years. Therefore, “he shall stand before kings; he shall stand not before obscure men,” and it is inappropriate to enumerate him among the wicked. And they paid it no heed. A Divine Voice emerged and said: “Shall His recompense be as you will it? For you loathe it, so that you must choose, and not I? Therefore, speak what you know” (Job 34:33). Only God, and not the people, determines who has a share in the World-to-Come.

Rabbi Yitzchak Breitowitz
Why we use secular insights for the understanding of human character and motivation is indeed a much more difficult question. Part of it is certainly a yeridas hadoros and hester panim in which Divine truth becomes accessible to us through popular and simplified culture which at its best can allow us to then see these truths in a deeper way within the Torah. The example would be the person who can only read Shakespeare in comic book form because the original is too deep and complicated.