Wisdom = Experience
A popular Hebrew saying is אין חכם כבעל נסיון (no one is wiser than the one who has experience). The first attestation of this saying in Hebrew literature is in the commentary of the Spanish Rabbi Isaac ben Moses Arama (c. 1420 – 1494) in his commentary on Genesis in his book Aqedat Yishaq. An earlier allusion to this saying is perhaps found in the Choice of Pearls, a collection of sayings translated from Arabic and often attributed to the Spanish poet Ibn Gabirol (d. 11th century). There we find: ואין מנהיג לבני האדם כבעל הנסיונות המשכיל (there is no better leader of people than the wise one who has had experiences).
Yisrael H. Taviov (d. 1920) thought that the idea behind the saying אין חכם כבעל נסיון is derived from a non-Jewish proverb, but that its wording is unique to Hebrew. However, the wording is probably Islamic:
Qutayba reported to us
saying: 'Abdallah b. Wahb reported to us
on the authority of 'Amr b. al-Harith,
on the authority of Darraj,
on the authority of Abi l-Haytham,
on the authority of Abu Sa'id [al-Khudri], saying: The Messenger of God (ﷺ) said: No one is more forbearing than the one who has stumbled [and gotten up]. No one is wiser than the one who has experience.
From the Sunan of al-Tirmidhi (d. 892)
حدثنا قتيبة
قال: حدثنا عبد الله بن وهب
عن عمرو بن الحارث
عن دراج
عن أبي الهيثم
عن أبي سعيد
قال: قال رسول الله ﷺ: لا حليم إلا ذو عثرة ولا حكيم إلا ذو تجربة
Originally this Hadith appears to have been attributed to Abu Sa'id al-Khudri, not the Prophet, as is indicated by a tradition in al-Adab al-Mufrad of al-Bukhari (d. 870). 'Abdallah b. Wahb (Egypt, d. 812) is probably responsible for adding the Prophet's name to the tradition. In the same work, we also find a similar saying attributed to the Umayyad Caliph Mu'awiya:
Farwa b. Abi l-Margha' reported to us
saying: 'Ali b. Mushir reported to us
on the authority of Hisham b. 'Urwa,
on the authority of his father [= 'Urwa b. al-Zubayr], saying: I was sitting in the presence of Mu'awiya and he was talking to himself [when he was ill]. Then, he came to his senses and said: There is no forbearing unless that it comes through experience. He repeated this thrice.
From al-Adab al-Mufrad of al-Bukhari
حدثنا فروة بن أبي المغراء
قال: حدثنا علي بن مسهر
عن هشام بن عروة
عن أبيه
قال: كنت جالسا عند معاوية فحدث نفسه ثم انتبه فقال: لا حلم إلا تجربة ، يعيدها ثلاثا
In his Sahih, al-Bukhari attributes this statement to Mu'awiya with a different wording:
ِAnd Mu'awiya said: No one is wiser than the one who has experience.
From Sahih of al-Bukhari
وقال معاوية: لا حكيم إلا ذو تجربة
Al-Bukhari was aware that the statement "no one is wiser than the one who has experience" was attributed to Mu'awiya, Abu Sa'id al-Khudri, and the Prophet. He likely thought that the attribution to Mu'awiya had the greatest claim to be genuine. Probably for this reason, he attributed this saying to Mu'awiya in the Sahih. Despite al-Bukhari's skepticism, al-Tirmidhi had no problem including it as a Prophetic saying in his own collection of genuine Hadith from the Prophet. Collectors like al-Bukhari and al-Tirmidhi helped make this statement famous. Eventually it entered Hebrew, where it is used until this day.