Makkot 24b
R. Gamliel, R. Elazar ben Azarya, R. Joshua, and R. Akiva... were walking towards Jerusalem. When they reached Mount Scopus [from which it is possible to see the Temple Mount], they tore their clothing. When they arrived at the Temple Mount, they saw a fox running out of the area where the Holy of Holies had been. They began to cry, while R. Akiva laughed. They said to him, "Why are you laughing?".... He replied, "Isaiah the Prophet said, ‘I will bring two reliable witnesses regarding my people, Uriah the Priest and Zecharia ben Yeverchyahu.'"(Isaiah 8:2)... the verse in Isaiah makes Zecharia's prophecy dependent on Uriah's. In Uriah's case, it is written, "Therefore, because of you, Zion will be plowed under like a field." (Michah 3:12) In the case of Zecharia, we find, "Yet again, elderly men and elderly women will sit in the streets of Jerusalem.... Now that I have seen Uriah's prophecy fulfilled in full detail, I know that Zecharia's prophecy will also be fulfilled." Hearing that, R. Akiva's colleagues said to him, "Akiva, you have comforted us. Akiva, you have comforted us."2
Martin Seligman, Founder of Positive Psychology Movement
Pessimists believe their flaws cannot be overcome, whereas optimists are convinced that they can.
Avot de-Rabbi Natan
What were R. Akiva's beginnings? It is said, up to the age of forty, he had not studied a thing. One time, while standing by the mouth of a well in Lydda, he inquired, "Who hollowed out this stone?" and was told, "It was water falling upon it constantly, day after day." They said, "Akiva, haven't you read that ‘water wears away stone' (Job 14:19)?" At that, R. Akiva asked himself all the more so, "Is my mind harder than this stone?" He immediately returned to study Tora, and he and his son sat with a children's teacher.... The teacher wrote down alef and bet for him... he went on learning until he had learned all five Books of Moses.9
Gemara
Then he went and sat before R. Eliezer and R. Joshua. "My masters," he said to them, "Reveal the sense of Mishna to me." When they told him one halacha, he went off to reason with himself. This alef, he wondered, what was it written for? That bet, what was it written for? This teaching, what was it written for? He kept coming back, kept inquiring of R. Eliezer and R. Joshua....
All the thirteen years that R. Akiva was with R. Eliezer, R. Eliezer paid little attention to him, so that when R. Akiva offered his first clinching argument, R. Joshua quoted the verse, "There is the army you paid no attention to; now go out and fight it."10
Seligman, 1998 Seoul Olympics
We had... simulated defeat under controlled conditions in the pool. Nort Thornton, Biondi's coach, had him swim the one-hundred-yard butterfly all out. Biondi swam it in 50.2 seconds, a very respectable time. But Thornton told him that he had swum 51.7, a very slow time for Biondi. Biondi looked disappointed and surprised. Thornton told him to rest up for a few minutes and then swim it again--all out. Biondi did. His actual time got faster--50.0. Because his explanatory style was highly optimistic and he had shown us that he got faster--not slower--after defeat, I felt he would bring back gold from Seoul. In his last five events in Seoul, Biondi won five gold medals.12
R. Meir Soloveichik
"Akiva" is essentially an Aramaic variant of Yaakov, or Jacob. Like Akiva, the patriarch Jacob is depicted as having a remarkable capacity to persevere, mainly by working for his deceitful uncle Laban for fourteen years in order to earn the right to marry his beloved Rachel. Moreover, the names Jacob and Akiva both derive from the word ekev, or heel.13 As my father, Rabbi Eliyahu Soloveichik, once pointed out, the heel is the lowest portion of the body, yet, at the same time, it is the first part of the body used to take a step forward. In other words, it is precisely one's initial downfall that can ultimately emerge as a key to progress.
Gemara Ketubot
R. Akiva worked as a shepherd for Kalba Savua. When Kalba Savua's daughter [Rachel], saw that even though Akiva was unassuming, there was something extraordinary about him, she said, "If I am willing to be betrothed to you, will you attend a house of study?" R. Akiva answered, "Yes." So she betrothed herself to him in secret. When Kalba Savua learned what she had done, he drove her out of his house and vowed that she was not to benefit from any of his property.
At that, she went off and [openly] married Akiva. When winter came, [they were so poor that] they had to sleep in a straw bin. As R. Akiva picked the straw from her hair, he would say, "If I had the means, I would give you a ‘Jerusalem of gold.'"22