There are two types of emunah. There is emunah peshutah, which means having belief without proving it. Then there is the emunah, the belief that is the product of philosophical discussions and proofs, questions and answers. Avraham Avinu started with philosophical emunah, and then he adapted the approach of emunah peshutah, as we will explain.
The Rambam (Avodah Zarah 1:3) writes, "As soon as this strong one (Avraham) was weaned, his mind began searching. He was young and was thinking day and night. He wondered, 'How can it be that the sun is always moving, and no one is turning it? He didn’t have anyone to teach him because he lived in Ur Kasdim among stupid idol worshipers (הטפשים כוכבים עובדי בין). His father, his mother, and the entire country worshiped the stars, and he worshiped the stars together with them. But his heart was searching... until he perceived the true path... He discovered that there is one G-d, He directs the sun, He created everything, and there is no G-d other than Him. He knew that everyone in the world was mistaken. He recognized the Creator when he was forty years old. Avraham began debating with the people of Ur Kasdim and admonished them, 'You aren't on the right path,' he would tell them. He broke their idols and told them that they should serve the Creator of the world. Avraham proved it to them with many proofs until the king wanted to kill him, but he was saved through a miracle, and he ran to Charan. Avraham proclaimed loudly to everyone that there is only one G-d, and we should serve Him alone. Thousands and tens of thousands followed Avraham. He planted emunah in their hearts, and he wrote sefarim."
This Rambam discusses Avraham's initial emunah, the approach of proofs and philosophical logic. He thought about the sun, about creation, and he discovered Hashem.
Nevertheless, after Avraham attained emunah, he adopted the ideal path for emunah, which is emunah peshutah, simple faith, without question. It states (15:4, 6), ...ממעיך היוצא אם כי זה יירשך לא 'בה והאמן, "[Hashem told Avraham], 'This one [Eliezer] won't inherit you, rather the child that will come from your loins...' And Avraham believed in Hashem..." Avraham believed Hashem that he would bear children, and he didn't question it. The Agra d'Kalah writes that this was the moment that Avraham adopted the path of emunah peshutah. והאמן is written without a ד"יו. The letter ד"יו represents chachmah, wisdom. The missing ד"יו in והאמן implies that Avraham believed in Hashem with emunah peshutah, with simple faith, without needing wisdom and proofs to support it. When Avraham Avinu heard that he would bear children, he understood that philosophy is a dangerous path for the masses and that if he continued with his philosophical approach, his children might also study philosophy to acquire an awareness of Hashem. “If my children are wise, they will succeed in recognizing Hashem through philosophy. But it is a risky route because if they aren't wise enough, they may end up with questions, and they won't know the answers, and they will deny Hashem." Therefore, when Avraham heard he would bear children, he changed paths, and he followed the path of emunah peshutah, as implied in 'בה והאמן.
It states (Tehillim 37:18), תמימים ימי 'ה יודע, when one believes in Hashem with temimus, with emunah peshutah, תהיה לעולם ונחתלם, his belief will continue forever. But the path of philosophy isn't guaranteed to continue through one’s children and descendants.
The Baal Shem Tov zt'l said to his students, "After all the perceptions that I perceived in the root of the Torah and the mitzvos, and after all the pleasures I had from my perceptions, I forgo them all, and I have emunah peshutah. גלייב איך און נער א בין איך, 'I am a fool and I believe.'" The Baal Shem Tov had ruach hakodesh and great levels of spiritual perceptions. He saw malachim and the neshamos in heaven. But he didn’t use these as the root or proof for his emunah. He believed in Hashem with emunah peshutah (Baal Shem Tov al HaTorah, parashas Shemos). This is because emunah peshutah is the highest form of emunah, preferred over recognizing Hashem through philosophical or intellectual proofs.
The Zera Kodesh explains that the intellect is limited, and when one's emunah is based on his intelligence, it is limited to the extent of one's intellect. But to believe in Hashem with emunah peshutah is limitless.