Faith vs Proof: A response to "The Leap of Faith."

Faith is the belief in something/ someone without it being physically present. People, however, cannot believe without having faith. How can you seriously know that 2+2=4? Because your teacher taught it to you? Wouldn't you have to have faith that your teacher actually knows what they are talking about to believe them? Yea, you can do the math for yourself with objects or even your fingers, but who is to say that addition isn't really subtraction and what we were taught is subtraction is really division? We had faith in those who taught us math to believe what they say and take it for the truth. People have faith in people,(trust) to teach them what is what sometimes without physical truth. Believing teachers and parents is the "Leap of Faith" that we take and then establish truth. Another example is religion. It has a lot to do with faith because one cannot see God, but those that are devout to Him knows that He is there. People who believe in religion believe that God is present in the atmosphere around us and do not need a physical being to know that He is there. The recording was talking about the difference about faith and proof. Well it seems that proof feeds into faith for some, if not many.
Another thing from yesterdays class that got me thinking was when the speaker was talking about people imagine they believe in religion and then you have those who truly do believe in religion. Religion,like i said in a previous post, isn't a physical thing; it is a spiritual and emotional thing. Those who supposedly "imagine the believe in God" may not have that connection with Him and don't acknowledge Him unless they need something. Also these people listen to sermons, but are absent minded while the sermons are going on and do not digest the word. They hear the pastor taking , but they don't understand or practice the Word of God. Those who truly believe try their best to please Jesus and listen whole-heartedly to the sermon digesting it and practicing it. Faith is a hard thing to have because we are spoiled to always have physical objects to cast our senses on. To get over not having faith, we must get over fully relying on our senses.