Faith

Jesus encountered responses to himself which he judged as "faith".

When Jesus returned to Capernaum, a Roman officer^[b] came and pleaded with him, “Lord, my young servant^[c] lies in bed, paralyzed and in terrible pain.”
Jesus said, “I will come and heal him.”
But the officer said, “Lord, I am not worthy to have you come into my home. Just say the word from where you are, and my servant will be healed. I know this because I am under the authority of my superior officers, and I have authority over my soldiers. I only need to say, ‘Go,’ and they go, or ‘Come,’ and they come. And if I say to my slaves, ‘Do this,’ they do it.”
When Jesus heard this, he was amazed. Turning to those who were following him, he said, “I tell you the truth, I haven’t seen faith like this in all Israel! And I tell you this, that many Gentiles will come from all over the world—from east and west—and sit down with Abraham, Isaac, and Jacob at the feast in the Kingdom of Heaven. But many Israelites—those for whom the Kingdom was prepared—will be thrown into outer darkness, where there will be weeping and gnashing of teeth.”
Then Jesus said to the Roman officer, “Go back home. Because you believed, it has happened.” And the young servant was healed that same hour. (Matthew 8: 5-13, NLT - all underlining in this post added by me.)

Even without a detachment of troops, how scary was it to see a Centurion coming forward? Surely it was all too clear who he was and what his job represented. (I suppose he was armed.) Had this soldier been seen before in the vicinity of Jesus? From Luke (8), it seems he was known. Luke also gives the impression the soldier, without becoming a Jew, may have been a person drawn to the LORD self-revealed in Scripture (ie, OT). He was certainly sympathetic to the Jews. (Judaism continued to be an allowed religion in the Empire.)

Matthew brings the officer before us here as a "stand-out". Somehow this man had become persuaded that Jesus would assuredly listen to him, and moreover, that Jesus was completely able to grant his request.  The Centurion surprised Jesus by his confidence in Jesus' healing power and mercy. In the end, the Centurion's "faith" (as the NRSV translates) was rewarded by the servant being restored to health. The idividual "outsider" stands in contrast with the "insider" group. Jesus had not previously found such a relationship.

Did Jesus look for faith in himself amongst his own people - the people of the Law? Remember these striking words from John, chapter 1: 10-13 (NRSV):
He was in the world, and the world came into being through him; yet the world did not know him. He came to what was his own,[c] and his own people did not accept him. But to all who received him, who believed in his name, he gave power to become children of God, who were born, not of blood or of the will of the flesh or of the will of man, but of God. The record shows some did receive him and hold to their trust in him, difficult as it may have been. Possibly, at Jesus' apparent end, the "receivers" were not all that numerous, but they did in the end turn the world upside down.

Matthew puts that episode of the centurion near the following clear contrast I am taking from Mark..... 

As evening came, Jesus said to his disciples, “Let’s cross to the other side of the lake.” So they took Jesus in the boat and started out, leaving the crowds behind (although other boats followed). But soon a fierce storm came up. High waves were breaking into the boat, and it began to fill with water.
Jesus was sleeping at the back of the boat with his head on a cushion. The disciples woke him up, shouting, “Teacher, don’t you care that we’re going to drown?”
When Jesus woke up, he rebuked the wind and said to the waves, “Silence! Be still!” Suddenly the wind stopped, and there was a great calm. Then he asked them, “Why are you afraid? Do you still have no faith?”
The disciples were absolutely terrified. “Who is this man?” they asked each other. “Even the wind and waves obey him!” (Mark 4: 35-41, NLT )

Their fears in the storm (Mark 4, above; also reported in Matthew and Luke) seem natural enough. Moreover,  professional fishermen would know the risk all too well. Then, in what way are they hindered by being unconfident? Should they have just known that no disaster could or would befall Jesus, and they were with him? (That interpretation seems beyond reasonable.) Surely they had been already assured that Jesus did care and that was beyond doubt? Could they have known that all they needed do was deliberately and trustingly turn their fearful need over to Jesus, even if it meant waking him? For sure their comprehension of Jesus needed to grow (as in fact it did), and thus their relationship develop. They are characterised here as lacking in belief or trust. (Matthew's version has that their faith was little, or few, or small or slight - the detour matter of variation again arises and I mention this below.) 

Note that Luke in his comparable report gives us the pointer that Jesus actively looked for people to take up this kind of relationship to him:  
Then he asked them, “Where is your faith?” The disciples were terrified and amazed. “Who is this man?” they asked each other. “When he gives a command, even the wind and waves obey him!” (Luke 8:40, NLT). Where....? Jesus asks. Something vital is lacking from their relationship to him.
 
Perhaps here we see Jesus again amazed, but this time for an opposite reason. As to their shocked question (“Who is this man?”) - they were coming to the answer during these weeks and months. So much so, after the resurrection of Jesus they boldly set Jerusalem authorities "on their ear". So, for example, they said to those authorities:  
But there is something we must tell you and everyone else in Israel. This man is standing here completely well because of the power of Jesus Christ from Nazareth. You put Jesus to death on a cross, but God raised him to life (Acts 4:10, CEV).

John has a Capernaum report which puts such a moment (or, the moment) even more starkly:
The official pleaded, “Lord, please come now before my little boy dies.” Then Jesus told him, “Go back home. Your son will live!” And the man believed what Jesus said and started home. (John 4:49-50, NLT)
 

An instance of use of the word "faith" early on in Matthew has men bringing another to Jesus for help: And just then some people were carrying a paralyzed man lying on a bed. When Jesus saw their faith, he said to the paralytic, “Take heart, son; your sins are forgiven.” (...text omitted)  But so that you may know that the Son of Man has authority on earth to forgive sins”—he then said to the paralytic—“Stand up, take your bed and go to your home.” And he stood up and went to his home. When the crowds saw it, they were filled with awe, and they glorified God, who had given such authority to human beings. (Matthew 9:2, 6-8 NRSV). Questions arise: Exactly whose faith did Jesus see - the four, or the five (assuming one man to each corner)? Whose idea was it to come? Why did the paralytic come - for healing, or for forgiveness? (Is there any difference?) Clear it is what kind of confidence and relationship to Jesus drives their action of coming/bringing to him the need. (Was this a time when Jesus found or saw in Israel the relationship he wanted; the reality that would change "everything"?)

Faith and gratitude are naturally associated. Luke has a report of an instructive event on this. (I have recently read expositions* of this passage which put forward guesses or assumptions as certainties. For this reason I substantially edited this segment of my post about the following, keeping questions as questions):
On his way to Jerusalem, Jesus went along the border between Samaria and Galilee. As he was going into a village, ten men with leprosy[a] came toward him. They stood at a distance and shouted, “Jesus, Master, have pity on us!”Jesus looked at them and said, “Go show yourselves to the priests.”[b]
On their way they were healed. When one of them discovered that he was healed, he came back, shouting praises to God. He bowed down at the feet of Jesus and thanked him. The man was from the country of Samaria.
Jesus asked, “Weren’t ten men healed? Where are the other nine? Why was this foreigner the only one who came back to thank God?” Then Jesus told the man, “You may get up and go. Your faith has made you well.” (Luke 17: 11-19, CEV).
We can notice that all 10 asked for Jesus' mercy. All 10 set off in simple (?) trusting obedience to Jesus' direction, fulfilment of which would establish in their society the fact that they were healed! Were all 10 showing the same faith in action? To which priest did that foreigner (Samaritan) start to go (he presumably was outside of the Jewish religion)? The Samaritan turned back to express his gratitude and Jesus commended him. Did the Samaritan then go on, as required, to "the priest"? Were the other 9 grateful - surely they should have been? Was Jesus surprised that the 9 did not join the one? If Jesus was disappointed in the 9 were they not healed nevertheless? Was there only the one Samaritan amongst the 10? And, I wonder, were the nine glad to see the back of the Samaritan? (Jews had no dealings with Samaritans, except, it would seem, in the shared misery of that disease. Even for those with experience of Jesus, cultural, social and religious distinctions may linger.) 

*Recent reading - assertions that the Samaritan ex-leper did not go to the priest. This claim was contained in a blog by a preacher and, more disconcertingly, in an article on "Leprosy" in the IVP Dictionary of Jesus and the Gospels. No evidence is given to support the assertion.  

"Faith" is actually a very frequent word in the NT (and the Bible as a whole). If considered along with the related word "believe" (verb - see, for example, Matthew 8:13 and John 1:12, above), the concept is even more prominent. It is a challenge to do enough justice to this key idea. I found that NRSV has faith 201 times in OT and 284 in NT. Believe is found in NRSV 28 times in OT and believe/d/s/rs 253 times in NT. In addition the word "persuade" (64 times in NT) is etymologically primary to "faith".

 So then, given the wealth of instances, there may be reason for a further post sometime on "faith". My core point here is that Jesus evaluates relationship to him. Many people may say many things, but what does Jesus say? This is what matters, and I think all of us, and any of us, can make a self-assessment, using the instances above.

Addendum detour, re that healing of the young male at Capernaum: Assuming the healing is the same event it is puzzling to reconcile the the accounts, even allowing for NT writers not having our idea of chronological exactness. The same applies to the order of events, and even the details of the Centurion's approach (example below). Some may find variations such as these a bother, or an excuse - I hope you do not; God will reward your trust and be pleased with your questions.

The other Synoptic Gospels report storm events similar to that in Mark 4 (see above). There are variations in the records (!). Here together from the RSV is that one instance:
Mark 4:40 He said to them, “Why are you afraid? Have you no faith?”
Matthew 8:26a And he said to them, “Why are you afraid, O men of little faith?”
Luke 8:25a He said to them, “Where is your faith?” And they were afraid... 
Matthew has Jesus using an unusual word to describe the defective trust (or lack of trust) shown by the disciples in the storm. Perhaps they were still at a childhood stage of development in their relationship to Jesus when they needed to be "grown ups"?
That particular expression occurs 6 times in the NT (Matthew 6: 30, 14:31, 16:8, 17:20 - the first is duplicated in Luke 12:28; not used by Mark, or John, or elsewhere) when Jesus speaks of having little or small faith, rather than none.

Scripture quotations marked (CEV) are from the Contemporary English Version Copyright © 1991, 1992, 1995 by American Bible Society, Used by Permission.
Scripture quotations marked (ESV) are from the ESV® Bible (The Holy Bible, English Standard Version®), copyright © 2001 by Crossway, a publishing ministry of Good News Publishers. Used by permission. All rights reserved.
Scripture quotations marked (NLT) are taken from the Holy Bible, New Living Translation, copyright ©1996, 2004, 2007, 2013 by Tyndale House Foundation. Used by permission of Tyndale House Publishers, Inc., Carol Stream, Illinois 60188. All rights reserved. Scripture quotations marked (NRSV) are from the New Revised Standard Version Bible, copyright © 1989 National Council of the Churches of Christ in the United States of America. Used by permission. All rights reserved.
Scripture quotations marked (RSV) are from the Revised Standard Version of the Bible, copyright © 1946, 1952, and 1971 the Division of Christian Education of the National Council of the Churches of Christ in the United States of America. Used by permission. All rights reserved.