While claiming to be wise, they became fools: 

They are filled with every form of wickedness, evil, greed, and malice; full of envy, murder, rivalry, treachery, spite, senseless, faithless, heartless. They are also ruthless, gossips
scandalmongers, rebellious toward their parents, insolent, haughty, boastful, ingenious in their wickedness, and they hate God.

They knew God and they did not accord him glory as God or give him thanks. Instead, they became vain in their reasoning, and their senseless minds were darkened.
They knew the just decree of God that all who practice such things deserve death, they not only do them but give approval to those who practice them.

Ever since the creation of the world, his invisible attributes of eternal power and divinity have been able to be understood and perceived in what he has made. As a result, they have no excuse.
For what can be known about God is evident to them, ( the wicked) because God made it evident to them. 

The Apostle Paul declares:  "For I am not ashamed of the gospel. It is the power of God for the salvation of everyone who believes: for Jew first, and then Greek. (at that time the conquest of Alexander the Great was evident through out the known world). God is my witness, whom I serve with my spirit in proclaiming the gospel of his Son, (Jesus Christ). For in it is revealed the righteousness of God from faith to faith;
as it is written, "The one who is righteous by faith will live." 
Bible:  Book of Romans   Chapeter 1:  (portions of it)
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Notes
These words were spoken by the Apostle Paul whose office was apostleship to the Gentiles. 
Greeks and non-Greeks: literally, "Greeks and barbarians." As a result of Alexander's conquests, Greek became the standard international language of the Mediterranean world. 
The principal theme of the letter is salvation through faith.
 
I am not ashamed of the gospel:  Paul is not ashamed to proclaim the gospel, despite the criticism that Jews and Gentiles leveled against the proclamation of the crucified savior (Jesus).
Paul affirms, however, that it is precisely through the crucifixion and resurrection of Jesus that God's saving will and power become manifest. Jew first means that Jews especially, in view of the example of Abraham, ought to be the leaders in the response of faith.

Greeks in Paul's statement therefore means people who know Greek or who have been influenced by Greek culture. Non-Greeks were people whose cultures remained substantially unaffected by Greek influences.

The gospel centers in Jesus Christ, in whom God's saving presence and righteousness in history have been made known. Faith is affirmation of the basic purpose and meaning of the Old Testament as proclamation of divine promise and exposure of the inability of humanity to effect its salvation even through covenant law.

 Faith is the gift of the holy Spirit and denotes acceptance of salvation as God's righteousness, that is, God's gift of a renewed relationship in forgiveness and power for a new life. Faith is response to God's total claim on people and their destiny.

Paul aims to show that all humanity is in a desperate plight and requires God's special intervention if it is to be saved.