Paul says that Jews ask for signs which is precisely what we see in the gospels. The religious leaders are constantly asking Jesus to validate his authority as messiah by performing some kind of sign or miracle. They believed that the messiah would be a mighty leader who would be able to expel the dirty Romans from Israel. But instead it was the Romans who killed Jesus. Therefore, the idea of proclaiming that this Jesus who was crucified was the messiah is nothing short of a scandal.
Paul says that Greeks seek wisdom. One of the trademarks of Greek culture was its philosophers and its constant search for wisdom. And a basic tenet of Greek philosophy was that God could not suffer, that God could not even change. This is because God, by definition, was perfect, and if he changed then, by definition, he would have to become something other than perfect. Therefore, the idea of God becoming a human being, and even more so, the idea of God dying was an absurdly foolish idea to any Greek philosopher or seeker of wisdom.
In contrast these ideas about God, Paul says "But we preached Christ crucified!" As modern day Christians, we also often forget how scandalous this proclamation is. We have come to see the cross as a religious symbol. It adorns our jewelry and our sanctuaries as a symbol of hope because we have come to associate it with the resurrection and the power of God to give us new life and save us from the power of sin (assuming, of course, that we haven't further reduced it to a mere trinket among other symbols of sentimentality). As a result, we forget that this was a state sanctioned instrument of torture, cruelty, and death. This is the electric chair. This is the gas chamber. Crucifixion was the death reserved for criminals but not just any criminals. It was for those convicted of rebelling against the rule of the Roman Empire. We have a word for those people today: terrorists. Jesus was convicted and sentenced to death on a cross as a terrorist, an enemy of the state, a threat to Roman superiority.
Paul reminds the Corinthians (and us) "Remember, this is the gospel in which you believed. And you think that is something that you can pursue as worldly wisdom, as a philosophy on how to get ahead in life, as a self-help manual? How absurd!" Paul says "We preach Christ crucified! A crucified messiah! Have you forgotten that? Have you forgotten how absurd the gospel you believed appears according to worldly standards of wisdom? No worldly system of wisdom believes in a crucified messiah!"
But Paul says that this word of the cross which is foolishness to those who are perishing is the power of God to those of us who believe. God's foolishness is wiser than men's wisdom and God's weakness is stronger than men's strength. Paul says that the Corinthians themselves are evidence of this. Paul reminds them that when God called them to be his Church not many of the Corinthians were wise, powerful, or well born. In fact, Paul says, this is how God works all the time. God is constantly choosing the weak, the lowly, the things that are not in order to shame the wise, the powerful, and the things that are. God doesn't choose the powerful and wise to display his power and wisdom. God chooses the weak and lowly so that then it will be evident that it is God who has done the powerful work and not us. Only a truly powerful and wise God could display his power and wisdom in the weakness and foolishness of a crucified messiah.
Therefore, Paul admonishes the Corinthians to stop their boasting. There is no room for boasting in a truly Christ-centered spirituality because it is God who has done the work. We have not saved ourselves. We have not mastered a new form of sophia. Instead, Paul urges the Corinthians to understand that Jesus Christ, that crucified messiah that is so shameful, scandalous, and foolish in the eyes of the world, has become wisdom to them. Jesus is God's wisdom revealed to us.
It is easy to see the end of verse 30 as simply a list of four things that Christ has become to us; wisdom, righteousness, sanctification, and redemption. However, in Paul's Greek, it seems more likely that he intends the last three to fill out the content of the first: "Christ, who has become to us the wisdom of God, which is righteousness, sanctification, and redemption." God's wisdom as revealed to us in Jesus is God's covenant faithfulness (righteousness) which sets those who believe free from sin (redemption) so that we might live holy lives to God (sanctification). Of course, this comes as no surprise because this is precisely what God has been about throughout the story of scripture; redeeming the people of Israel from their slavery in Egypt, making a covenant with them at Sinai so that they could be set apart and learn to be in right relationship with God and each other, living lives of holiness to God. It is that God who was revealed at the Exodus and at Mt Sinai who is also revealed in Jesus and who has set us apart by his Holy Spirit. It is that God of deliverance and covenant who in His wisdom has extended deliverance and covenant to us by way of the foolish idea of a crucified messiah.