“But God has chosen the foolish things of the world to put to shame the wise, and God has chosen the weak things of the world to put to shame the things which are mighty; and the base things of the world and the things which are despised God has chosen, and the things which are not, to bring to nothing the things that are, that no flesh should glory in His presence.”

God has chosen

The basic theme of these verses is that God chooses people and things who are not valued highly in our earthly material perspective to show that we all depend completely upon him, and that none of us have any reason for pride or self-glorification.

Idolatry

When we think of all that we have as our own, we like to include our power of logic, reason and knowledge gained through our hard study, our strength and fitness gained through our hard exercise, our property and wealth gained through our hard work, and our friends and loved ones gained through our generosity and kindness.
It took me a long time to learn that “possessing” those things had nothing to do with me. All of my efforts were no more than a preparation to receive those gifts from God. They are all given by Him to be used for his good purpose for a limited time only, and they will all be taken away in due course.
So, when people worship God’s gifts, such as education, strength, health and wealth (all of which are idols in our time), we are turning away and rejecting the eternal giver of those things, and devoting ourselves to temporary things that perish. It’s a form of idolatry and rebellion against God, or sin.

We see God’s response to this. In the NIV and NKJV it’s “to shame” the wise, but in the KJV it’s “to confound” (or confuse). So, God’s response may be to impede people’s self-glorification, and thereby limit the extent of our sin.

Things That Are Not

I can see two interpretations for “the things that are not”:
(1) People and things that are lowly and despised can be invisible to the proud and arrogant, as if they don’t exist, so it’s another way of saying the lowly and despised, or not important;
(2) But it may also refer to the things that are not of this material and visible world. Things like compassion and empathy, humility before God and man, unconditional love, faith and trust, repentance and sorrow for sin, and a hunger for God’s righteousness, are all above and beyond the fallen man’s material view of this world, and his measurement of profit and loss, status, power and influence. But they are gifts of God, and people who are willing to receive them are those whom God uses for His good purpose, and whom he draws close to Him.