An interesting thing about men is that the wealthier that they are - the more that we tend to give them the benefit of the doubt when it comes to intelligence and wisdom. We assume that because they have accumulated wealth that a certain amount of wisdom and knowledge were used in doing so. This may be the case, but when a rich man begins to be "wise in his own eyes," his wealth is only a facade to cover his foolishness.
The rich are often wise in their own eyes. This is because wealth can buy you a lot of things - including a group of well paid sycophants who will tell you that you are a genius. This is the age old "yes-man" who follows about his benefactor telling him how brilliant he is publically, even though privately he man consider the rich man a moron. But while on the dole, this person gives the rich man a sense that he is wise. Unless his wisdom is gained from Scripture - this is only wisdom in his own eyes. The problem with being wise in our own eyes is that one, we can easily impress ourselves - and two, once we have impressed ourselves our pride can shut out any other evaluation others may try to give.
But this proverb tells us that the poor man who has understanding can see right through the foolish rich man. The word for understanding here means the ability to discern. The poor man examines the rich man wise in his own eyes. He discerns the difference between wisdom gained of experience and God, and that paid for with money. He discerns that those who praise the rich man are all paid patrons of his supposed wisdom. He also knows that if the money flow stops, the truth concerning this man's foolishness will not be tolerated - and he will be abandoned by his fair weather pals.
Wisdom knows others who are wise. Since that wisdom comes from God, there is no need to brag about it. Since it comes from God, there is also no price that can be paid for it. Such wisdom is given by grace - and gained by the teaching of the Holy Spirit as we daily search the Scriptures and learn to listen to God.