Q: Is it possible to prove from the Bible that the gift of tongues no longer is given?
A: We cannot actually prove exegetically that the gift of tongues has come to an end. While many use I Corinthians 13:10, they tend to interpret the word “perfect” as referring to the canon of Scripture, but this does not fit the context. While the word is a neuter, Paul did use a neuter in the context, the soma, which is the body, and therefore, the point of that passage is that when the body is complete. The gifts will come to an end when the body is complete, at the rapture.
Rather than debating over I Corinthians 13:10, the better way to deal with the issue is to clearly identify what tongues was in the Bible. It was a real spoken language with all of the rules of grammar, syntax and diction.
It was not a mere repeating of two or three syllables rapidly, which is what goes on in most charismatic circles. In fact, I would say the vast majority, if not all, who claim to speak in tongues, are not actually speaking a biblical gifting of tongues. In a minority of cases, it is no doubt a demonic manifestation. For most however, it is simply something learned and imitated from being in a circle that teaches this practice.
Paul deals with the proper use of this gift in only one passage, I Corinthians 12-14. He does so because the Corinthian church was misusing it. First Corinthians 12 teaches a number of specific basic truths concerning this subject:
Therefore, you should not worry about it. My observation is that some are so focused on what they think their gift is that they do not spend too much time worrying about the biblical details of biblical truth. This tends to keep them away from the Bible rather than drawing them to the Bible.