Determining the exact positional relationship between mandibular third molar (M3) and inferior alveolar nerve (IAN) is important for surgical extractions. Panoramic radiography is the most common dental imaging test. The purposes of this study were to develop an artificial intelligence (AI) model to determine two positional relationships (true contact and bucco-lingual position) between M3 and IAN when they were overlapped in panoramic radiographs and compare its performance with that of oral and maxillofacial surgery (OMFS) specialists. A total of 571 panoramic images of M3 from 394 patients was used for this study. Among the images, 202 were classified as true contact, 246 as intimate, 61 as IAN buccal position, and 62 as IAN lingual position. A deep convolutional neural network model with ResNet-50 architecture was trained for each task. We randomly split the dataset into 75% for training and validation and 25% for testing. Model performance was superior in bucco-lingual position determination (accuracy 0.76, precision 0.83, recall 0.67, and F1 score 0.73) to true contact position determination (accuracy 0.63, precision 0.62, recall 0.63, and F1 score 0.61). AI exhibited much higher accuracy in both position determinations compared to OMFS specialists. In determining true contact position, OMFS specialists demonstrated an accuracy of 52.68% to 69.64%, while the AI showed an accuracy of 72.32%. In determining bucco-lingual position, OMFS specialists showed an accuracy of 32.26% to 48.39%, and the AI showed an accuracy of 80.65%. Moreover, Cohen's kappa exhibited a substantial level of agreement for the AI (0.61) and poor agreements for OMFS specialists in bucco-lingual position determination. Determining the position relationship between M3 and IAN is possible using AI, especially in bucco-lingual positioning. The model could be used to support clinicians in the decision-making process for M3 treatment.