Artificial intelligence (AI) has made significant advances in various domains, with pathology being one of the most promising fields for its application. AI's potential to enhance diagnostic accuracy, efficiency, and consistency in pathology is particularly notable. In this work, the significant role of AI algorithms in developing an automated diagnosis system related to cytopathological images is addressed. The focus on thyroid malignancy detection using fine needle aspiration biopsy thyroid cytopathology images is presented. This work provides an overview of AI algorithms, a detailed case study on AI implementation in thyroid cancer diagnosis, and a practical use case. The convolutional neural network (CNN) with appropriate arrangement of layers, filter functions and activation functions are used to implement on thyroid fine needle aspiration cytopathological images and perform binary classification of normal and abnormal thyroid nodules. A relative evaluation is also carried out between the existing results obtained from machine learning algorithms and a few deep learning algorithms. From the observations made among the AI algorithms analyzed, it has arrived a conclusion that support vector machines (SVMs) in machine learning and convolutional neural networks in deep learning are performing well on the classification of thyroid cytopathological images with a classification accuracy of 96.6%.