The use of technologies in mathematics education at all levels has been discussed extensively for a number of years. It is one of the few themes that was the object of two ICMI studies, the most recent being published in 2010. Two new approaches, emerging lately in the teaching and learning of Mathematics at all levels, will be discussed: Computational Thinking (CT) and Artificial Intelligence (AI). I will discuss both in comparison, arguing they are very different and can even induce very different directions to Mathematics Education. Considering the CT approach as a variation on the theme of Problem Solving puts it as a skill that is as fundamental as numeracy. AI is also connected to problem solving as an emulator of human problem-solving approaches. Inappropriate use of AI has been considered problematic, being called a 'stochastic parrot'. I will try here to compare CT and AI using Curriculum Analysis: which are the educational purposes, which relevant experiences can we point out, how can these be implemented in school, how are they effective. I will argue that CT is important in introducing an 'algorithmic dimension of mathematics' in Mathematics Teaching and that AI in its present form as Generative AI is not adequate to develop concepts of mathematical literacy. I will show how the 'algorithmic dimension of mathematics' can be implemented in school with the example of the curricular options that were made in the new curriculum for Mathematics in Portugal.