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In mathematics, there are two distinct approaches to reasoning: informal inferences based on simple reasoning and formal derivations through step-by-step proofs. This centuries-old approach to mathematical reasoning has been revolutionized by the advent of computers and symbolic systems. Initially, symbolic systems were developed to construct proofs step-by-step based on formal derivations. Subsequently, with the advent of deep learning, particularly in the form of large language models, we were able to construct neural network-based structures that, like humans, are capable of both inductive and deductive reasoning. It is important to note that both symbolic systems and deep learning systems, in their respective ways, have their own set of successes and failures. This presentation will examine the distinctions between symbolic systems and deep learning-based systems, with a focus on the capabilities of large language models in problem solving, theorem proving, mathematical reasoning, generating new conjectures, and their performance when used with agents. Additionally, it will explore the potential for integrating language models with formal systems and the benefits of this integration.