The article discusses the differences between constructive logic and algebraization in mathematics. It explores how intuitionistic proofs can be just as complex as classical proofs, and how certain weaknesses in constructive logic can be corrected in practice. The researchers also highlight the importance of additional skills needed for successful applications of certain mathematical strategies. By comparing algebraization with logical contributions, the study shows how different approaches can lead to significant insights in mathematics, particularly in the context of finiteness theorems in number theory. Overall, the research emphasizes the importance of choosing the right mathematical tools and strategies for solving complex problems in mathematics.