Why did logic and mathematics become closely linked in the modern era?

In the modern era, logic and mathematics became closely linked primarily due to the efforts of philosophers and mathematicians seeking to establish a secure, reliable foundation for mathematical practice. This movement was driven by the desire to demonstrate that mathematics is certain and trustworthy by showing that its concepts and modes of reasoning could be derived from pure logic.12

The most prominent school of thought in this endeavor was logicism, championed by figures such as Gottlob Frege and Bertrand Russell. Logicists contended that all of mathematics could be reduced to logical laws, effectively arguing that mathematical truths are ultimately logical truths. This project culminated in monumental works like Principia Mathematica, which attempted to define basic mathematical notions—such as number—using only logical terms.31452

While the discovery of paradoxes in naive set theory and later results, such as Kurt Gödel’s incompleteness theorem, challenged the possibility of deriving all of mathematics from a single logical theory, the two fields remain deeply intertwined. Today, most mathematical argumentation is carried out in logical terms, and the two disciplines continue to share concepts, techniques, and foundational concerns.521