Why was Leonhard Euler important to the history of number theory?

Leonhard Euler is credited with bringing number theory into the mathematical mainstream, transforming it from a niche interest into a legitimate field of study.1

His contributions were pivotal for several reasons:

• Validation of Fermat’s Work: Euler spent decades providing rigorous proofs for many of Pierre de Fermat’s assertions, including Fermat’s little theorem and the theorem regarding primes of the form $4k+1$ as sums of two squares.1
• Correction and Expansion: He famously disproved Fermat’s conjecture that all numbers of the form $2^{2^n}+1$ are prime by factoring the case where $n=5$. Additionally, he significantly expanded the known set of amicable numbers and clarified the structure of perfect numbers.1
• Foundational Influence: By publishing over a thousand pages of research, Euler established the mathematical legitimacy of the field, paving the way for successors like Joseph-Louis Lagrange to make further rapid progress.1

Though he could not solve every problem—such as the Goldbach conjecture—his prolific output ensured that number theory could no longer be ignored by the scientific community.1