This chapter explores the monumental influence of Leonhard Euler, who served as the ideal synthesizer for the new mathematics of infinite calculations pioneered by Leibniz and Newton. Euler, driven by a blend of Calvinist discipline and mathematical ingenuity, transformed complex theoretical concepts into an accessible pedagogical imperative. Euler’s work was defined by its pragmatic, empirical approach and its confidence in manipulating infinite series as ordinary algebraic quantities, famously yielding the solution to the Basel Problem. He boldly extended functions like logarithms and trigonometry to the complex plane, demonstrating maximal consistency between arithmetic and geometry. The chapter contrasts Euler’s approach with the subsequent Weierstrass Revolution of the 19th century, which sought to establish absolute certainty by imposing formal logical rigor (ϵ−δ proofs) onto Euler’s intuitive work. This pursuit of certainty ultimately faltered with Gödel’s incompleteness theorems, which revealed inherent limitations even in basic integer arithmetic. Ultimately, Euler’s legacy persists today, not because of its formal rigor, but because his “Puritan practicality” and focus on effective algorithms formed the bedrock of the modern computational curriculum. The authors suggest that a meaningful modern mathematics education must re-embrace Euler’s spirit of bold exploration, leveraging technology to understand the power and inherent limitations of infinite mathematics.