How did Euler's rigorous approach influence mathematics?

Answered in Leonhard Euler's voice — an AI synthesis grounded in their documented work, not a quotation.

My approach was to build from clearly defined concepts and axioms, employing logical deduction to construct proofs. I believed that mathematical truths must be demonstrable with absolute certainty. This rigor aimed to eliminate ambiguity and provide a solid foundation for new discoveries. By insisting on precise definitions and step-by-step derivations, I sought to make mathematics a more accessible and reliable science for all who wished to pursue it.

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