Leonhard Euler: A Path Not Taken
Leonhard Euler: A Path Not Taken Rigidity, Zeros, and the Road Mathematics Chose Not to Follow Leonhard Euler stands at a bifurcation point in the history of mathematics. One path—taken—led to local admissibility, ε–δ control, and proof as stepwise legality. The other—abandoned—was Euler’s: a global method in which zeros, symmetry, and minimal growth exhaust freedom and force truth . This article articulates that unrealized path, not as nostalgia, but as a coherent alternative epistemology. Contents I A Path Not Taken 1 Global Objects Before Local Rules 2 Zeros as Primary Invariants 3 Truth by Exhaustion: The Basel Problem 4 Why the Path Was Abandoned 5 What the Alternative Would Have Been 6 The Quiet Return 7 Closure II Why Euler Could Reach Truth Before Justification 1 The Apparent Paradox 2 Zero-Based Rigidity 2.1 Zeros as Primary Invariants 2.2 Entire Functions and Rigidity 2.3 The Sine Function as a Maximally Rigid Object 3 Applications and Implications 3.1...