Various approaches have tried to tackle the Riemann Hypothesis, many of which come from fields outside of analytic number theory.
A notable example is the de Bruijn-Newman constant.

This topic was first introduced by de Bruijn in his paper on “The Roots of Trigonometric Integrals,” where comments related to the Riemann Hypothesis appeared only in the final section. Newman later expanded on this theory in his article about “Fourier Transforms with Only Real Zeros”. While this paper focused more on the Riemann Hypothesis, it is also noteworthy to highlight the connection between the zeros of Fourier transforms and areas such as statistical mechanics and quantum field theory. 

Newman proposed a conjecture that would remain unresolved for nearly 50 years.