According to various experts in the field, the statement that the Navier-Stokes equations are the most difficult mathematical equation known to mankind is accurate. These equations present a complex set of partial differential equations that are challenging to solve, particularly for turbulent fluid flows.

The Navier-Stokes equations were first introduced by Claude-Louis Navier and George Gabriel Stokes in the 19th century and have been an important part of fluid mechanics ever since. Despite significant advancements in computational power and numerical methods, solving the Navier-Stokes equations for real-world fluid problems remains a difficult challenge.

Over the years, many different techniques have been developed to try and solve the Navier-Stokes equations, including numerical methods, asymptotic methods, and perturbation methods. These methods have provided insights into the behavior of fluids in motion and have contributed greatly to the field of fluid mechanics.

In recent years, the Navier-Stokes equations have become one of the Millennium Prize Problems, with a $1 million prize for anyone who can provide a solution by 2035. While progress has been made in solving special cases of the Navier-Stokes equations, a general solution has yet to be found.

Sources:

"Navier-Stokes Equations." Encyclopædia Britannica. Encyclopædia Britannica, Inc., n.d. Web. 23 June 2021. https://www.britannica.com/science/Navier-Stokes-equations.
"Millennium Prize Problems." Clay Mathematics Institute. Clay Mathematics Institute, n.d. Web. 23 June 2021. https://www.claymath.org/millennium-problems/navier%E2%80%93stokes-equation.
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