Gifted’s Navier-Stokes math problem explained and has it ever been solved?

Talented centers on the Navier-Stokes problem, prompting many viewers of the 2017 drama to wonder what the unsolved math problem is — and whether real-life mathematicians have since solved it. Directed by Marc Webb, Talented Follows seven-year-old Mary Adler (Mckenna Grace), a young mathematical genius who is sent to live with her uncle, Frank Adler (Chris Evans in one of his best roles), in the wake of her mom’s death. Mary’s late mother, Diane, was also a brilliant mathematicianBut she is seemingly driven to death by suicide after failing to solve the Navier-Stokes problem.

Determined to give Mary a different life, Frank sends the young girl to a traditional elementary school. However, Mary’s teacher quickly realizes her pupil’s promise as a mathematician. Eventually, Frank winds up fighting his estranged mathematician mother, Evelyn (Lindsey Duncan), for custody of Mary. Unlike Frank, Evelyn believes that it is Mary’s responsibility to devote herself to Matt. If Evelyn has her way, Mary will spend her life on the Navier-Stokes problem as well, cementing the equation as a key plot detail. As a result, to understand the status of the Navier-Stokes problem in the real world further Talented is of central importance.

What the Navier-Stokes problem is and why it is so important

The Navier-Stokes existence and smoothness is one of the unsolved Millennium Prize problems

To fully understand what the Navier-Stokes problem is, it is important to recognize the context surrounding it. In 2000, the Clay Mathematics Institute (CMI), a nonprofit foundation, pledged $1 million dollars to whoever first solved the so-called Millennium Prize problems. At the time, the complex mathematical problems were deemed unsolvable. A century earlier, mathematician David Hilbert composed a set of 23 then-unsolvable problems, prompting those who participated in solving them to drive progress in the fields of 20th-century mathematics and science. CMI believed that the Millennium Prize problems could, similarly, initiate progress In 21st century mathematics.

In fluid mechanics, the Navier-Stokes equation is “A partial differential equation that describes the flow of incompressible fluids“(by Britannica). The partial differential equations are able to describe the motion of viscous liquid substancesmaking them useful in understanding the physics of phenomena that occur in scientific and engineering disciplines. For example, these equations are useful in modeling ocean currents or the weather. Even though the Navier-Stokes equations are widely used, they often factor in turbulence – the greatest unsolved problem of physics.

“The complex vortices and turbulence, or chaos, that occur in three-dimensional fluid (including gas) flows as velocity increases have proven intractable to any but approximate numerical analysis methods,” Britannica notes. Essentially, Mathematicians have not been able to prove whetherSmooth solutions“Always exist In three dimensions (by Lindo Systems Inc.). As a result, the existence and smoothness of Navier-Stokes is one of the seemingly impenetrable quandaries of the field.

People have claimed to have solved the Navier-Stokes problem after poison

Only one of CMI’s Millennium Prize problems has been solved successfully

Although Talented Not based on a true story, it seems accurate Trying to find a clear solution to the Navier-Stokes problem could consume his life. Over the past two decades, several mathematicians have claimed to have solved the Navier-Stokes problem as outlined by CMI. However, the Clay Mathematics Institute still lists it as “Unsolved.“The supposed solutions all turned out to be wrong, according to CMI, likely because the Navier-Stokes equations for an incompressible fluid are inherently flawed. Although the equations work,”There is no proof that solutions exist for all possible situations“(by NewScientist).

Since the Navier-Stokes equations are partial differential equations, which means the solution would change depending on the initial values ​​used and other fundamental circumstances. (Fluids behave differently depending on the space they inhabit, for example.) There is nothing constant about the Navier-Stokes problem – and there is no one right, end-all solution. That said, CMI wanted mathematicians to prove something more extensive about the Navier-Stokes’ existence and smoothness. That said, it’s even more complicated than Chris Evans’ underrated drama, Talentedreveals.

Sources: Britannica, Lindo Systems Inc., NewScientist