What was the Original Need/Purpose for Defining Bernstein Polynomials?

Question

I am interested in learning about the reason as to why Bernstein Polynomials were first defined.

After consulting the Wikipedia article on Bernstein Polynomials, these appear to be polynomials that follow a certain pattern:

My Question: Does anyone know what lead to the Bernstein Polynomials being defined - after all, why were they defined using a specific basis function? I have heard that the Bernstein Polynomials were first used to prove the Stone-Weierstrass Approximation Theorem - was Sergei Bernstein trying to find a new way to prove the Stone-Weierstrass Theorem and as a result developed the Bernstein Polynomials?

Thanks!

References:

• https://en.wikipedia.org/wiki/Stone%E2%80%93Weierstrass_theorem
• https://en.wikipedia.org/wiki/Bernstein_polynomial
• https://nonagon.org/ExLibris/bernstein-proves-weierstrass