Is it really difficult for some men to believe women can be both smart and beautiful?

Well that's irritating, I don't like that association that models are dumb or pretty people in general are stupid. Your face doesn't effect your brain's intellect.

I know female doctorates in neuro science and physics (male dominated fields of science) and they are very often overlooked or even reduced for no other reason than being female.
One such scientist who has an MD doctorates as well as working on her Ph.D in Neuroscience now, was told by her boss that she dresses very nicely and would look good in a receptionist role.
Another Neuroscientist told me about a networking event where she and her second author (someone who contributed to a study she did) were approached by someone high up the food chain, and instead of asking her about her work, he asked her assistant... He fully assumed that the male was the driving force behind the study.
This is common, it happens everyday and all over the world.

Oh! I have to say this as I have just learned about it in my social psy class:
They did a study where the let people ( both men and women) read a scenario of a manager solving a problem with an employee. The story was always the same, the only thing that differed was the picture of the manager they showed along with the story.
In one condition it was an average man, in another an attractive one. I yet another condition it was an average female, in another an attractive one.
The men always scored higher, with the attractive male scoring the highest, and of the females the most attractive one scored the worst. Both men and women expressed that this manager might have gotten to her position for no other reason than that she was attractive and certainly not because she was skilled.
This would mean that both men AND women have a hard time accepting attractive women as anything more than eye-candy.

She's a stud! And she should absolutely be a role model for girls everywhere.

Look I'm not trying to take anything away from her and I have no reason to doubt she's very intelligent and a talented programmer, but working for the 841st fastest growing company doesn't sound like much.
Like, if there are 1,000,000+ companies in the US then yeah that's pretty good. Good on ya.

Women as just as shallow, let's not make this about men being pigs.