[Feel free to read this poor little unrigorous and unsourced post in JK Simmons' voice. That is entirely optional and you are of course free to read it in any voice you like; I only thought it might be interesting in the light of what is mentioned in the edit at the bottom of the text]
Nowadays, it seems that the correlation between sciency stuff, social ineptitude, and uncoolness, is cemented in the mind of the public. But this seems to be very era-specific, even time-specific.
As a lesswronger, I find what follows ironic: In Islamic countries, "scientists" are called with the same word use for religious leaders and other teachers, "olama", literally "knowers"; historically, there's been a huge overlap between the two, and, when one of these folks speaks, you're supposed to shut up and listen. This is still true to this day. There might not be much wealth to be gained from marrying a scientist, but there was status; amusingly enough, it's in modern-day materialism that is pushing them into irrelevance as money becomes, more and more, the sole measure of status.
In the West, in the XIXth century, Science and Progress were hip and awesome. Being a scientist of some sort was practically a requirement for any pulp hero. In the USA, an era of great works of engineering that had a dramatic impact on life quality made engineers heroes of popular fiction, men of knowledge and rigour who would not bow down to money and lawyer-cushioned bourgeois, or to corrupt and fickle politicians, men who would stand up against injustice and get the job done no matter what. Everyone wanted to call themselves an engineer, and the word was rampantly abused into meaninglessness; florists called themselves "flower engineers"! That's how cool being an engineer was.
In the Soviet Union, as long as they didn't step on the toes of the Party, scientists were highly acclaimed and respected, they got tons of honour and status. There was a huge emphasis on technological progress, on mankind reaching its full potential (at least on paper).
Nowadays, nearly the entire leadership of China is made of technicians and engineers. Not lawyers, or economists, or literati. These people only care about one thing, getting the job done - and that's what Science does.
So, I've really got to ask, when and *how* did Science and Engineering become "uncool", and why are they termed "geek", the term used for sideshow circus performers whose speciality was eating chickens alive (or something like that), and which, before that, used to be synonymous with freak and fook? When and how did we become worse than clowns in the eyes of society? Most importantly: how can the process be reversed?
After all, from a utilitarian standpoint, Science being cool and appreciated and respectable is kind of important.
EDIT: There's also the strange relationship, in the public mind, between science and dangerous, callous, abusive insanity, with a long tradition in popular fiction from Victor Von Frankenstein and Captain Nemo to Tony Stark and GLaDOS, and some Real Life counterparts, especially in brutal totalitarian regimes. Wikipedia has an interesting article on the topic, and how the characterization and prevalence of the Mad Scientist related to time-pertinent perceptions of Science.
For some reason, that aspect is often treated as cool and dramatic and impressive (besides being characterized as repulsive), perhaps because it involves displays of power over others, which is a high-status thing to do. Is that one of the existing paths to social prestige? Achieving power, and being inconsiderate about flaunting it? I'd like to hear more constructive alternatives, because that one doesn't seem viable, from where I stand.
I do everything I can to show people that a scientist can still be awesome, e.g. this, singing karaoke every week (and being very exuberant at it), etc.; also, I try to bring up Feynman and his awesomeness in conversation whenever I get a chance.