Is there any research or clues about whether anxious/calm people are more/less likely to be inventive / creative / develop innovations?
I am interested about this both on an individual and cultural (peoples) level.
"Mr. Scott? We need more POWER!" is the common call made to engineering from the bridge of the fictional Starship Enterprise. It seems common in science fiction for engineers to flourish under high amounts of pressure and overcome all odds. However this does not reflect reality.
For this answer I think it best to turn to Individual Psychology as the creative process is more about a person's preference and comfort than a series of predefined conditions or mental states. Creativity flourishes in certain environments. High gain/high anxiety reward based systems do not encourage creativity. Creative people can be taught to cope with the existence of a reward and overcome the pressure. Extrinsic motivation fosters competition and dependence on rewards which leads to performance anxiety. Intrinsic motivation leads to performance for one's own betterment at ones own pace and while it produces less results.
Depression, Bipolar and Schizophrenia are thought to be caused by stress and anxiety acting on a biological vulnerability. So creativity may be a response and outlet to the anxiety the illness or life causes for these individuals.
By themselves, artistic and creative people tend to experience higher anxiety and depression. However there are no conclusive causal relationships between depression and creativity. There have been stronger relationships between more serious mental illness like schizo typical and bipolar.
A study looking at 300,000 persons with schizophrenia, bipolar disorder or unipolar depression, and their relatives, found overrepresentation in creative professions for those with bipolar disorder as well as for undiagnosed siblings of those with schizophrenia or bipolar disorder.