Final answer:
The experience greatly influencing a career in psychiatry varies, including personal encounters with mental illness, artistic expressions of psychological states, and influential theoretical frameworks, alongside overcoming societal obstacles and contributing to medical science.
Step-by-step explanation:
The experience greatly influencing a career in psychiatry can be multifaceted, as seen in historical figures such as Gericault, Sigmund Freud, and Jean-Etienne-Dominique Esquirol. Personal family history of mental illness and the creation of artworks reflecting psychological states were significant for Géricault, while Freud was influenced by modernist philosophers, great writers, Darwin's work, and his ambition to establish psychology as a credible science. Additionally, Fuller's advancements in the field were no less important, with his extensive research and publication of a major study on Alzheimer's disease, despite the professional discrimination of the era.