A mad scientist is rarely an actual scientist. If I were to go on a "career path" to be a mad scientist, I would avoid getting degrees in the sciences, focusing instead on practical applications of knowledge, such as engineering. A "mad scientist" is typically an engineer with a vision going into scientific fields in the hope of finding recognition (and/or financing), and finding none. When one wants to "show them all", it's primarily as a last-resort practical showcase of a principle or device said to be - or laughed out as - theoretically impossible or unfeasible by the 'actual scientists'.