der Genius
genius
A person with exceptional intellectual creativity, intelligence, or talent.
Marie Curie gilt als ein wissenschaftlicher Genius des 20. Jahrhunderts.
Marie Curie is considered a scientific genius of the 20th century.

genius / spirit
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genius
A person with exceptional intellectual creativity, intelligence, or talent.
Marie Curie gilt als ein wissenschaftlicher Genius des 20. Jahrhunderts.
Marie Curie is considered a scientific genius of the 20th century.

If 'Genius' refers to a person, it means a human being with extraordinary talent. If it refers to a place, a time, or an idea (often with a genitive such as 'des Ortes' (of the place)), it means the characteristic 'Geist' (spirit).
Albert Einstein gilt als wissenschaftlicher Genius.
Albert Einstein is considered a scientific genius.
This word is used for people with truly exceptional, often historically significant talent. In everyday language, it is rare and can sound exaggerated.
Mozart war ohne Zweifel ein musikalischer Genius.
Mozart was without doubt a musical genius.
This meaning is very elevated and is used almost only in literary or philosophical texts. It describes an abstract, invisible force or atmosphere.
In seinen frühen Romanen zeigt sich der rebellische Genius des Autors.
In his early novels, the author's rebellious spirit becomes apparent.
spirit / mind
'der Geist' and 'der Genius' can both refer to something intellectual or creative. However, 'der Geist' is much more general: it can describe a person's mind or the special spirit of something. 'der Genius' is stronger and more elevated. It means either a particularly gifted person or the special creative power of a person, place, or period. The words can be confused because both are connected with intelligence and inner power. For ordinary thinking, people usually say 'Geist'; 'Genius' fits better when you want to emphasize extraordinary talent or a special creative effect.

Viele bewundern den Genius dieser Komponistin, weil ihre Musik so neu klingt.
Many admire this composer's genius because her music sounds so new.
Der Geist dieses Projekts ist Zusammenarbeit statt Konkurrenz.
The spirit of this project is cooperation rather than competition.