Does mental illness indicate intelligence?

Is mental illness common in great scientists, mathematicians, engineers, and artists relative to the general public?

Are only certain mental illnesses common in these groups or are they all equally common?

Does the mental illness cause great work, or does the ability to do great work lead to the mental illness?

Is it worthwhile to indulge in a mental illness to wire yourself to think in a unique way and possibly create something great, or is it actually detrimental to great work?

What is conducive to
>Newton
>Einstein
>Euler
>Gauss
>Euclid
>Archimedes
>Fermat
>Shakespeare
>Maxwell
>Da Vinci
>Michelangelo
>Plato
>Aristotle
>Feynman
>Pasteur
>Darwin
>Pauling
>Heisenberg
>Curie
>Galileo
>Gödel
>Bohr
>Fermi
>Von Neumann
>Turing
>Fourier
>Picasso
>van Gogh
>Hemingway
>Dickens
>Tolstoy
>Twain
>Mozart
>Beethoven
and so on, to becoming who they became and completing such invaluable work? Did they all work very hard? Were they all mentally ill and just happened to think in an odd way which led to a new idea? Should we all cater to becoming mentally ill so that we also become great?