Faraday was the quintessential "non-formal" Scientist. He was proof that you don't have to always formalize everything mathematically (in a domain) before understanding and contributing to it. While formalization is important it is not the be-all and end-all that it is often made out to be.
Here is a great communication from Faraday to Maxwell on receiving one of Maxwell's paper;
Maxwell sent this paper to Faraday, who replied: "I was at first almost frightened when I saw so much mathematical force made to bear upon the subject, and then wondered to see that the subject stood it so well." [Faraday to Maxwell, March 25, 1857. Campbell, Life, p. 200].
In a later letter, Faraday elaborated:
"I hang on to your words because they are to me weighty.... There is one thing I would be glad to ask you. When a mathematician engaged in investigating physical actions and results has arrived at his conclusions, may they not be expressed in common language as fully, clearly, and definitely as in mathematical formulae? If so, would it not be a great boon to such as I to express them so? translating them out of their hieroglyphics ... I have always found that you could convey to me a perfectly clear idea of your conclusions ... neither above nor below the truth, and so clear in character that I can think and work from them". [Faraday to Maxwell, November 13, 1857. Life, p. 206]
PS: You can read Faraday's (and other 19th century scientists) letters at the Epsilon website - https://epsilon.ac.uk/
This letter from Maxwell to Faraday: https://epsilon.ac.uk/view/faraday/letters/Faraday3354 is very surprising to me. Already they are thinking of gravity in field theoretic terms. Just to set context: Riemann's Habilitationsschrift was just 3 years earlier but not to be published till late 1860s.
Faraday actually did some experiments to try and show that Electricity and Gravity were related and in 1851 published On the possible relation of Gravity to Electricity in "Philosophical Transactions" of the Royal Society!
His ability to conceptualize/intuit and devise theories/experiments-to-test-theories was unparalleled. Maxwell could not have come up with his formal mathematical equations if he did not have Faraday's conceptual work on which to build upon. It goes to show that concepts/intuition must always go ahead of formalization.
Here is a great communication from Faraday to Maxwell on receiving one of Maxwell's paper;
Maxwell sent this paper to Faraday, who replied: "I was at first almost frightened when I saw so much mathematical force made to bear upon the subject, and then wondered to see that the subject stood it so well." [Faraday to Maxwell, March 25, 1857. Campbell, Life, p. 200].
In a later letter, Faraday elaborated:
"I hang on to your words because they are to me weighty.... There is one thing I would be glad to ask you. When a mathematician engaged in investigating physical actions and results has arrived at his conclusions, may they not be expressed in common language as fully, clearly, and definitely as in mathematical formulae? If so, would it not be a great boon to such as I to express them so? translating them out of their hieroglyphics ... I have always found that you could convey to me a perfectly clear idea of your conclusions ... neither above nor below the truth, and so clear in character that I can think and work from them". [Faraday to Maxwell, November 13, 1857. Life, p. 206]
PS: You can read Faraday's (and other 19th century scientists) letters at the Epsilon website - https://epsilon.ac.uk/