Since it took me years to figure out that I learn math intuitively, not rationally as most mathematicians do, I find the distinction between the two methods fascinating. Once I figured that point out, everything became much easier because I finally knew where I was standing. I knew that my approach was valid even though I still have a hard time deciphering math. I knew how to start Googling concepts (i.e. simply add "intuitive" to the query and quickly find the sensible explanation of an otherwise too-abstract concept). I also knew how to begin finding others who do the same. I think I found one:
A Path Less Taken to the Peak of the Math World | (Quanta). This article doesn't go into the distinction between intuitive and rational math, but there are little hints throughout which indicate the way Huh thinks is more syncretic than analytic, more geometric than algebraic. Here's one example, emphasis mine:
It's hard to overstate how little Hodge theory would seem to relate to graphs or matroids. The cohomology rings in Hodge theory arise from smooth functions that come packaged with a concept of the infinite. By contrast, combinatorial objects like graphs and matroids are purely discrete objects — assemblages of dots and sticks. To ask what Hodge theory means in the context of matroids is a little like asking how to take the square root of a sphere. The question doesn’t appear to make any sense.
Another clue:
"The talk was somehow very polished and very clear; it just went to the right points. It’s a bit unusual for a beginning graduate student to give such clean talks," said Mircea Mustata, a mathematician at Michigan.
And another, again emphasis mine:
A bad score on an elementary school test convinced him that he was not very good at math. As a teenager he dreamed of becoming a poet. He didn't major in math, and when he finally applied to graduate school, he was rejected by every university save one.
These are little clues that Huh's approach to math is more intuitive than the general case. If I'm right, he'll be making more discoveries that bridge other widely-separated areas of mathematics before his story is finished. That's the intuitive way, to see the forest in a mess of trees.