I think there isn't enough distinction in the term "genius". How do you even compare their contributions? It is easy when you have someone like Euclid or Newton, who's work is taught in pre-college grades. Who is the last person to have an impact on pre-collegiate math syllabi? It's been centuries. Then you look at someone like Einstein who was discussed in every major magazine and newspaper at the time his general theory was articulated. I think Hawking got the similar treatment, but has he impacted what is taught in 4-year college the way Einstein did? I think Hawking's genius is too esoteric.
There needs to be a new term. "Genius" is too limp to describe individuals who radically alter the curriculum taught to undergraduate students.
> Who is the last person to have an impact on pre-collegiate math syllabi?
Shrodinger, maybe? He is a really large part of the reason people study matrices before college, and then go and complain because nobody can show them a use for the thing.
Yes, matrices got everywhere in the 20th century. There is basically no field that doesn't use them nowadays.
But any demonstration requires modern knowledge, and matrices are one of the very few modern thing students see. If you want to show them 3D graphics, you will need to teach programing first. Yeah, some will know it by them, but schools also can't rely on that.
(As an aside, chemistry also has some weirdly modern knowledge on its curriculum. Also out of context, just thrown in there because it's important.)
The nearest application I can think of is for modeling stochastic processes, but students see so little statistics that I imagine that will only change the object on the "why am I even studying X?" complaint.
You don't have to teach programming to teach computer graphics at the level of pedagogical example. The programming is bookkeeping for assets and occasionally a clever optimization(e.g. a Bresenham line rasterization, instead of one done by linear interpolation); the algorithms that are most critical to understanding graphics are often one-liners and analytic in nature, and so can directly reflect the underlying mathematics.
The kind of example you would get for matrix math would be something like: "Here is a triangle described by these points, here is a matrix that projects them in a 3D camera. In such-and-such 3D library, points are projected with the matrix by doing these steps. Compute and plot the result of applying the matrix to each point." And then in successive examples you can add some details about how you go about building up the matrix by computing the camera, translating the poly and so forth, and make comparisons to how it can be done in some scenarios using only trigonometry, and further comparisons to camera lenses and artist's 3D projection with horizon and vanishing points. If you put all those connections there in one place, you have the starting point, and then it can be elaborated on into both the pure math topics(why does this mathematical representation work) and the computing topics(how do I automate the process of plotting points).
What tends to happen is that the text doesn't allow enough of a detour to make all of those connections, so you instead get an extraordinarily brief allusion to application in a single word problem, after a completely abstract introduction.
There needs to be a new term. "Genius" is too limp to describe individuals who radically alter the curriculum taught to undergraduate students.