So

when i think of the globe as a whole, the curvature at every point, it's obviously the curvature of a spherei's a ball, which means it's positive, whereas the curvature of a flat piece of paper, a map, is zero at every point. So that's to stood of a two line proof that you can't possibly turn

a flat sphere, a round sphere, on to a flat map. Marcus,

can you develop the notion that he would have shifted mathematics on by 50 years had he published more? He he said one of the things wastha, the centre of math atic shifted from france to germany because of him and his influence. Hir local influence from tha, small university, he emanated great power. But can

ho just develop that a bit? Yes, i think er, you know, the centre of mathematical activity when gaus started was france. The french revolution had really initiated great new discoveries, but it was a very much utilitarian view of mathematics. Mathematics was going to serve state and a actually, french mathematicians ere rather dismissed if they were just interested in matter for its own sake. But we see a real change in gaus's part of this. And er humboldt, who was defining the education system within germany, said, no, i think we should value a pure knowledge for its own sake in our education system. And this actually helped transfer a kind of the centre of mathematics from france to germany, because it allowed people like gaus to think of just ideas for their own sake, which then would go on to be a applied in interesting new ways that no one had ever thought of. And so gaus in getingan. Gerting was this tiny little place, not a centre of europe, but gaus begins to make this really the hub of mathematicse. I was going to spend anywhere, do know where would i want to be in the nineteenth tury to do my mathematics? I would choose gertingan. And it er from gaus right up to er, the beginning of the second world war, when hitler just blew the place to pieces by er kicking out all the jewish mathematicians, and it just collapsed as a centre. This was where all the great mathematics was being done, especially by a lot of gauss's students, people like bernhardt reman, a dedicant. So i think gauss can be credited with really making this shift, not only from er, from france to germany, but also from a kind of utilitarian view of mass being useful to tomass being the queen of the sciences, yes, it serves the sciences, but it is kind of at the top. It's the regal top of science.