Can You explain these for me ?
Japanese mathematics professor Kokichi Sugihara spends much of his time in a world where up is down and three dimensions are really only two. Professor Sugihara is one of the world's leading exponents of optical illusion, a mathematical art-form that he says could have application in the real world

I don't get it . Specially this part ( a world where up is down and three dimensions are really only two ) is that impossible ?

Question

Can You explain these for me ?
Japanese mathematics professor Kokichi Sugihara spends much of his time in a world where up is down and three dimensions are really only two. Professor Sugihara is one of the world's leading exponents of optical illusion, a mathematical art-form that he says could have application in the real world

I don't get it . Specially this part (  a world where up is down and three dimensions are really only two ) is that impossible ?

Answer

He studies optical illusions, so in the world he creates things are distorted, they are seen and perceived differently, not the way people usually see them. Three dimensions are represented as two (probably in the form of two dimensional drawings or something) and the "up" (like the ceiling) becomes "down" (like the floor, for example). That is the way I understood the passage.

Answer

Interesting

Answer

I believe they are trying to describe how strange and interesting what Kokichi Sugihara is doing.
In his "world" Up looks like Down, and while he doing things in 2 dimensions it looks like he operates in 3 dimensional world.
Illusions.
They want you to imagine this.
My guess.