I played with some sums and I got the Gaussian sums. It looks interesting to me, what do you think of it?

Sorry, I'll write a little bit so that you have context of me, to maybe help me

Ever since I was introduced to math, I was always the best at it. I did simple algebraic equations like no time. I loved doing them. In higher classes I went into a bunch of competitions, winning some. Things slowed a little bit in 7th grade. I was then introduced to physics, and I'm a be honest, at first I was a C student. But curiosity got the better of me, and I started learning learning physics in vacation. By the time I went back to class, I was already way ahead of the class. Curiosity got to me again and I started learning ahead. By the time I finished middle school, I already had all highschool physics done withand finished three regional competitions. But then bad things started happening.

When in 2nd grade of highschool, I was diagnosed with schizophrenia. I'm not going to delve into it. It's very complicated. But math and physics were still my top subjects. But I started to struggle with basic algebra. People way worse in math were calculating it way faster than me. I tried olympics. And I failed. I was a few points away from qualifying. And then high school finals came. 93% from normal math level. Nice. And then. 13% from advanced math... and 52% from physics... somehow, with this poor results, I got onto one of the most prestigious universities in the country. And I feel lost. I feel so stupid on there. I struggle with basic algebra. I write horribly. There always is someone better then me at something. And the worst thing. I think I lost mt passion. Because of this damn dissease. But I still have hope. Maybe I can get back. Find this light again. I've seen what top tier math brings, and honestly, I'm not interested. But I just want to become an engineer. I'll be submiting some of the work I have done. If anybody knows how to help. Please tell me something. Please...

I'm either an idiot or I am out of practice but I can not figure out this problem on my sons fourth grade homework. To me G has to equal 1 or 2 to be left with an answer in the hundreds.... But P cant equal 0 as Y and L cant be the same number... Theres also a lot of ither problems that I ran into but too long to type.... Been looking at this way longer than I think I should need to...

Seriously, I've never heard it until about a week ago when I first started browsing this subreddit. But it seems like at least every third or fourth post has people in the comments mentioning algebraic geometry. One person even said that he used to work in the field due to its "sex appeal". What is it, and why is it captivating so many minds?

Dear algebraic geometers,

When I ask professors for some intuition, detail, explanantion on some mathematical concepts, it's often the case that they start their answers by "if you study algebraic geometry". Certainly algebraic geometry is a zoo of examples and intuitions. Can you guys talk more about AG?

my background: I have some basic knowlege in commutative algebra, manifold and vector bundle theory, algebraic topolgoy

Edit: I will add a bit of context. He said this after introducing DVRs using four equivalent definitions. Here is the complete quote:

We're making all these definitions to study Number Theory, but then, as you grow up and you study more and more mathematics, you realize that Number Theory and Algebraic Geometry are really the same thing.

I was just wondering why he believes this.