I don’t have a mathematical background and am looking for an “intuitively satisfying” explanation (so, for example, the Wikipedia article is way too technical). Perhaps this is not possible in which case, fair enough.
I understand (I think) what a polynomial is and I believe algebraic geometry is about understanding the solutions to polynomial equations using abstract algebraic techniques and geometry. I rapidly get lost when the discussion shifts to rings, fields, schemes and so on. However, I’m not looking to understand all these different concepts but rather get a high level overview.
One day, I’d like to understand how Grothendieck revolutionized the discipline but that may be far too ambitious 🙂
In: Mathematics
Geometry is the study of shapes.
Algebra is reducing complex things to basic rules, then understanding the complex things in terms of those rules.
Algebraic geometry involves breaking shapes down to simpler structures and understanding/extending those shapes from those structures.
Sort of like how a square can be broken into triangles. If you understand the triangles, you can say a lot about the square.
(I should mention I’m not an expert, my exposure to algebraic geometry is limited to a course which I struggled in. I did pass though).
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