The discussion centers on the exploration of mathematical fields that extend beyond abstract algebra. Participants suggest several advanced areas, including Category Theory, Algebraic Topology, Algebraic Number Theory, and Algebraic Geometry. Set Theory is highlighted as a foundational field that underpins many mathematical disciplines, including Category Theory and Mathematical Analysis. The consensus is that these fields are not hierarchically ordered but represent different dimensions of abstract mathematics.
PREREQUISITESMathematicians, graduate students in mathematics, and anyone interested in advanced mathematical concepts and their interrelations.
I would say Set Theory. Set theorists keep adding axioms to their Set theory and expect us to do math(such as category theory, mathematical analysis and pretty much all of the known math) withing their formal Axiomatic Set Theory.alvin51015 said:I was wondering if there is a field of mathematics which lies beyond and higher than abstract algebra? If it exists could someone tell me the name of that field? Thanks.