How has mathematics gotten so abstract?

Today, mathematics is regarded as a supremely abstract science. On forums such as Stack Exchange, trained mathematicians may sneer at newcomers who ask for intuitive explanations of mathematical constructs. Indeed, persistently trying to relate the foundations of math to reality has become the calling card of online cranks. The article delves into the historical evolution of mathematical abstraction, from the intuitive understanding of numbers to the formal axiomatic systems of Peano arithmetic and set theory. It explains how these abstract frameworks, especially in dealing with concepts like infinity and cardinality, lead to counter-intuitive but logically consistent results, such as non-commutative addition with infinite ordinals and the existence of different sizes of infinity demonstrated by Cantor's diagonalization argument. The author explores the philosophical implications of these abstractions and their role in modern mathematics.