Decolonising Mathematics

Abstract

Mathematics is not universal.Traditional (normal) mathematics accepts both deductive and empirical proofs like science.Colonial education replaced it with formal mathematics, the unique feature of which is not the use of reasoning but exclusion of the empirical.The coloniser never critically compared normal and formal mathematics, and tries to block such a comparison today.In Western dogma (of the church theology of reason) deduction is infallible.In fact, deduction is fallible.(1) An invalid deductive proof may be mistaken as valid.Doubts about validity can only be settled inductively.In practice, doubts are settled by invoking authority.Hence, deductive proofs are always more fallible than empirical proofs.(2) The postulates of formal math cannot be empirically checked; they are metaphysics (a metaphysics of infinity is needed even for the formal math of 1+1=2).Thus, far from being eternal truths, formal mathematical theorems may not even be approximately valid knowledge.(3) Formal math dogmatically assumes two-valued logic (on the superstition that logic binds God).But logic is neither culturally universal (e.g.Buddhist logic) nor empirically certain (quantum logic).Therefore, the theorems of formal math (even if valid) are not even truths relative to postulates.Hence, colonial/formal math is inferior and should be rejected.This does not affect the practical value of math -what 'works'which all comes from normal math which we should, accordingly, teach.I describe two actual decolonised math courses being taught: decolonised geometry in school, and decolonised calculus in the university.Decolonised (string) geometry that is indigenous to Africa and India, is superior to the geometry currently taught in terms of conceptual clarity (points, angle, distance), ease of learning, and practical applications.Decolonised calculus teaches calculus as normal math, the way it originated in India as a numerical technique to solve differential equations, together with non-Archimedean arithmetic (instead of formal 'real' numbers) and zeroism (instead of limits) used to sum infinite series.Europeans stole calculus from India, and falsely attributed it to Newton and Leibniz, who failed to understand how to sum infinite series due to the Western superstition (since Plato) that mathematics is eternal truth, and hence exact.Eventually, they introduced a metaphysics of infinity allied to church dogmas of eternityset theory, formal real numbers, and limitsas taught in university today.This metaphysics is irrelevant for any practical application of calculus, such as sending a rocket to the moon, but makes calculus very difficult.Decolonised calculus is easy, requires almost no background, and results in better science.It enables students to solve harder problems not covered in usual calculus courses.However, it excludes the ability to slip politically convenient dogmas into science through the metaphysics of formal math, and is, hence, resisted by the coloniser today.