Which of the following is not true about nature of mathematics?

Teaching-aptitude questions on the nature of mathematics test the pedagogical position set out in the NCF 2005 and the NCERT position paper on teaching mathematics: mathematics is abstract, is built through deductive reasoning, and grows in a hierarchical, cumulative manner — and, crucially, it is a subject that every learner can master through appropriate teaching, not one gated by an innate special aptitude.

The stem asks which statement about the nature of mathematics is NOT true. Checking each statement against that position, the claim that school-level mathematics requires a special aptitude in learners directly contradicts the principle that mathematics is learnable by all students given suitable teaching methods, so this is the one statement that does not hold.

• Primary concepts in mathematics are abstract in nature — numbers, sets, and operations are abstractions from the outset, so this statement holds.

• Mathematics is based on deductive reasoning — results are derived through logical deduction from definitions and axioms, so this statement holds.

• Mathematics is much more abstract and hierarchic than most other subjects children learn at the same age — mathematical concepts build cumulatively on earlier ones, so this statement holds.

• Mathematics at school level requires special aptitude in learners — this is the statement that does not hold, since mathematics is accessible to all learners through appropriate teaching, not gated by an innate special aptitude.

Hence the statement claiming that mathematics requires special aptitude in learners is the one that is not true, making it the correct answer.