Duplicate of Math Vocab in TOK

mathematics without the use of coordinates, formulae, etc. that uses less writing and fewer calculations

the study of geometrical shapes (plane and solid) and figures based on different axioms and theorems

a form of realism that says we discover mathematical facts through research, like in any of the sciences.

an unprovable rule or first principle accepted as true because it is self-evident or particularly useful

an ordered set of numbers, where each number is formed by the addition of the two previous ones

a probability puzzle; a famous paradox that has a solution so absurd, most people refuse to believe it’s true

there can be no mathematical theory of everything, no unification of what's provable and what's true

unsolved theory that every even whole number greater than 2 is the sum of two prime numbers

a step-by-step solution; each step has clear instructions.

term that frequently refers to hyperbolic and spherical geometry

making assumptions that are false in order to simplify the understanding of a phenomenon

numbers are timeless and abstract objects, independent of symbols used to represent them

a shape bordered by ones on both sides, every number inside is the sum of the two numbers directly above it.

a conclusion suspected to be true due to preliminary supporting evidence, but there is no proof or disproof

all mathematics can be reduced to rules for manipulating formulas without any reference to the meanings of the formulas

shows a statement to be true using definitions, theorems, and postulates

the completed classification of finite simple groups; over 10,000 pages in 500-ish articles by over 100 authors

the ability of using logic to figure things

knowledge considered to be true based on experience, observation, or existing data

an abstract structure used for inferring theorems from axioms according to a set of rules

knowledge that comes from the power of reasoning based on statements that one believes is true

drawing a conclusion from something known; reasoning used in almost every step in a mathematical argument.

a statement that has been proved, or can be proved, in mathematics