Theoremhood and truth Until the end of the 19th century and the foundational crisis of mathematics, all mathematical theories were built from a few basic properties that were considered as self-evident; for example, the facts that every natural number has a successor, and that there is exactly one line that passes through two given distinct points. These basic properties that were considered as absolutely evident were called postulates or axioms; for example Euclid's postulates. All theorems were proved by using implicitly or explicitly these basic properties, and, because of the evidence of these basic properties, a proved theorem was considered as a definitive truth, unless there was an error in the proof. For example, the sum of the interior angles of a triangle equals 180°, and this was considered as an undoubtable fact.
Theoremhood and truth Until the end of the 19th century and the foundational crisis of mathematics, all mathematical theories were built from a few basic properties that were considered as self-evident; for example, the facts that every natural number has a successor, and that there is exactly one line that passes through two given distinct points. These basic properties that were considered as absolutely evident were called postulates or axioms; for example Euclid's postulates. All theorems were proved by using implicitly or explicitly these basic properties, and, because of the evidence of these basic properties, a proved theorem was considered as a definitive truth, unless there was an error in the proof. For example, the sum of the interior angles of a triangle equals 180°, and this was considered as an undoubtable fact.