Mathematics and Technology Flashcard

Front

Formalist view of mathematics

Back

Mathematics is a creation of the human mind with no intrinsic reality.

Front

The concept of mathematical proof is central to which school of thought in the foundations of mathematics?

Back

Formalist

Front

Who is considered the founder of formalism in mathematics?

Back

David Hilbert

Front

Which of the following best represents a formalist view of mathematical objects?

Back

They are defined entirely by axioms and rules of manipulation.

Front

What is the main critique of the formalist view of mathematics?

Back

It denies the existence of mathematical truths.

Front

According to Hilbert's program, what is the goal of mathematics?

Back

To prove all mathematical truths based on axioms and formal systems.

Front

What is Gödel's incompleteness theorem?

Back

No formal system can prove every truth about arithmetic.

Front

What is true about the axiom of choice in set theory?

Back

It allows for the selection of elements from infinite sets in a non-constructive manner.

Front

Which concept is central to the constructivist philosophy of mathematics?

Back

Mathematical objects only exist if they can be constructed explicitly.

Front

mathematical logic

Back

The study of the logical structure underlying mathematical proofs and systems.