Mathematics: Discovered or Invented?

What did the Pythagoreans believe about numbers?

• They were mere abstractions.

• They were living entities and universal principles.

• They were created by humans.

• They were only useful for counting.

Which philosopher argued that mathematical concepts were as real and concrete as the universe itself?

• Socrates

• Euclid

• Aristotle

• Plato

Who is known as the father of geometry?

• Euclid

• Archimedes

• Leibniz

• Pythagoras

What did Leopold Kronecker famously state?

• Mathematics is the language of the universe.

• God created the natural numbers, all else is the work of man.

• Mathematics is a human invention.

• Numbers are living entities.

What did David Hilbert attempt to do?

• Invent a new number system.

• Disprove Euclidean geometry.

• Axiomatize all of mathematics.

• Prove the existence of God.

What did Henri Poincaré argue about Euclidean geometry?

• It is the only true geometry.

• It is a specific outcome of a particular set of rules.

• It is a universal truth.

• It is irrelevant to the real world.

Who coined the phrase 'unreasonable effectiveness of mathematics'?

• Albert Einstein

• Isaac Newton

• Gottfried Hardy

• Eugene Wigner

What unexpected application was found for Gottfried Hardy's number theory?

• Cryptography and genetics

• Medicine

• Economics

• Astronomy

What did Fibonacci's sequence initially describe?

• Idealized rabbit populations

• Planetary orbits

• Human anatomy

• Chemical reactions

What did Bernhard Riemann's non-Euclidean work become the foundation for?

• String theory

• Quantum mechanics

• Classical mechanics

• General relativity