TED-Ed: Is math discovered or invented? - Jeff Dekofsky

The video explores the age-old debate on whether mathematics is discovered or invented. It presents historical perspectives from ancient philosophers like the Pythagoreans, Plato, and Euclid, who viewed math as a real and independent entity. In contrast, others like Kronecker and Hilbert saw it as a human invention. The video also highlights the effectiveness of math in explaining the universe, citing examples like Hardy's number theory and Fibonacci's sequence. It concludes by reflecting on the philosophical and spiritual nature of this debate.

Which ancient group believed that numbers were both living entities and universal principles?

• The Egyptians

• The Romans

• The Pythagoreans

• The Babylonians

Who famously stated, 'God created the natural numbers, all else is the work of man'?

• Leopold Kronecker

• Henri Poincaré

• David Hilbert

• Eugene Wigner

What did Henri Poincaré believe about non-Euclidean geometry?

• It was a universal truth

• It was a discovery of the 20th century

• It was a result of specific game rules

• It was irrelevant to mathematics

Which mathematician's work in number theory unexpectedly contributed to cryptography?

• Fibonacci

• David Hilbert

• Bernhard Riemann

• Gottfried Hardy

What natural phenomenon did Fibonacci's sequence help to describe?

• The movement of tectonic plates

• The orbit of planets

• The growth of rabbit populations

• The flow of rivers

Which theory, developed in the 18th century, was later used to explain DNA replication?

• String theory

• Game theory

• Chaos theory

• Knot theory

What philosophical question is posed about the existence of numbers in a forest?

• Can numbers exist without being counted?

• Are numbers a human invention?

• Is mathematics a universal language?

• Do numbers have a physical form?