Sabine Hossenfelder explains what differential equations are, go through two simple examples, explain the relevance of initial conditions and how differential equations generally work, and then discuss what this means to the question whether the future is determined already.

Time Index:

  • 0:00 Motivation and Content Summary
  • 0:55 Example Disease Spread
  • 3:25 Example Newton’s Law
  • 5:18 Initial Values
  • 6:15 What are Differential Equations used for?
  • 7:08 How Differential Equations determine the Future

Mathematics describes the real world of atoms and acorns, stars and stairs, with remarkable precision.

Is mathematics invented by humans just like chisels and hammers and pieces of music?

Or is mathematics discovered—always out there, somewhere, like mysterious islands waiting to be found?