Solving exponential equations using properties of exponents
Creativity break: How are math and creativity changing the world?
(light music) (typewriter typing) - Maths underpins everything in our universe, so it impacts every corner of our society. But over the past decade in particular, the advances in computer technology and the introduction of machine learning and artificial intelligence has been massive. And we're only learning more and more and building better and better systems. And maths underpins all of that and it's fundamental to all of those systems. And in fact, computer science is inherently linear algebra, so it's really foundational to those scientific advances. - One relatively recent example that really inspired me was the first real photo that scientists were able to capture of a black hole, those mysterious remnants of giant stars that lurk all over the universe. And it is the way the scientists used creativity and math to solve the problem that was so fascinating. You see, these black holes are do distant that there is no single telescope that is large enough to be able to actually see them. And the scientists came up with this clever idea, creating a network of small telescopes distributed all across the globe that were synchronized to capture and focus the same object at the same time, creating a giant virtual telescope. Now, the aperture of this giant virtual telescope is nearly the same size as the diameter of the Earth. And with that in place, the scientists and engineers were able to capture all the bits and pieces of data and put it all together into the first image of a black hole that is 53 million light-years, which is 318 quintillion miles away. Now, that's an impressive use of creativity and maths. (light music continues)