Up until the late 1990s, astronomers couldn't be certain that any planets existed outside our solar system. These days, not only are astronomers confident that planets are out there, but new ones are being discovered all the time.
We talk to early career mathematicians who spent some of their summer holiday solving problems posed by industry — such as how to blend a perfect smoothie!
Don't like plant-based meat alternatives, but want to spare animals and the environment? There's hope on the horizon, aided by a good helping of maths.