The words of the scientist, who died in March at 76, were broadcast at a London launch event for his final book "Brief Answers To The Big Questions."
Hawking warned that education and science are "in danger now more than ever before." He cited the election of U.S. President Donald Trump and Britain's 2016 vote to leave the European Union as part of "a global revolt against experts and that includes scientists."
Acknowledging that science had yet to overcome major challenges for the world - including climate change, overpopulation, species extinction, deforestation and the degradation of the oceans - the physicist still urged young people "to look up at the stars and not down at your feet."
"Try to make sense of what you see, and wonder about what makes the universe exist," he said. "It matters that you don't give up. Unleash your imagination. Shape the future."
Hawking lived for more than five decades with motor neuron disease that left him paralyzed, communicating through a voice-generating computer. In June, his ashes were buried in Westminster Abbey, between the graves of Charles Darwin and Isaac Newton.
Hawking's daughter Lucy, who attended the book launch, said hearing her father's unmistakable voice had been "very emotional."
"I turned away, because I had tears forming in my eyes," she said. "I feel sometimes like he's still here because we talk about him and we hear his voice and we see images of him, and then we have the reminder that he's left us."
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