The Briton was known for his work with black holes and relativity, and wrote several popular science books including A Brief History of Time.
At the age of 22 Prof Hawking was given only a few years to live after being diagnosed with a rare form of motor neurone disease.
The illness left him wheelchair-bound and largely unable to speak except through a voice synthesiser
In a statement his children, Lucy, Robert and Tim, said:
“We are deeply saddened that our beloved father passed away today.
“He was a great scientist and an extraordinary man whose work and legacy will live on for many years.”
They praised his “courage and persistence” and said his “brilliance and humour” inspired people across the world.
“He once said, ‘It would not be much of a universe if it wasn’t home to the people you love.’ We will miss him forever.”
Prof Hawking was the first to set out a theory of cosmology as a union of relativity and quantum mechanics.
He also discovered that black holes leak energy and fade to nothing – a phenomenon that would later become known as Hawking radiation.
The scientist gained popularity outside the academic world and appeared in several TV shows including The Simpsons, Red Dwarf and The Big Bang Theory..
Hawking was considered one of the leading voices in science because of his extensive research and work related to understanding the universe.
“I never expected to reach 75, so I feel very fortunate to be able to reflect on my legacy,” Hawking said in a BBC interview last year.
He made several major discoveries throughout his career, and once said said his greatest achievement was his discovery that black holes are not entirely black.
“I think my greatest achievement will be my discovery that black holes are not entirely black,” he said, adding how that discovery would be critical to “understanding how paradoxes between quantum mechanics and general relativity can be resolved.”
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