In 1963, Cambridge University astrophysics student Stephen Hawking begins a relationship with literature student Jane Wilde . Although Stephen excels at mathematics and physics, his friends and professors are concerned over his lack of a thesis topic. After Stephen and his professor Dennis Sciama attend a lecture on black holes, Stephen speculates that black holes may have been part of the creation of the universe and decides to write his thesis on time.
While pursuing his research, Stephen’s muscles begin to fail, eventually causing him to fall and hit his head. He learns he has motor neurone disease; he will be unable to talk, swallow, breathe or move most of his body, and has approximately two years to live. Stephen asks what will happen to his brain. The doctor tells Stephen that the disease doesn’t affect the brain and that Stephen’s thoughts won’t change but eventually, no one will know what they are. As Stephen becomes reclusive, focusing on his work, Jane confesses her love to him. She tells Stephen’s father she intends to stay with Stephen even as his condition worsens. They marry and have a son.
Stephen presents his thesis to the examination board, arguing that a black hole created the universe in a Big Bang, that it will emit heat, and that it will end in a Big Crunch. While celebrating with Jane and his friends, Stephen realises he cannot walk and begins using a wheelchair.
After having a second child, a daughter, Stephen develops a theory about the visibility of black holes and becomes a world-renowned physicist. While focusing on the children, Stephen’s health and his increasing fame, Jane is unable to work on her own thesis and is frustrated; Stephen tells her he understands if she needs help. She joins the church choir, where she meets widower Jonathan . She and Jonathan become close friends, and she employs him as a piano teacher for her son. Jonathan befriends the entire family, helping Stephen with his illness, supporting Jane, and playing with the children.
When Jane gives birth to another son, Stephen’s mother asks Jane if the baby is Jonathan’s. Jane is appalled; seeing that Jonathan overheard the conversation, when they are alone they admit their feelings for one another. Jonathan stays away from the family, but Stephen visits him, saying that Jane needs him.
While Jane and Jonathan take the children camping, Stephen is invited to attend an opera performance in Bordeaux and contracts pneumonia. While in the hospital, the doctors tell Jane that Stephen needs a tracheotomy, which will leave him unable to speak. She agrees to the surgery.
Stephen learns to use a spelling board and uses it to communicate with Elaine , his new nurse. He receives a computer with a built-in voice synthesiser, and uses it to write a book, A Brief History of Time, which becomes an international best-seller.
Stephen tells Jane that he has been invited to America to accept an award and will be taking Elaine with him. Jane faces the realisation that her and Stephen’s marriage has not been working, telling him she “did her best.” Jane and Stephen agree to divorce. Stephen goes to the lecture with Elaine, the two having fallen in love, and Jane and Jonathan reunite. At the lecture, Stephen sees a student drop a pen; he imagines getting up to return it, almost crying at the reminder of how his disease has affected him. He goes on to give an inspiring speech, saying, “There should be no boundaries to human endeavor. We are all different. However bad life may seem, there is always something you can do, and succeed at. While there’s life, there is hope.”
Stephen invites Jane to meet the Queen with him; they share a happy day together with their children, with Stephen saying “Look what we made”.
An extended closing series comprises select moments from the film shown in reverse back to the moment Stephen first saw Jane. A final title sequence brings the lives of the lead characters up to date. Jane and Jonathan are happily married and she has completed her PhD. She and Stephen remain close friends. Stephen declines a knighthood and continues his research with no plans to retire.