William and Kate visit Cambridge
The Duke of Cambridge has spoken of his "immense pride" at being associated with Cambridge as he and the duchess toured the city.
Crowds lined the streets to welcome the royal couple in their first official trip to the city since they married.
Prince William made a speech at the university's Senate House after the pair met well-wishers who had gathered to see them.
The royal couple also opened the new 612-bed Peterborough City Hospital.
During the lunchtime reception at Senate House, Prince William said the couple had looked forward to visiting Cambridge ever since they adopted their titles on their wedding day in April 2011.
He said: "We both feel immense pride at being associated with Cambridge, a place renowned the world over for its dynamism, beauty and learning, and it is lovely for us to be here together today."
The duke also paid tribute to the work of Cambridge University, saying its academic record down the centuries left them both feeling "very humble".
"Within a mile of us, gravity and DNA were discovered," he said.
"Many of the brilliant minds who, through their later work at Bletchley Park, did so much to save our country and the free world, were given first flowering to their genius here at Cambridge.Waved to crowds
"This university has more Nobel prize-winners to its name than all but a couple of countries."
Prince William also joked at his brother's expense about their visit to Trinity College in the city five years ago, saying: "It's the closest Harry's ever got to university."
Another speech by Prince William; another chance to tease his younger brother, with a dig at his academic abilities.
The brothers are close and competitive. Prince Harry gives as good as he gets.
In the past, Harry's public comments have been peppered with references to the follicly-challenged nature of the 30-year-old future king.
In Cambridge, the royal hairstyle was being debated - hers not his.
A fringe is not just a fringe when it adorns the head of this duchess.
During a day in the city which is home to their dukedom, the couple met many people.
But there was one notable absentee, Cambridge's MP, Julian Huppert.
A republican, he was invited to meet them.
Mr Huppert's office insisted the local MP wasn't snubbing William and Kate; he just had too much to do at Westminster.
Earlier the royal couple spoke to some of the hundreds of people who had gathered and waved to crowds in Market Square from the balcony of Cambridge Guildhall.
Reflecting the public's desire for a new royal baby, one admirer gave the duke - an RAF search-and-rescue pilot - a baby's romper suit, emblazoned with a picture of a helicopter and the words "Daddy's little co-pilot".
The pair also met children at Manor School, where the duchess was presented with a portrait of the couple by two pupils, and officially opened a 24-hour centre for rough sleepers run by charity Jimmy's.
At the multi-million pound Peterborough City Hospital, the duke and duchess met patients including seven-year-old Emma Henson, who suffers from a rare disorder meaning her arteries and veins are entangled.
She said: "Kate was very pretty".
Cambridge Mayor Sheila Stuart said the royal visit was "absolutely huge", adding: "The thing for Cambridge is this day is going to be in people's memories for the rest of their lives. In 50 and 60 years, people are going to be telling their grandchildren about it."