The Duke of Cambridge has spoken of his "immense pride" at being associated with Cambridge as he and the Duchess toured the city.
The royal couple received a rapturous welcome from hundreds of well-wishers who lined the streets of Cambridge to greet them on their first official joint visit to the city since their marriage.
Speaking at a reception in the university's Senate House, William said he and Kate had looked forward to visiting Cambridge ever since they adopted their titles on their wedding day in April last year.
"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," he said.
William 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.
"This university has more Nobel prize-winners to its name than all but a couple of countries."
On a more light-hearted note, William joked at his brother's expense about their visit to Trinity College, Cambridge, five years ago.
"My brother Harry and I were fortunate enough to come to Cambridge five years ago, when we spent a couple of days at Trinity," he said.
"I have to say, it's the closest Harry's ever got to university."
Kate and William later met students and academics from Cambridge University at a marquee reception inside Senate House.
Chris Humpleby, 21, a third year undergraduate studying education at Emmanuel College, met Kate.
He said: "I think they are lovely, they don't have easy lives, to be constantly watched and judged wherever you go is difficult. I think they are amazing."
Kate also met Moos Peeters, 26, a postgraduate from the Netherlands who is studying neuroscience, who said: "All my friends were very jealous when they heard I was going to meet them."
William drew laughter too when he referred to the traditional rivalry between Oxford and Cambridge, in reference to Cambridge's record on Nobel prizes.
"That fact alone must shake even that other place along the M40 - it that must not be named - to its very foundations," he said.
Fergus Todd, 21, an undergraduate studying economics at Clare College, from Edinburgh, also met Kate at the reception. He said: "She was lovely - she was extremely good at asking questions."
During the Senate reception, Kate revealed she is a fan of the BBC quiz show University Challenge as she chatted with two Clare College students.
"I love watching University Challenge," she told economics undergraduate Fergus Todd, 20, and neurosciences postgraduate Moos Peeters, 26.
The 30-year-old Duchess asked: "Are the colleges competitive? Do you take part in University Challenge?"
Todd, who is president of his college's student union, said afterwards: "We told her absolutely not. That is for the absolute elite."
William also proved to be a fan of the quiz presented by Jeremy Paxman, telling one guest: "I watched Trinity annihilate York. I could manage one question. The brain power in here is palpable. I'm finding it quite intimidating."
Kate met a relative during the reception - Dr Penny Barton, a graduate tutor at Homerton College, who is her father Michael Middleton's first cousin and attended the royal wedding.
They greeted each other warmly and Dr Barton said after the meeting: "She did look a bit surprised, although I think she knew I would be here.
"I only saw her in the distance at the royal wedding, to be honest, but we've had another family get-together since, so we've seen her in the last year or so.
"The family is terribly thrilled and very, very proud because we think she does a good job and it's not easy walking about talking to lots of people and being genuinely interested in who she meets."