The ways in which popular culture presents mathematics often has a significant impact on public perceptions of the subject. Positive representations can spur fascination and wonder among children and adults alike. One only has to look at the huge influence Star Trek had on youngsters when it first aired in the 1960s, inspiring a new generation of budding scientists and engineers.

Sadly, popular culture can also reinforce negative stereotypes of mathematics and its practitioners, which might prevent people from pursuing an interest or career in the field. Let's examine some examples of mathematics in popular culture, including the good, the bad and, in some cases, the incorrect or 'bogus'.

Good Will Hunting starred Matt Damon as self-taught mathematics prodigy Will Hunting, whose criminal behaviour eventually leads to him crossing paths with Fields Medal-winning professor Gerald Lambeau (Stellan Skarsgård). The film tracks Hunting as he learns advanced mathematics under Lambeau's tutelage and battles his inner demons through therapy sessions with psychology teacher Dr Sean Maguire (Robin Williams).

Good Will Hunting was a huge critical and commercial success, launching the acting careers of Damon and Ben Affleck, who played Hunting's best friend Chuckie. The movie was also nominated for nine Academy Awards, winning in the Best Supporting Actor (Williams) and Best Original Screenplay (Damon and Affleck) categories.

But was Good Will Hunting an accurate representation of mathematics? Well, the film has been criticised for perpetuating the idea that gifted individuals often struggle to fit into society. Biographical movies of real-life mathematicians also tend to emphasise these issues, including John Nash's schizophrenia in A Beautiful Mind and Alan Turing's eccentricities in The Imitation Game.

Good Will Hunting also contains inaccuracies from a practical perspective. The film has a pivotal scene where Hunting solves a mathematics problem that supposedly took Professor Lambeau and his colleagues two years to complete:

"How many (non-isomorphic) homeomorphically irreducible trees are there on 10 vertices?"

While the problem may sound challenging due to the terminology involved, in reality, the puzzle is simple enough for most people to solve relatively quickly with a pen and paper.

Numb3rs was an American crime drama that starred David Krumholtz as Charlie Eppes, a mathematics prodigy who assists his FBI agent brother Don Eppes (Don Morrow) with investigations. Most episodes saw Charlie utilising complex mathematics, including probability and statistics, algebra and differential equations, to solve crimes.

The show was lauded for making mathematics a suitable topic for prime time Friday night viewing, with 10 million Americans regularly tuning in to watch each episode.

Creators Cheryl Heuton and Nick Falacci also received the Carl Sagan Award for Public Appreciation of Science in 2005 for their work on Numb3rs.

Academics particularly praised Krumholtz's performance as a socially capable, family-oriented mathematician who is able to apply his abstract skills to multiple real-world scenarios. In fact, many of the episodes are based on actual events, including the pilot where Charlie tracks the likely home of a serial rapist by analysing the location pattern of his crimes.

Gary Lorden, Professor of Mathematics at the California Institute of Technology (Caltech), was one of the consultants on the programme. In a 2005 interview with Talk of the Nation, Professor Lorden said he and a number of other consultants "do Charlie's thinking for him" to ensure the mathematical integrity of the show. He admitted that while there are some stretches of the imagination, Numb3rs nevertheless maintains incredible accuracy.

Mathematics doesn't often take centre stage in popular culture, but that's certainly not the case with Tom Stoppard's clever play Arcadia. The drama unfolds across two time periods at an English estate, Sidley Park. Some acts take place in the 19th Century, with a flamboyant tutor, Septimus, teaching a brilliant young mathematician named Thomasina. In the present day, two scholars - writer Hannah Jarvis and literature professor Bernard Nightingale - visit Sidley Park to investigate two separate historical incidents.

Mathematics is just one of several themes in this multiple award-winning play, yet Stoppard draws heavily on recognised theorems and concepts such as Fermat's last theorem, chaos theory and the second law of thermodynamics. Notably, Thomasina discovers a link between functional iteration and functional geometry, a revelation that was not uncovered in real life until the second half of the 20th century.

Alex Kasman, Professor of Mathematics at the College of Charleston, believes one of Arcadia's strengths is that it uses accurate, real-life mathematics in a fictional setting. Showing Thomasina connecting functional iteration and functional geometry confirms her status as a genius to audience members who are familiar with mathematics, while introducing a fascinating topic in a novel way to laypeople.

Critics also celebrated Arcadia's portrayal of a female mathematician in a central role, helping to address gender issues in the field. Interestingly, Lord Byron - father of esteemed mathematician Ada Lovelace - is an offstage character in the play.

Dan Brown's The Da Vinci Code is a thriller novel that reportedly sold more than 80 million copies worldwide,      while inspiring a film with the same name that achieved one of the best box office opening weekends of all time.      The book spent 166 weeks on the New York Times Bestsellers List - the seventh-longest run since the rankings began in 1931.

The Da Vinci Code's main protagonist is Harvard professor and symbologist Robert Langdon, who is called upon to assist with the murder investigation of Jacques Saunière, curator of The Louvre museum in Paris. The novel follows Langdon as he solves cryptic clues Saunière left before his death, uncovering clandestine organisations, revelations about Christianity and links to the Holy Grail during his search for the truth.

Cryptography features heavily in the novel, and Brown explains various mathematical concepts such as Fibonacci sequences and the Golden Ratio. The Da Vinci Code has received criticism for its historical and religious inaccuracies, but how do the mathematics hold up to scrutiny? On first appearances, relatively well - yet some discrepancies appear after scratching below the surface.

For example, Professor Langdon discusses the eerie presence of the Golden Ratio - or Phi - in multiple natural phenomena, including beehive populations, the spirals of nautilus shells and the arrangement of sunflower seeds. The omnipresence of Phi is a debated topic in mathematics circles, and analysis from the University of Notre Dame suggested the accuracy of the Da Vinci Code's examples are somewhat hit and miss.