Plenty of films and TV shows employ military experts, police officers or doctors to serve as technical advisers, but Farley believes his company – Hollywood Math and Science Film Consulting – fills an unmet need.

Many movie mathematicians seem to luck into the job.

“A Beautiful Mind” director Ron Howard hired Barnard College math professor Dave Bayer after he read a review of the play “Proof” that Bayer wrote for the American Mathematical Society.

Before he consulted for “Good Will Hunting,” University of Toronto physics professor Patrick O’Donnell was hired as an extra. A producer stopped him on the street and asked him to play a drunk in a bar scene with Robin Williams. O’Donnell later helped actor Matt Damon with the math his character, a troubled genius, would be tackling on screen.

“Hollywood is not a math class,” O’Donnell said. “Every scene was accurate, but you wouldn’t learn mathematics from it.”

Farley, 35, co-founded his company with Lizzie Burns, a London-based biochemist he met studying at the University of Oxford a decade ago. Farley said he and Burns are philosophically at odds over how mathematically accurate movies should be.

“To make a film really credible,” Burns said, “it’s important to get the science right.”

Farley, on the other hand, said he knows filmmakers sometimes sacrifice scientific accuracy in the name of entertainment.

“I just think there’s a way of making the science not look ridiculous, as you often find in many science-fiction shows and movies,” he said.

Farley has recruited some of his colleagues, including Harvard postdoctoral fellow Anthony Harkin, to serve as consultants. Harkin said mathematicians love to police TV programs and movies for errors. One of the most famous, he added, comes from “The Wizard of Oz.”

“When the scarecrow gets his brain, he incorrectly states the Pythagorean theorem,” Harkin said. “If any mathematician would have looked at it, they could have easily fixed that flaw.”

Farley gives high marks to the makers of “Numb3rs” for what he says is an accurate portrayal of how mathematicians work and interact with each other.

“Getting the math right is very important to our creators,” said Andy Black, a researcher for the show. “We do want to have that kind of credibility.”

After “Numb3rs” premiered in January, Farley e-mailed the show’s producers and offered his services. He traded messages with Black, who agreed to start sending him copies of unfinished scripts. Farley won’t disclose what his company is paid for advice.

“Jonathan seemed very enthusiastic about pitching in,” Black said.

Farley and Harkin check the scripts for errors, scribble suggestions in the margins and send them to Black, who passes them on to the show’s head writers.

“He presents nice, concise suggestions,” Black said. “It’s up to the writers to implement them.”

Farley said he objected to a scene where one of the main characters, an older mathematician played by Peter MacNicol, talks about his “brazen attack on the Lorenz invariance.”

“I asked a string-theory friend, and he said it doesn’t make sense,” he said. “I told them, but they didn’t change it.”

The show also works closely with Gary Lorden, who chairs the math department at the California Institute of Technology. Lorden comes up with some of the formulas that Charley scribbles on chalkboards. In early episodes, one of his younger graduate student’s hands filled in for those of the math genius, played by David Krumholtz.

Lorden said he sees the job as a lark, not a business opportunity.

“I grew up seeing virtually nothing about math in the popular media,” he said. “I’m really hoping ‘Numb3rs’ spawns some imitators.”

Farley and his agent Caron Knauer, a former associate producer at 20th Century Fox, are banking on that happening. “More and more projects are featuring math on the forefront,” Knauer said. “It’s the Hollywood bandwagon mentality.”