The show gets it wrong. Worse than having an opportunity and not doing anything with it is having an opportunity and doing damage with it. Math problems are not solved in minutes! Certainly an hour of a guy doing scratch work wouldn’t make good TV, but the show could be true to the fact that mathematics takes hours/days/months without boring the viewer — but it doesn’t even try.
The accusation of unrealism is perfectly correct. On Numb3rs, Charlie solves math problems lickety-split; and if he makes a false step, it’s rectified well before we get down to the car-chase-and-shootout portion of the episode. In real life, math problems take a long time to solve. But you know what? In real life, serial killers take a long time to catch! And in real life, when the cops are in a gun battle with bad guys, the bad guys sometimes don’t miss! And in real life, when you spin your car out, sometimes you crash!
And so on, and so on. Numb3rs is a cop show. As such, it’s bound to very stringent genre conventions, and one of those conventions is speed. If you want to break those conventions and remain on TV, I think you need either a fanatically loyal fanbase, truly brilliant writers, or a home on a network unpopular enough that low ratings don’t matter so much — in fact, my only example of an action show that successfully “worked slow” is season 7 of Buffy, the Vampire Slayer, which had all three.
I had always conjectured that the writers of Numb3rs just sprinkled the dialog with random permutations of words from math book indices.
Not so far off, except that Wikipedia is preferred. The people who write the show are professional TV writers, not mathematicians, so the math content in the draft scripts is often a bit “kinda sorta.” I was one of four or five math consultants to the show in season 2; our role was to tweak the “mathy” sections to bring them into line with the overall plot of the episode. But not to mess around with the plot, which comes first. One doesn’t sense that stories are generated by a writer musing, “Hey, we should build an episode around the cohomology of flag varieties; what crime would that solve?”
Poorly crafted analogies are everywhere, and results are always attributed to a mindblowing theory we’re told about but never see… I don’t learning anything about math or logic with numb3rs. Certainly the subject matter is a bit more dense, but it could be done. As examples, I could see an episode that fully taught an induction proof or presented the complete proof of the solvability of chess. That would have people talking at the water cooler the next day!
Yeah, it might sound something like: “Hey, I cleaned my whole basement last night in the hour of free time I used to spend watching Numb3rs!”
Actually, I think both of my commenter’s suggestions, presented correctly, would indeed make excellent pegs for an episode of the show. The commenter is right that, at times, the show relies too much on big words and gee-whiz. But just as often it presents a real mathematical idea in a vivid way.
As in the premiere, when the cops stare baffled at the pushpin map of the serial killer’s killing spots. As far as they can see, it’s completely random; pushpins distributed evenly all over LA. The mathematician observes: randomly chosen locations don’t form a nice even-looking distribution. The absence of clumps suggests that the killer is intentionally choosing new victims far away from his previous ones. Is there a five-minute lecture on the topic? No; but a viewer should certainly come away having learned a non-obvious piece of mathematics.
But all this is, to me, beside the point. Numb3rs does offer us an opportunity, as my commenter says; but not the opportunity to teach mathematics to a mass audience, a task for which I think a cop show is spectacularly poorly suited. The opportunity presented is the chance to battle a popular story about mathematics — that it’s a chore, that it’s for nerds, that it’s never used in “the real world” — and thereby to bring new students into mathematics courses who otherwise might not have considered them. Nine out of ten may leave disappointed when they find out we don’t actually fight crime. But one out of ten will see what mathematics is really like and think it’s great, and they’ll stay. And we’ll have CBS to thank!