The mathematical crimes of the Young Sherlock Holmes series: a mathematician's critique of on-screen equations

Kit Yates (The Conversation), University of Bath, analyzes the mathematics depicted in the Amazon Prime series Young Sherlock Holmes, explaining how a five-root polynomial, imaginary numbers, and the quadratic formula are portrayed and where the show goes wrong. He emphasizes the distinction between real and imaginary numbers and why precise mathematical reasoning matters in fiction.

Introduction

Kit Yates, Professor of Mathematical Biology and Public Engagement at the University of Bath, analyzes the math in The Conversation's piece about the new Young Sherlock Holmes series on Amazon Prime. The article warns spoilers and uses the on-screen blackboard scene to explore how mathematics drives plot points, both correctly and incorrectly.

On-screen mathematics and key concepts

The author notes that the blackboard equation x^5 + x^4 + x^3 + x^2 + x + 1 = 0 is presented as if it has five solutions, showcasing the role of polynomial equations in the scene. He explains the square root operation and how squaring a number can yield a positive result, while the concept of imaginary numbers arises from needing roots of negative numbers. The piece clarifies that the imaginary unit i is defined as the square root of -1 and that square roots of negative numbers are multiples of i, with examples like the roots of -9 being ±3i. There is a quoted moment where imaginary numbers appear as a plot point, highlighting the importance of accurate terminology in storytelling.

"Complex numbers aren’t targets you can’t see, but well-defined, mainstream mathematical quantities and there’s no sense in which you "aim at" a complex solution to an equation." - Kit Yates

Mathematical blunders and plot devices

The author argues that the blackboard solutions include mistakes typical of an undergraduate tutorial, and that the narrative compounds the error by having Moriarty also write incorrect forms of solutions. The piece discusses the line, "These solutions, they’re not real. They’re imaginary." which, while capturing a common depiction, conflates complex and imaginary terminology. The author emphasizes that writing a correct quadratic solution is not enough if the surrounding dialogue misapplies the concepts; the mathematics should be precise and consistent to maintain credibility.

"This equation is not finished." - Moriarty, the future maths professor

Death by numbers and a GCSE moment

In the finale, the characters encounter a polynomial z^3 + 4 z^2 - 10 z + 12 = 0, depicted as the key to a purported chemical weapon. The author notes the mismatch between the plotted chemical reaction and the shown mathematical scrap, and he explains that factoring and solving the quadratic z^2 – 2 z + 2 = 0 yields z = 1 ± i, illustrating why the on-screen treatment is not justified and how a GCSE quadratic formula would have properly produced the later results. The piece mocks the idea that a simple equation could serve as a secret recipe for a nerve agent, calling the notion nonsensical without proper context.

He adds that Moriarty eventually finds a correct solution for one root, but the rest of the reasoning is a reformulation rather than a rigorous derivation, highlighting the gap between dramatic storytelling and mathematical accuracy.

Takeaways for viewers and educators

The article closes by urging writers to get mathematics right when it is central to a plot, especially when a science-driven series aims to educate or inspire curiosity. The author suggests that clear, correct arithmetic and careful use of terms like imaginary and complex numbers can enhance rather than undermine the narrative, and he encourages viewers to engage with the genuine ideas behind the equations rather than accept sloppy metaphors or misrepresentations.

Conclusion

Yates acknowledges the entertainment value of Young Sherlock Holmes but underlines the responsibility of portraying mathematics accurately, particularly when a show uses it as a pivotal plot device. He argues that accurate math not only improves believability but can also serve as an educational moment for audiences to appreciate the beauty and structure of mathematical ideas.

"If maths is going to be a pivotal plot point in your blockbuster series, then you’ll probably want to make sure you get it right." - Kit Yates