IB May 2026 (M26) TOK Title #5 Model Response
To what extent do you agree with the claim that “all things are numbers” (Pythagoras)? Discuss with reference to the arts and the human sciences.
- The essay below is written as a teaching draft to illustrate the structure, tone, and depth of analysis expected in a high-scoring Theory of Knowledge essay.
- It includes call-outs after each paragraph that explain why particular choices were made and how they align with the IB assessment criteria.
- In a formal submission, you would need to provide proper references and citations (using MLA, APA, or the referencing style your school/IB requires).
Introduction
When Pythagoras claimed that “all things are numbers,” he was pointing to a world where patterns, ratios, and proportions underpinned reality. In TOK, the challenge is to ask whether everything in knowledge can truly be reduced to numbers. At a literal level, the claim is too strong: not all things in the arts or human sciences can be quantified without loss. Yet at a structural level, numbers often provide the scaffolding that holds knowledge together. I argue that Pythagoras’s claim is true to a considerable extent: numbers are indispensable tools, but they do not capture the whole of meaning, interpretation, or lived experience.
Note- This intro defines the terms (“all,” “numbers”), rejects the absolutism of the title, and stakes a clear position (“considerable extent”).
- It avoids fence-sitting, which examiners dislike, and frames the evaluation to come.
Arts I: Where Numbers Generate Form
Music is the most obvious case where numbers create knowledge. Frequency ratios explain consonance and dissonance, beats per minute define rhythm, and digital recordings reduce sound to binary code. Even in visual art, proportion, symmetry, and perspective, from the golden ratio in Da Vinci’s Vitruvian Man to geometric precision in Islamic mosaics, are grounded in numbers. In these cases, numbers are not just measurements after the fact but the building blocks of the art itself. To this extent, the claim that “all things are numbers” feels persuasive.
Hint- Here I start with the strongest “Yes” case.
- Music and proportion in art are familiar examples, but framed to show numbers as generative, not just descriptive.
- That shows deeper conceptual control.
Arts II: Where Numbers Cannot Capture Meaning
But numbers fall silent when it comes to interpretation. A Chopin nocturne can be scored in notes and tempos, yet the reason it makes someone cry is not in the numbers. Abstract art goes further, sometimes created to resist reduction altogether. A Jackson Pollock canvas may be analysed in terms of paint viscosity or fractal geometry, but its meaning lies in subjective response. Numbers can chart structure, but they cannot exhaust significance. In the arts, numbers are powerful lenses, but they never give the whole view.
