Knowledge Nobody Reads Still Changes the World

If you take a mathematical theorem proved on paper, whether a person sees it or not doesn’t make it any less true. A history of war that nobody reads still describes the war. Despite this, neither one changes what people believe. 

This suggests knowledge holds two distinct types of power: the power to justify belief, which comes from evidence, and the power to impact knowers, which depends on how knowledge is conveyed. In mathematics, conveyance mostly affects how far and how fast knowledge spreads, but not whether it is justified. In history, conveyance plays a much larger role: it can shape the knowledge itself. In both areas, however, conveyance has a limit. It can increase or delay the power of knowledge, but it is incapable of replacing justification.

At first glance, mathematics seems least affected by presentation. Elisha Loomis collected 367 proofs of Pythagoras’ theorem — algebraic, geometric — yet the theorem is equally true in each. Its power comes from the logic of proof, not the style of a specific proof.

However, the history of mathematics shows conveyance matters enormously for what mathematics can do. In 1202, Fibonacci introduced Hindu-Arabic numerals to European merchants. He added no new truth about numbers. Calculating with Roman numerals wasn’t incorrect, it just took significantly longer — multiplying CCXLVII by XLIX takes far more time than 247 × 49. The new numerals changed who could calculate and how quickly, playing a large role in the growth of banking. Interestingly, in 1299 the bankers’ guild of Florence banned Arabic numerals because a 0 could easily be altered to a 6 or 9. The same knowledge was interpreted as both useful and dangerous precisely because of how it presented information.

Newton and Leibniz developed calculus separately with the same results. The only difference: Leibniz wrote the derivative as dy/dx, which looks like a fraction so that concepts like chain rule become easier to visualise. Newton used dots over letters, hiding this structure. British mathematicians used Newton’s notation out of loyalty, while European mathematicians like Euler and Bernoulli used Leibniz’s and made significantly faster progress. Mathematical notation isn’t simply aesthetic — it is a tool for thinking. Knowledge conveyed well can lead to the discovery of new knowledge.

These examples concern the power to use knowledge. A better test is a proof that is correct but presented badly. In 2002, Grigori Perelman published three short essays online claiming to prove the Poincaré conjecture without sending them to a journal or including many typical steps. Teams spent three years filling in gaps before formally accepting it. The poor presentation delayed the proof’s power but didn’t change what it said.

Shinichi Mochizuki’s claimed proof of the abc conjecture seems to suggest the opposite. Released in 2012 across more than 500 pages of unusual terminology, most experts remain unconvinced over a decade later. However, the issue is not style. In 2018, Peter Scholze and Jakob Stix argued that one specific step does not work. Mathematicians refuse to accept it not because it’s hard to understand, but because they cannot check that the claims are justified. In mathematics, conveyance acts as a gatekeeper — it controls when others can reach justification, but the justification itself lies in the proof.

History is different. Historians work with imperfect sources and must choose which to use and how to arrange them. E.H. Carr rejected the idea that historical facts are like fish on a fishmonger’s slab; they are like fish in an ocean — what the historian catches depends on where they choose to fish. Hayden White took this further, arguing that the same events can be told as tragedy, comedy, romance, or satire, and the evidence alone cannot decide which. If White is right, then the way history is told doesn’t just influence the knowledge — it shapes it completely.

The figure of six million Jewish people murdered in the Holocaust is precise and well established. Still, for many readers, The Diary of Anne Frank did more to convey what happened. Translated into more than seventy languages, the diary shows something numbers cannot: what it felt like. Conveyance gives the reader a different kind of knowledge.

David Irving presents a counter-argument. Known for detailed, footnote-heavy history books, Irving impressed reviewers and sold tens of thousands of copies. When historian Richard Evans checked Irving’s footnotes against original sources, he found Irving had repeatedly distorted them. In 2000, the judge ruled that Irving had “persistently and deliberately misrepresented and manipulated historical evidence.” Irving’s work had power because of how it was presented. Once tested against evidence, it lost almost all authority. Even in history, evidence sets a limit.

The power of knowledge is not entirely determined by how it is conveyed, but it is not independent of it either. In mathematics, conveyance decides how fast truth spreads; proof decides whether it is true. In history, conveyance shapes what is known, but must answer to evidence. The more open an area is to interpretation, the more its power depends on conveyance.