The popular claim that “if you can’t explain it to a 5-year-old, you don’t understand it” — often misattributed to Einstein — is not only false but actively harmful to how people approach learning and communication about complex topics. The speaker dismantles this myth from multiple angles and offers a more honest framework for thinking about explanation, understanding, and the real difficulties of learning advanced material.
The Einstein attribution is wrong
Einstein never said this. In fact, he implicitly rejected the idea when he declined to enter a 1920s Scientific American competition that asked him to explain his own theory of relativity in 5,000 words to a general audience — not even a 5-year-old, but educated adults. He had 5,000 words and still chose not to do it.
Feynman made a similar point when a reporter asked him to explain quantum electrodynamics (QED): “If I could explain it to you, then it wouldn’t be worth the Nobel Prize."
"Simple” is a feeling created by familiarity, not an inherent property of concepts
What people call “simple” — like logarithms, exponentiation, or addition — only feels simple after months or years of drilling in school. There is nothing inherently simple about these ideas; the simplicity is a product of repeated exposure and practice.
Judging whether something is simple based on one’s own familiarity is circular reasoning.
Deep understanding and the ability to explain are only mildly correlated
At research universities like the University of Toronto, professors are hired for their research knowledge, not their teaching ability. Being a great explainer and being a great understander are different skill sets.
The arbitrary age cutoff of “5-year-old” is also baseless — why not 15, 25, or 2?
The explanation trilemma: you can only have two of three
When explaining anything, you can only pick two of the following: succinctness, simplicity, and accuracy.
Accurate and succinct, but not simple: A classifying space BG for a group G is a topological space such that principal G-bundles over any space X are classified by maps from X to BG up to homotopy. This is correct and brief, but incomprehensible without extensive background.
Simple and succinct, but not accurate: “A classifying space shows all possible ways some object or group can be organized.” This is easy to say but vague and misleading.
Simple and accurate, but not succinct: Textbooks like Hatcher’s Algebraic Topology or Bredon’s Topology and Geometry start from basics and are fully accurate, but they are hundreds of pages long.
Most “explain it to a 5-year-old” attempts fall into the second category — they sound good but convey almost nothing useful. In some cases, saying nothing would be more honest.
Some truths resist simplification by nature
Certain spiritual and philosophical traditions hold that language fundamentally fails to capture the deepest aspects of reality or consciousness, and that speaking about them distorts them. Wittgenstein echoed similar views.
Grasping a concept like “emptiness” in Buddhist philosophy takes months or years of meditation and wrestling with texts like Cohen’s. A 5-year-old’s concept of “empty” would be, appropriately, empty.
Compression doesn’t distill a message to its essential core — it modifies it. Removing the CN Tower from a photo of Toronto doesn’t give you the essence of Toronto; it gives you a misleading picture.
Some things can be compressed meaningfully — Taylor expansions, Picasso’s line drawings — but this requires deep expertise and is not a straightforward process. Picasso took decades to develop that skill.
Mathematically, not all functions are analytic, meaning they cannot be reconstructed from local information. The entire video can be summarized as: “Not all concepts are analytic.” That statement is succinct and accurate, but not simple.
”Explain it at five levels” videos are often misleading
The speaker critiques a video by Professor Emily Riehl titled “Explaining Infinity at Five Levels.” The title is misleading: she is not explaining infinity at five levels; she is explaining five different ideas related to infinity at increasing levels of sophistication.
To a 9-year-old: infinity is what’s unbounded.
To a 13-year-old: Hilbert’s Hotel paradox.
To an undergrad: cardinality.
To a PhD student: the axiom of choice and ZFC equivalences.
To a professor: casual conversation about what’s fascinating regarding infinity — not really an explanation at all.
It would be implausible to argue that the axiom of choice or the continuum hypothesis was explained to a 9-year-old, let alone a 5-year-old. Even researchers would struggle to do so without assistance.
A better test of whether an explanation worked is to have the listener explain it back to you.
Oversimplified explanations can be worse than nothing
Telling a child that “babies come from storks” is simple but false. Even a simplified truth — “daddy puts his penis in mommy” — leaves the child with no real understanding of how reproduction works.
When people demand “simple terms,” they often mean: “Explain it so I don’t feel stupid, and let me blame you if I don’t understand, rather than face the fact that I lack the background.”
The rubber band problem: analogies eventually cheat
Feynman pointed out that if you explain magnetic attraction by saying magnets are like rubber bands pulling together, you’ve cheated — because then someone will ask why rubber bands pull back together, and you’ll have to explain that in terms of electrical forces, which is what you were trying to explain in the first place.
You cannot explain something in truly simple terms because those simple terms themselves require training to comprehend. This is the same trilemma at work.
Demanding simplicity is a demand for certainty — and it should be resisted
People are told to “embrace the unknown,” but then become upset when a speaker can’t simplify extremely abstract concepts. These two impulses are contradictory.
Demanding simplicity at every level is tantamount to demanding certainty. Instead, we should embrace complexity.
There is a large, underserved hunger among educated audiences for technical rigor. The speaker’s own channel, Theories of Everything, features highly technical content — such as an interview with Claudia de Rham on VDVZ discontinuities and massive spin-2 bosons — that garnered nearly a million views. Claudia herself said it was the most technical interview she’d ever done.
The lesson: people can handle far more than what popularizers spoon-feed them.
The real difficulty: unconscious sticking points
Often, when someone feels something is left unexplained, they can’t articulate what’s bothering them. The confusion comes from unconscious questions that never get asked.
Example: The bowling-ball-on-a-mattress analogy for General Relativity raises unconscious questions — why is the ball constrained to the mattress? Why must it move at all? These questions don’t get answered by pop-sci explanations, leaving a vague sense that something is missing.
Similarly, a learner may be stuck on a derivative concept because of a wrong intuition about a subconcept, without realizing it.
Example: Someone might not understand how the ring of integers forms a group because they read the inverse notation as “2 to the power of negative 1” (which isn’t an integer) rather than as the inverse with respect to addition. Only after correcting this can they move forward.
Because learners often don’t know where their misunderstanding is, they can’t simply tell a teacher. Teachers must throw many examples at students and watch where they falter to triangulate the sticking point.
Without a learner, you must repeatedly look up concepts and examples, often getting more confused, until a sudden realization clicks. “Your ignorance about your ignorance is the issue — and that’s fine.”
A physical analogy for learning
Learning technical material is like physical training. If a bodybuilder tells you to deadlift 450 lbs and you can’t, saying “you must not understand the 450 lbs” is absurd. Placing blame on the teacher robs you of the opportunity to improve.
John von Neumann reportedly said, “You don’t understand mathematics, you just become used to it.” This is partly a joke, but it contains truth: part of understanding complex ideas is overcoming the intimidation and anxiety that comes with unfamiliar terms. As you become more familiar, you can grasp the spirit of concepts even before you fully understand the details.
Three levels of explanation
Gist: A rough sense of what something is about.
Rigor: A precise, technically accurate account.
Fluency: The ability to move smoothly between gist and rigor, understanding how to derive one from the other and even invent new concepts. This comes from familiarity and copious calculation.
The goal is not to “drink from the fire hose” but to “just get wet.” Even if you don’t fully understand something technical, exposure reduces intimidation and builds familiarity. It’s okay if you don’t swim — the point is to get wet.
