Before there was a symbol for temperature, people still felt hot and cold.
Before the gene became a scientific concept, traits were still inherited.
Before eigenvalues were defined, linear transformations already had the structures that eigenvalues would later reveal.
Nature does not label its own variables for us.
Scientists invent—or discover—concepts that make patterns intelligible.
That may be one of the hardest parts of science to automate.
Prefer to watch? Continue with the video below, or keep reading.
Solving a Problem Is Easier Once the Language Exists
Consider a mathematical problem.
If the definitions are given, the theorem is stated, and the allowed logical rules are clear, an AI can search for a proof.
This can be extremely difficult.
But the problem already comes with a language.
Now imagine something different.
No one has defined the right variable.
No one knows which objects should be grouped together.
The current representation makes the problem look complicated.
Then someone introduces a new concept and suddenly the structure becomes simple.
This kind of move appears repeatedly in scientific history.
The hard part was not solving the equation.
It was finding the right thing to write an equation about.
Concepts Compress the World
A useful concept performs a kind of compression.
Instead of memorizing thousands of observations separately, we introduce an abstraction that organizes them.
Take the idea of force.
Rather than describing every motion as an isolated event, we connect changes in motion to interactions.
Or consider entropy.
It packages a vast number of microscopic possibilities into a macroscopic quantity with predictive power.
A strong scientific concept therefore does several things at once:
- compresses observations,
- supports prediction,
- connects different phenomena,
- suggests new experiments,
- fits into a broader explanatory structure.
This is more than naming a cluster in a dataset.
AI Is Already Good at Representation Learning
Modern AI systems learn internal representations all the time.
A neural network may discover features that separate classes.
A language model forms embeddings in which related concepts occupy structured regions.
A scientific model may learn latent variables that efficiently predict future behavior.
In that sense, AI already creates internal abstractions.
But there is an important distinction.
A useful internal feature is not automatically a scientific concept.
A scientific concept must often be stable, communicable, interpretable, and useful across different contexts.
Humans need to be able to reason with it.
Experiments need to be designed around it.
Other theories may need to connect to it.
The gap between a latent vector and a new scientific idea is large.
The Three-Birds Problem
Imagine a system observing:
three birds,
three stones,
three trees.
A human child can eventually abstract the concept of three independently of what is being counted.
The objects differ completely.
The relationship is structural.
Now ask what an AI system must do to make an analogous scientific abstraction.
It has to notice that very different observations share a hidden pattern.
Then it has to separate that pattern from the surface details.
Then it must represent the pattern in a reusable way.
This is not ordinary interpolation.
It is abstraction across contexts.
Recombination Is Not the Same as Concept Formation
Large language models are extremely good at combining existing ideas.
Given chemistry, materials science, and optimization literature, they can propose combinations that no one has explicitly written before.
Some of those combinations may be genuinely useful.
But a skeptic may ask:
Is this discovery, or very powerful recombination?
The distinction is difficult because human creativity also relies heavily on recombination.
Scientists rarely create concepts from nothing.
They borrow analogies, transfer mathematical structures, and reinterpret old ideas in new domains.
The deeper question is whether AI can recognize when the existing vocabulary itself is inadequate.
That is a much higher bar.
Anomaly Is Often the Doorway
New concepts frequently begin with something that does not fit.
A theory explains most observations.
Then one stubborn result refuses to cooperate.
A weaker system treats the result as noise.
A better scientist asks whether the anomaly reveals a missing variable, a hidden mechanism, or an entirely new regime.
Concept formation may therefore require a special relationship with error.
The system must know when not to smooth the anomaly away.
It must sometimes say:
Perhaps the problem is not the data. Perhaps our way of describing the system is wrong.
That is a remarkable intellectual move.
Can We Engineer Concept Formation?
One possible strategy is to ask AI to search explicitly for representations that make scientific relationships simpler.
Suppose raw observations are described by a complicated space $X$.
We search for a transformation
\[ \phi:X\rightarrow Z \]
such that the dynamics or relationships in $Z$ become simpler.
Perhaps
\[ z_{t+1}=F(z_t) \]
has a compact form even though the original dynamics in $X$ are messy.
If the learned variable $z$ is robust, interpretable, and transferable, it may begin to resemble a scientific concept.
A striking glimpse came from a 2022 Columbia Engineering study. Researchers gave an AI raw video of dynamical systems such as a double pendulum and asked it to find a minimal set of state variables that could describe the motion. The system recovered the expected dimensionality surprisingly well, but some learned variables did not map cleanly onto familiar human concepts such as angle or velocity. The result did not prove that AI had invented a new law of physics, but it showed that a machine can construct useful internal coordinates that scientists did not explicitly provide.
This idea appears in representation learning, dimensionality reduction, system identification, and automated discovery of governing equations.
The difficult part is deciding when the representation is meaningful rather than merely convenient.
Scientific Concepts Carry Counterfactual Power
A good concept does not only summarize what we observed.
It helps us reason about what we did not observe.
If we understand pressure, we can predict what happens when pressure changes.
If we understand charge, we can reason about a new configuration of particles.
If we understand a symmetry, we can infer consequences in systems we have never measured directly.
This counterfactual power may be a useful test.
A representation that only compresses the training data is one thing.
A concept that supports reasoning under new interventions is something more.
Language Matters
There is also a communication problem.
Suppose an AI discovers an internal representation that perfectly organizes a new class of physical phenomena.
But the representation consists of a 20,000-dimensional vector with no intelligible structure.
Has it created a concept?
For the AI, perhaps.
For human science, the answer is less satisfying.
Science is a social activity.
Ideas must be compared, criticized, taught, and connected with other ideas.
A machine-generated concept becomes much more valuable if it can be translated into a form that scientists can manipulate.
This may require symbolic abstraction.
That is one reason the old debate between neural and symbolic AI is becoming relevant again.
Maybe Human and Machine Concepts Will Differ
There is another possibility.
Perhaps future AI systems will develop useful scientific representations that are not naturally human-readable.
Humans evolved to think in three-dimensional space, objects, causes, agents, and relatively low-dimensional abstractions.
An AI may be comfortable with structures that are impossible for us to visualize.
Would we reject a theory because we cannot intuitively understand its concepts?
Probably not, if it predicts and controls nature extraordinarily well.
But science would change.
We might increasingly rely on translation layers between machine concepts and human concepts.
The AI would reason in one representation.
Humans would receive a compressed explanation in another.
The Last Mile of Discovery?
As AI becomes stronger at deduction, search, and optimization, concept formation may emerge as one of the deepest remaining challenges.
A system that can solve problems inside an existing representation is powerful.
A system that can invent a better representation can change the field.
That is what many major scientists have done.
They did not merely answer old questions.
They changed the language in which future questions could be asked.
Whether AI can do that reliably remains open.
But if it can, AI4S will have crossed an important threshold.
And one possible ingredient may come from combining two traditions that AI research has often treated separately:
learning from data and reasoning with symbols.
Next in the series: Neural, Symbolic, and Neuro-Symbolic Science
0 comments