Position: LLMs can’t jump
Tom Zahavy1
Abstract
How do we fundamentally discover new things?
In a letter to Maurice Solovine, Albert Einstein
conceptualized discovery as a cyclical process
involving an intuitive ’jump’ from sensory expe-
rience to axioms, followed by logical deduction.
While Generative AI has mastered Induction (sta-
tistical pattern matching) and is rapidly conquer-
ing Deduction (formal proof), we argue it lacks
the mechanism for Abduction—the generation of
novel explanatory hypotheses. Using Einstein’s
formulation of General Relativity as a computa-
tional case study, we demonstrate that the prevail-
ing theory of ”creativity as data compression” (in-
duction) fails to account for discoveries where ob-
servational data is scarce. This position paper ar-
gues that while a modern Large Language Model
could plausibly execute the deductive phase of
proving theorems from established premises, it
is structurally incapable of the abductive ’Jump’
required to formulate those premises. We identify
the translation of simulation into formal axioms
as the critical bottleneck in artificial scientific in-
vention, and propose that physically consistent,
multimodal world models offer the necessary sen-
sory grounding to bridge this divide.
1. Introduction
What characterizes the cognitive leap required for scientific
invention? A prevailing view in the AI community, notably
championed by Schmidhuber (2008), suggests that scientific
discovery is fundamentally a problem of compression—the
search for a simple program that concisely explains obser-
vations. This view implicitly frames discovery asInduction:
inferring general rules from observations based on statis-
tical frequency. Concurrently, the success of systems like
AlphaProof (Hubert et al., 2025) in Olympiad-level mathe-
1Google DeepMind, London, United Kingdom. Correspon-
dence to: Tom Zahavy<tomzahavy@gmail.com>.
Proceedings of the 43 rd International Conference on Machine
Learning, Seoul, South Korea. PMLR 306, 2026. Copyright 2026
by the author(s).
Figure 1.A generative AI reconstruction of Einstein’s E-J-A dia-
gram. Einstein drew this diagram in a letter to Maurice Solovine,
showing a cyclical line jumping from Sense Experience (E) to Ax-
ioms (A) via a Jump (J), and then deducing logical consequences.
Ironically, the hallucination of the axiomatic symbols highlights
the very difficulty of automating the jump.
matics suggests that AI is masteringDeduction: the formal
derivation of theorems from established premises.
If scientific discovery were merely the sum of these two
parts, modern Large Language Models (LLMs) should theo-
retically be capable of inventing theories like General Rela-
tivity given sufficient compute.
In this paper, we challenge this reductionist premise by
treating Albert Einstein’s formulation of General Relativity
as a computational case study. Adopting Einstein’s cyclical
model of invention—illustrated in Figure 1—we map the
process from Sense Experience (E) to a System of Axioms
(A) via a conceptual Jump (J), followed by the deduction
and verification of theorems. While we concede that a
modern LLM could plausibly perform the deductive work if
initialized with Einstein’s assumptions, the formulation of
the axioms remains the bottleneck.
By reconstructing the historical context in Section 2, we
show that the scarcity of experimental data precludes in-
duction as an explanation. Since axioms also cannot be
deduced (being premises), we propose that scientific discov-
ery requires a cognitive mechanism beyond induction and
deduction: Abduction.
To formalize this, we adopt the framework of Peirce (1934),
which categorizes inference based on the structural permu-
tation of aRule(function definition), aCase(input), and a
Result(return value):
1

LLMs can’t jump
• Deduction( Rule+Case→Result ) is the analytic
application of a Rule to a Case to predict a Result. It
is the only mode that guarantees truth (e.g., executing
code to verify output).
• Induction( Case+Result→Rule ) is the synthetic
derivation of a Rule from the accumulation of Cases
and Results. It validates hypotheses through statistical
frequency (e.g., generating a function to satisfy unit
tests).
• Abduction( Rule+Result→Case ) is the inference of
a Case (or a new Rule) to explain a surprising Result.
Unlike deduction, which guarantees truth, or induction,
which finds pattern that generalize in data, abduction is
a creative leap that invents a cause for a singular phe-
nomenon. Crucially, Einstein achieved this via embodied
simulation—using thought experiments to ground abstract
symbols in physical sensation—enabling him to formulate
axioms where no symbolic data previously existed.
We argue that while Large Language Models have mas-
tered the inductive compression of data and the deduc-
tive verification of theorems, they are structurally in-
capable of the abductive ’jump’ required for scientific
invention. We posit that this creative leap demands not
just better language processing, but the integration of
physically consistent World Models that ground abstract
symbols in sensory simulation.
2. Background
2.1. Mechanics
In the 19th century, mechanics was regarded as the founda-
tion of all physics. Through the lens of partial differential
equations, scientists could explain a vast array of phenom-
ena: the propagation of sound, hydrodynamics, the motion
of discrete masses, and even the kinetic theory of gases
(linking viscosity, heat conduction, and diffusion). At the
time, even light was understood through this mechanical
framework, described as a wave moving through the ether.
Yet, the mechanical worldview began to fracture. Through
the contributions of Maxwell, Faraday, Hertz, and Mach,
the laws of electromagnetism were unified into Maxwell’s
equations. Newtonian mechanics struggled to explain these
electromagnetic fields, signaling the end of mechanics as
the sole governing paradigm of physics. Physics found itself
divided into two conceptual elements: material points with
forces at a distance between them and continuous fields.
Einstein found this division unacceptable and was driven to
create a field theory for gravity that would replace the old
idea of action at a distance.
Meanwhile, a crisis was brewing regarding the nature of
light. Because light behaves as a wave, scientists assumed it
traveled through a medium they called the ether. However,
the famous Michelson-Morley experiment in the late 19th
century shattered this assumption. They attempted to mea-
sure Earth’s velocity relative to the ether but failed to do so.
Even more shocking was the observation that the speed of
light did not vary with the Earth’s movement around the Sun.
Attempts to salvage the ether theory resulted in increasingly
complex and artificial explanations, such as ether wind, all
of which ultimately proved futile.
In addition, Newton’s theory of gravitation was incred-
ibly robust, accurate to an astonishingly small margin
of error. Newton confirmed Galileo’s discovery that all
bodies fall at the same speed regardless of mass by per-
forming pendulum experiments. In particular we have,
Fgrav =m i d2x
dt2 =m gg, so if mi =m g we have that
the acceleration is constant d2x
dt2 =g and independent of
mass. Newton’s experiments validated that mi
mg
= 1 with
an accuracy of 10−3. Over the centuries, this precision was
refined even further—Laplace achieved 10−7 and E¨otv¨os
reached10−9.
In fact, there was only one known anomaly: a tiny shift in
Mercury’s orbit known as the advance of perihelion (Lever-
rier 1845). Scientists were so confident in Newton’s laws
that they didn’t question the theory; instead, they hypoth-
esized that an undiscovered planet, dubbed ’Vulcan,’ was
hiding near the Sun and causing the disturbance.
2.2. Special relativity
In 1905, Einstein resolved the contradictions of the
Michelson-Morley experiment in a way that fully aligned
with Maxwell’s equations. He founded his new theory on
two key postulates.Principle of relativity:The laws of
physics are identical in all inertial frames of reference.In-
variance of the speed of light:The speed of light in a vac-
uum,c, is constant in all inertial frames of reference.
The Michelson-Morely experiment was designed to detect
Earth’s movement through a hypothetical ether, and found
that there is no change in light speed; Light always travels
atc so its speed doesn’t change relative to a moving Earth,
exactly the second postulate.
From the two postulates, Einstein derived the Lorentz trans-
formation, which relates the coordinates of a rest frame to
one moving at a constant relative velocityv. The resulting
transformation for time is:
t′ = t− v
c2xq
1− v2
c2
.(1)
Historically, predecessors like Poincar´e referred to the vari-
ablet′ as ’fictitious time’. However, Einstein’s interpreta-
2

LLMs can’t jump
tion was radical. He argued that t′ was not a calculation
artifact, but ”time plain and simple”. To demonstrate this,
he introduced the concept of time dilation: if two originally
synchronized clocks are separated and one undergoes mo-
tion at velocityv, they will no longer report the same time
upon clearer reunification. With this insight, Einstein shat-
tered the Newtonian paradigm of absolute, universal time,
replacing it with a temporal reality that is local to every
observer.
2.3. General relativity
Einstein’s new theory was intrinsically limited toinertial
frames—observers moving at constant velocities without
acceleration. This specific constraint is the origin of the
name ’special’ relativity. Motivated by the earlier work of
Ernst Mach, Einstein was convinced that inertial frames
should hold no privileged status. Consequently, he sought
a generalization of the theory applicable to any frame of
reference, embarking on the quest forGeneralrelativity.
This seven-year odyssey was characterized by profound
physical hunches, vivid thought experiments, and rigorous
mathematical formalization, interspersed with periods of
exhaustion and error. In the following analysis, we adopt the
framework of Norton (2020), examining Einstein’s progress
through three distinct phases.
Ideation (1907-1912).Einstein took his first concrete steps
toward General Relativity in 1907, when Johannes Stark
commissioned him to write a comprehensive review of rela-
tivity. The task initially seemed straightforward: Einstein
needed to examine established branches of physics to ensure
they fit within the new framework of space and time he had
proposed in 1905.
The work progressed smoothly. Electrodynamics required
no changes, as it was already compatible with the Lorentz
transformation. Mechanics needed some adjustment, specif-
ically regarding energy, momentum, and mass, which led
Einstein to formalize the equivalence of mass and energy
(E=mc 2). He even sketched out a relativistic treatment
for thermodynamics.
However, as he finalized the review, Einstein felt a com-
pelling need to go further. He wanted to generalize the
principle of relativity to include not just constant motion,
but accelerated motion. He was struck by a profound in-
sight—later calling it his ’happiest thought’—that accel-
eration mimics gravity, suggesting that inertia itself is a
gravitational effect. These ideas culminated in his 1912 the-
ory of static gravitational fields, where he boldly proposed
that gravity bends light, slows down clocks, and that the
speed of light is not constant, but varies depending on the
gravitational potential.
Consolidation (1912-1913).The pivotal transition toward
General Relativity occurred between the summer of 1912
and early 1913. Struggling to translate his physical intuition
into a rigorous theory, Einstein realized that the mathemat-
ics of curvature was the key. To master this complex field,
he turned to his friend and mathematician, Marcel Gross-
mann, in Zurich. Their collaboration was documented in
the famous ”Zurich Notebook” and culminated in the 1913
paper known as the Entwurf (”Sketch”).
Einstein consolidated a set of physical requirements and
conceptual pillars that he intended the new theory to satisfy
(see Section A for more details):
1. Generalized Relativity Principle: Extension of special
relativity to accelerated frames
2. Equivalence Principle: Indistinguishability of gravity
and acceleration
3. Geodesic Principle: The motion of free-falling bodies
in spacetime
4. ”Gravity Gravitates”: Gravitational energy itself acts
as a source
5. Stress-Energy Tensor: The source of the gravitational
field
6. Generalized Poisson Equation: The field equation
structure
7. Newtonian Limit: Recovery of classical gravity
The Fatal Error.In the mathematical section, Grossmann
came agonizingly close to the final answer. He identified
the Riemann curvature tensor as the correct measure for
spacetime curvature. He even contracted this tensor to de-
rive a quantity (Gik) that is nearly identical to the modern
Einstein tensor. From a modern perspective, the finish line
was in sight. But despite all of this, they stopped short. The
new equations had to pass a crucial test: they needed to
reproduce Newton’s simple law of gravity in weak, static
fields (Principle 7). In a fatal error, Grossmann concluded
that their candidate tensor did not reduce to the Newtonian
expression. However, as they only figured out later, the
error lay not in the geometry, but in the assumption about
the static field itself.
Believing this path was blocked, they abandoned it. Einstein
was forced to construct a set of field equations based purely
on physical clues, such as conservation laws and his earlier
work on static fields. The result was a mess: instead of one
simple Newtonian equation, he produced ten complicated,
non-linear equations with no clear geometric meaning—a
detour that would delay the final theory for two more years.
3

LLMs can’t jump
Mathematical validation (1913-1915).The years 1913
to 1915 were defined by a grueling struggle to correct and
perfect the 1913 draft. With the publication of the ’Entwurf’
paper in mid-1913, Einstein initially believed the heavy
lifting was done and only details remained. This feeling
was short-lived. As months turned into years, he found
himself working harder and harder to justify a theory that
was misshapen.
By the summer of 1915, the evidence against his old theory
was mounting. He knew it failed to explain the anomalous
orbit of Mercury. He discovered it could not account for
rotational motion. Finally, he realized that his sophisticated
attempts to prove the theory’s uniqueness in late 1914 were
flawed. In a state of mounting desperation, Einstein aban-
doned the ’adapted’ coordinate systems of the ’Entwurf’
and returned to his earlier intuition from 1912: the theory
needed to work in all coordinate systems.
What ensued was perhaps the most intense month of Ein-
stein’s career. Spurred by the knowledge that the renowned
mathematician David Hilbert was racing to solve the same
problem, Einstein entered a frenzy of productivity, submit-
ting a new paper to the Prussian Academy every week for
four consecutive weeks. His first communication on Novem-
ber 4 proposed a solution, yet errors persisted. By November
11, he had refined the theory but difficulties remained; how-
ever, on November 18, he announced the thrilling result that
his evolving equations correctly predicted the anomalous
orbit of Mercury. Finally, on November 25, the fourth com-
munication unveiled the equations of General Relativity:
Rik− 1
2gikR=−κT ik.(2)
Here,Rik is the Ricci curvature tensor,R is the Ricci scalar,
Tik is the Stress-Energy tensor, and gik is the metric ten-
sor. The expression on the left represents the geometry of
spacetime (curvature) as determined by the metric, while
the expression on the right represents the matter and energy.
3. Alternative Views
3.1. The Limits of Inductive Inference
”One not infrequently hears the viewpoint ex-
pressed that physicists are merely noticing pat-
terns... It seems to me, however, that such a view-
point is extraordinarily wide of its mark... When
Einstein’s theory was first put forward, there was
really no need for it on observational grounds.
...Einstein was not just ‘noticing patterns’ in the
behavior of physical objects. He was uncovering
profound mathematical structure that was already
hidden in the very working of the world.”
– Roger Penrose
This distinction between noticing patterns and uncovering
structure highlights the boundary between AI as it exists
today and the AI required for scientific invention. The pre-
vailing view in machine learning aligns with the ”Theory of
Compression Progress,” (Schmidhuber, 2008) which posits
that scientific discovery is driven by the inductive desire to
compress data. In this framework, the ”joy” of discovery is
the rate at which complex observations become subjectively
simpler through better prediction. This inductive approach
has yielded impressive results in data rich environments:
sparse optimization has successfully extracted partial differ-
ential equations from data (Schaeffer, 2017), and the ”AI
Physicist” (Wu & Tegmark, 2019) successfully rediscovered
conservation laws from simulated trajectories.
However, we argue that this inductive framework is insuffi-
cient to explain the invention of General Relativity. While
Einstein sought logical simplicity, his process was not driven
by data compression—primarily because there was no sta-
tistically significant supervised training set to compress.
At the time of invention, Newtonian gravity faced no em-
pirical crisis. The equivalence of inertial and gravitational
mass had been verified to a precision of10−9, and Newton’s
laws were accurate to an astonishingly small margin of er-
ror. The only known anomaly—the advance of Mercury’s
perihelion—was viewed not as a failure, but as evidence of
a hidden variable: the undiscovered planet ”Vulcan”.
This highlights the fundamental limitation of ”creativity as
compression”: scientific invention often occurs in the ab-
sence of a supervised error signal. An AI operating as an
inductive optimization engine would have found the New-
tonian loss function to be near-zero. Without a significant
discrepancy between prediction and observation, there is no
gradient to drive the system toward a foundational restruc-
turing of spacetime.
If modern Transformer models struggle to reverse-engineer
basic arithmetic rules (Gambardella et al., 2024; Yang et al.,
2024), it is difficult to see how it could invent a new physics
in the absence of massive datasets. Furthermore, even
when data is available, inductive systems risk converging
on heuristic shortcuts rather than causal laws. Vafa et al.
(2025) demonstrate that without the correct inductive bias,
foundation models often discover flawed world models that
satisfy the data but fail to capture the underlying structure.
The empirical evidence required to validate General Rela-
tivity—from the Eddington experiment to relativistic GPS
corrections—arrived after the theory was formulated. Ein-
stein was not compressing a noisy dataset to fit a regression
curve; he was constructing a logical framework to uncover
a physical structure that the data had not yet revealed.
Lastly, it could be argued that while Einstein was not com-
pressing data, he was compressing the hypothesis space by
4

LLMs can’t jump
seeking to unify the laws of inertia and gravity into a sin-
gle framework (Minimum Description Length). However,
logical simplicity is often a retrospective property. While
the final theory of General Relativity is elegant, the search
path to get there was paved with complexity, abandoned
tensors, and incorrect equations. A compression-driven AI
might prefer to patch Newtonian gravity with a parameter
like the ’Vulcan’ planet hypothesis rather than expanding
the hypothesis space to include non-Euclidean geometry,
which increases complexity before it simplifies it.
3.2. The Limits of Deduction
”I see on one side the totality of sense experiences,
and on the other, the totality of the concepts and
propositions that are laid down in books. The re-
lations between concepts and propositions among
themselves are of a logical nature... The concepts
and propositions get ’meaning’, or ’content’, only
through their connection with sense experiences.”
– Albert Einstein
Einstein explicitly distinguished between the domain of
sensory experience and the domain of logical processing. In
our framework, this latter domain corresponds to Deduction
(A→S ): the rigorous derivation of theorems from a fixed
set of axioms.
Even the motivation to begin the search for General Relativ-
ity contained a strong deductive component. Einstein’s drive
was not sparked by data anomalies. There was no ”error
signal” in the Newtonian observation history, but by a con-
ceptual inconsistency: the clash between mechanical action
at a distance and the emerging field theories of electromag-
netism. While modern LLMs will struggle to find such an
idea due to the ”weak signal” (there was no requirement to
replace Newton’s gravity), the structural task of proposing a
field theory for gravity by mimicking Maxwell’s equations
is fundamentally a deduction operation.
It is plausible that a modern AI, optimized to search for
inconsistencies in scientific literature, could identify this
contradiction. Much like a system identifying ”buggy code,”
an AI could flag that the constant speed of light in Maxwell’s
equations is incompatible with Newtonian absolute time.
However, identifying the error is distinct from generating
the fix. While the structural task of proposing a field theory
for gravity is a deductive operation, selecting the correct
axioms to resolve the conflict requires more than logical
consistency.
The period between 1913 and 1915 illustrates this deduc-
tive struggle. It was defined not by flashes of insight, but
by a grueling, mechanical search to identify the correct
mathematical framework to satisfy Einstein’s postulates.
This phase closely mirrors the capabilities of modern neuro-
symbolic AI. Einstein’s collaboration with Marcel Gross-
mann was essentially a ”search” process over geometric
constraints. Notably, they identified the Riemann curvature
tensor as the correct object but discarded it due to a ”fatal er-
ror”—the mistaken belief that it did not reduce to Newtonian
gravity in static fields. It took two years of exhaustion to
debug this assumption and produce the final field equations.
The landscape of mathematical discovery has been recently
transformed by automation. Proof assistants based on de-
pendent type theory, such as Lean, have matured into robust
platforms supported by extensive libraries (mathlib Commu-
nity, 2019). In 2024 LLMs have achieved remarkable flu-
ency in proof generation: AlphaProof (Hubert et al., 2025)
achieved silver-medal performance on IMO problems. Suc-
cessors like Gemini, DeepSeekMathV2, and GPT-5 attained
gold-level performance in 2025 and systems like Aristotle
(Achim et al., 2025) produced verified solutions to open
research questions.
”At the age of twelve I experienced a second won-
der of totally different nature - in a little book
dealing with Euclidean plan geometry, ..., were as-
sertions, that could be proved with such certainty
that any doubt appeared to be out of question.
This lucidity and certainty made an indescribable
impression on me.”
– Albert Einstein
Given this trajectory, we posit that a modern LLM, initial-
ized with the specific physical assumptions available to Ein-
stein in 1915, could plausibly derive General Relativity. The
derivation of the perihelion precession of Mercury, once the
field equations are set, is a verifiable logical task (A→S ).
Furthermore, current systems are theoretically capable of
identifying and eliminating erroneous constraints—such as
Einstein’s error regarding static fields—by systematically
optimizing over subsets of axioms.
However, this capability comes with a critical caveat. An AI
can deduce the consequences of ”The Equivalence Principle”
only if those concepts are provided as inputs. As Einstein
noted, logical thinking is limited to connections between
concepts; it cannot generate the concepts themselves from
raw sensory data. The 1913 derivation failed not because
the logic was flawed, but because the axioms were incorrect.
This leads us to the fundamental bottleneck: what cognitive
process allowed Einstein to generate the ”Equivalence Prin-
ciple” in the first place? To understand this, we must look
beyond logic to the mechanism of the ”Jump” (J).
Finally, even if an AI possesses the deductive capacity to
derive Einstein’s equations from his postulates, a funda-
mental problem of intent remains. Unlike formal theorem
5

LLMs can’t jump
proving, where the goal is a specific open conjecture, Ein-
stein was not trying to prove a theorem but to construct
a predictive model of reality. While the anomalous peri-
helion of Mercury offered a verification target, it was not
considered important enough. Crucially, the definitive val-
idation—measuring the gravitational bending of starlight
passing near the Sun by Eddington—arrived years after the
theory was formulated. Deduction ( A→S ) is strictly a
downstream process: it unfolds the logical consequences of
a theory, but it lacks both the upstream capacity to generate
axioms and the external grounding to validate them.
4. Abduction: The missing Jump
”Then there occurred to me the happiest thought
of my life... for an observer falling freely from
the roof of a house there exists—at least in his
immediate surroundings—no gravitational field...
The observer therefore has the right to interpret
his state as ’at rest.’ Because of this idea, the un-
commonly peculiar experimental law that in the
gravitational field all bodies fall with the same ac-
celeration attained at once a deep physical mean-
ing.”
– Albert Einstein
How does the mind formulate new axioms in the absence
of sufficient data? Einstein’s ’happiest thought’ provides
the answer: Manipulative Abduction (Magnani et al., 2009).
This process relies on embodied simulation—an active inter-
action with mental models to generate hypotheses through
thinking by doing, thereby accessing knowledge beyond the
reach of pure deduction. Einstein did not bridge Special
Relativity and gravitation by gathering observations, but
by simulating the physical feelings of an observer inside a
sealed environment.
To make this concept of manipulative abduction more
accessible, we can look to a simpler, classical example:
Archimedes’ discovery of his buoyancy principle. Tasked
Figure 2.Einstein’s thought experiment of the equivalence princi-
ple (AI generated).
with determining if a crown was made of pure gold with-
out damaging it, Archimedes made his abductive leap not
through mathematical derivation, but while stepping into
a bath. By experiencing the bodily sensation of water ris-
ing and being displaced by his own volume, he performed
an embodied sensory simulation. This raw physical feed-
back allowed him to bridge a sensory experience directly
to a new axiomatic concept—volume displacement—which
could not be deduced from the existing mathematical or
linguistic theories of his era. Just as Archimedes used the
physical sensation of displacement to formulate a new law,
Einstein used the simulated sensation of gravity.
We conceptualize this thought experiment as a two-stage
process. First, an observation is imagined viasimulation.
Second, an explanation is derived for that observation via
abductivereasoning. Modern benchmarks like ARC-AGI
(Chollet et al., 2025) already test the latter. In ARC, mod-
els must infer hidden rules from sparse examples (2–5 grid
pairs). Since the data is too sparse for statistical induction
and lacks the explicit instructions required for deduction,
the solver must make an abductive leap to the most plau-
sible explanation. However, as we argue next, while ARC
captures thelogicalleap, it misses themanipulativecompo-
nent—the physical sensation and embodied simulation that
drove Einstein’s insight.
Simulation as Physical Variation.The first pro-
cess—inventing a question to force progress—can be
viewed through the lens of modern AI as Test Time Re-
inforcement Learning. This paradigm involves inventing
new variations of a problem and learning to solve them, a
strategy successfully applied to solve the Penrose position
in chess (Zahavy et al., 2024) and to achieve silver medal
standards in the IMO (Hubert et al., 2025).
However, a critical distinction remains. While symbolic
variations in chess and mathematics are bounded by fixed
rules (axioms), Einstein’s variation required inventing new
axioms based on a physical intuition that did not yet exist
in the mathematics. He envisioned a physicist inside an
elevator being uniformly accelerated through deep space
(Figure 2). Inside this enclosure, the sensory experience re-
veals a specific pattern: when objects are released, the floor
rushes up to meet them. To the physicist, the objects appear
to fall with identical acceleration, regardless of composition.
Thus, the simulation here was not a permutation of symbols,
but a manipulation of perceptual experience.
Abduction and the Physical Prior. The second process is
Abductive Reasoning: the inference to the best explanation.
Unlike deduction, which guarantees truth from premises,
abduction seeks the simplest, most likely cause for an ob-
servation.
In Einstein’s scenario, the existing Newtonian framework
6

LLMs can’t jump
offered no satisfying explanation for his imagined observa-
tion. He faced a silence in the space of language—a lack of
prior symbolic representation:
”The words or the language, as they are written
or spoken, do not seem to play any role in my
mechanism of thought.”
– Albert Einstein
To fill this void, he relied on a physical prior. Because
the simulated sensory experience of acceleration was indis-
tinguishable from the remembered sensory experience of
gravity, Einstein abducted that they must be the same phe-
nomenon. The field inside the box was not a fake inertial
effect; it was, by definition, a genuine gravitational field.
From Chinese Rooms to World Models. This cognitive
process—anchoring abstract symbols in tangible physical
simulations—is known as manipulative abduction (Magnani
et al., 2009). This stands in sharp contrast to the operational
mechanics of LLMs.
While LLMs excel at Induction (finding patterns in data),
they lack the sensory agency required to ground these sym-
bols in physical reality. They operate as high-dimensional
”Chinese Rooms” (Harnad, 1990), manipulating the lan-
guage of physics without access to the physical referents
that give that language meaning. This limitation prevents
the AI from making the Abductive Jump (E→A ). While
Einstein could ground his axioms in the physical experi-
ence of a falling body, an LLM is confined to the logical
deduction of existing texts.
It is worth addressing whether emerging techniques such as
prompt engineering, in-context learning, or iterative context
refinement might unlock abductive capabilities in LLMs.
While these techniques significantly improve reasoning per-
formance within an established symbolic space—enabling
the model to navigate and recombine existing concepts
more efficiently—they are fundamentally constrained by
the boundaries of that symbolic space. Prompting cannot
provide the sensory grounding required for manipulative ab-
duction, which entails generating axioms without symbolic
precedent. It cannot bridge the gap between abstract tokens
and raw, un-symbolized physical experience.
This deficit in physical grounding is central to recent cri-
tiques of AI. Experts contend that despite linguistic mastery,
current systems lack the spatial intelligence(Li, 2025) and in-
ternal world models(LeCun, 2022) required to reason about
physical reality. Without the ability to perceive or interact
with the world, LLMs struggle with spatial reasoning tasks
that are trivial for toddlers .
The emergence of World Models offers a pathway to bridge
this divide, but a critical distinction must be drawn be-
tween visual prediction and interactive simulation. Cur-
rent video generation models like Veo exhibit intuitive
physics(Hassabis, 2025) primarily as a byproduct of sta-
tistical correlation; they correctly generate a falling apple
not because they model gravity, but because falling is the
dominant continuation of unsupported object in their train-
ing distribution.
However, recent architectures like Genie (Bruce et al.,
2024) mark a fundamental shift by introducing action-
controllability into generative world models. Unlike passive
video generators, Genie learns an action space that allows
for agentic intervention—a prerequisite for Manipulative
Abduction (thinking by doing). To replicate Einstein’s eleva-
tor thought experiment, an AI cannot merely watch a video
of an elevator; it must possess the capacity for counterfac-
tual intervention (Pearl & Mackenzie, 2018). It must be able
to essentially take control of the simulation to conceptually
cut the cable.
We argue that physically consistent, action-controllable
world models are not just useful, but are theoretically suffi-
cient to enable abductive leaps. An interactive world model
functions as a ”synthetic laboratory” where an agent can
run counterfactual simulations and test reasoning that goes
beyond standard linguistic training data. Rather than merely
predicting the next token or frame based on statistical cor-
relation, the world model allows the agent to manipulate
the environment, observe the consequences of novel actions,
and abduce underlying rules. The sensory and interactive
feedback from this synthetic laboratory serves as the ground-
ing mechanism necessary to propose new axioms where no
symbolic precedents exist in the language data. We propose
that future iterations of such interactive environments, oper-
ating on a consistent latent physics manifold rather than just
pixels, will provide the substrate necessary to transform the
Abductive Jump from a mystical insight into a reproducible
algorithmic process.
Lastly, its important to note that Einstein relied on his Phys-
ical Prior, using the sensation of gravity to prune the search
space of possible axioms. However, manipulative abduction
extends beyond physics. Historical scientific revolutions are
often driven by strong, pre-symbolic intuitions—whether
Kepler’s Neoplatonic belief in the centrality of the Sun or
the ’objective anger’ that drove Marx’s modeling of capital.
To automate invention, we may need systems that do not
just simulate the world, but hold strong beliefs or priors
about how that world should be structured, using simulation
to test those specific intuitions.
5. Conclusion
In this paper, we posed a fundamental question: Could a
modern Artificial Intelligence, given the knowledge avail-
7

LLMs can’t jump
able to Einstein, invent General Relativity? Our investiga-
tion suggests that for current Large Language Models, the
answer is no. While the field has successfully mechanized
Induction (via statistical compression) and Deduction (via
formal verification), these mechanisms alone are insufficient
to sustain the cycle of scientific invention.
The prevailing Creativity as Compression hypothesis fails to
account for this discovery because it presumes the existence
of a pervasive error signal. Yet, the Newtonian paradigm
faced no such crisis, and the data required to validate Gen-
eral Relativity did not exist until years after its formulation.
Furthermore, while the deduction paradigm offers a path to
derive field equations once axioms are set, it is ultimately a
downstream process—a verification step within the inven-
tion loop, rather than the mechanism of invention.
This limitation is visible even in the apex of today’s auto-
mated discovery systems. Agents such as Sakana’s AI Scien-
tist (Lu et al., 2024) and Google DeepMind’s AlphaEvolve
(Novikov et al., 2025) demonstrate the immense power of
mechanizing scientific loops and evolutionary optimization.
However, they highlight the very abductive gap we identify.
The AI Scientist recombines existing symbolic concepts
to optimize metrics—a sophisticated ”Chinese Room” op-
eration that lacks the sensory grounding to invent axioms
without symbolic precedent. Similarly, while AlphaEvolve
excels at optimization within a fixed framework, it relies on
a gradient; Einstein, by contrast, had no error signal from
Newtonian mechanics to drive his discovery. These systems
lack the embodied world model required to perform the
counterfactual physical simulations that drive the abductive
Jump to entirely new paradigms.
Our analysis suggests that the critical bottleneck is this
intuitive Jump from sensory experience to formal axioms
(E→A ). We frame this work not as a definitive proof, but
as establishing a theoretical framework to guide future em-
pirical testing of abductive capabilities in generative systems.
Einstein did not discover General Relativity by searching
over symbols; he discovered it by simulating the sensual
experience of a falling observer. The formulation of the
Equivalence Principle was a self-contained act of physi-
cal abduction, where the premises were established solely
through internal simulation, independent of immediate ex-
ternal verification.
To build an AI capable of true invention, we must there-
fore move beyond systems that merely read scientific liter-
ature to systems that can perceive the physical world. The
emergence of physically consistent World Models offers a
pathway to a synthetic laboratory. By enabling agents to
run counterfactual simulations—to experience the physi-
cal consequences of a thought experiment—we may finally
mechanize the feedback loop between intuition and logic.
Finally, we emphasize that this proposal is specifically tai-
lored to the physical sciences, where the object of study is
external material reality. In abstract domains such as Mathe-
matics or Computer Science, the Sense Experience (E) may
be grounded in high-dimensional topology or have other
goals such as generality or minimality. While the necessity
of the Abductive Jump remains universal, the nature of the
simulation must be adapted to the ontology of the discipline:
for physics, the substrate is the world; for mathematics, it is
the abstract landscape of formal systems.
References
Achim, T., Best, A., Bietti, A., Der, K., F´ed´erico, M., Gukov,
S., Halpern-Leistner, D., Henningsgard, K., Kudryashov,
Y ., Meiburg, A., Michelsen, M., Patterson, R., Rodriguez,
E., Scharff, L., Shanker, V ., Sicca, V ., Sowrirajan, H.,
Swope, A., Tamas, M., Tenev, V ., Thomm, J., Williams,
H., and Wu, L. Aristotle: Imo-level automated theorem
proving, 2025. URL https://arxiv.org/abs/
2510.01346.
Bruce, J., Dennis, M., Edwards, A., Parker-Holder, J.,
Shi, Y ., Hughes, E., Lai, M., Mavalankar, A., Steiger-
wald, R., Apps, C., Aytar, Y ., Bechtle, S., Behbahani,
F., Chan, S., Heess, N., Gonzalez, L., Osindero, S.,
Ozair, S., Reed, S., Zhang, J., Zolna, K., Clune, J.,
de Freitas, N., Singh, S., and Rockt ¨aschel, T. Ge-
nie: Generative interactive environments, 2024. URL
https://arxiv.org/abs/2402.15391.
Chollet, F., Knoop, M., Kamradt, G., and Landers, B. Arc
prize 2024: Technical report, 2025. URL https://
arxiv.org/abs/2412.04604.
Gambardella, A., Iwasawa, Y ., and Matsuo, Y . Language
models do hard arithmetic tasks easily and hardly do easy
arithmetic tasks, 2024. URL https://arxiv.org/
abs/2406.02356.
Harnad, S. The symbol grounding problem.Physica D:
Nonlinear Phenomena, 42(1-3):335–346, 1990.
Hassabis, D. Demis hassabis: Future of ai, simulating
reality, physics and video games — lex fridman pod-
cast 475, 2025. URL https://lexfridman.com/
demis-hassabis-2-transcript/.
Hubert, T., Mehta, R., Sartran, L., Horv ´ath, M. Z., ˇZuˇzi´c,
G., Wieser, E., Huang, A., Schrittwieser, J., Schroecker,
Y ., Masoom, H., Bertolli, O., Zahavy, T., Mandhane, A.,
Yung, J., Beloshapka, I., Ibarz, B., Veeriah, V ., Yu, L.,
Nash, O., Lezeau, P., Mercuri, S., S¨onne, C., Mehta, B.,
Davies, A., Zheng, D., Pedregosa, F., Li, Y ., von Glehn,
I., Rowland, M., Albanie, S., Velingker, A., Schmitt,
8

LLMs can’t jump
S., Lockhart, E., Michalewski, H., Sonnerat, N., Hass-
abis, D., Kohli, P., and Silver, D. Olympiad-level for-
mal mathematical reasoning with reinforcement learning.
Nature, 2025. URL https://www.nature.com/
articles/s41586-025-09833-y.
LeCun, Y . A path towards autonomous machine intelligence
version 0.9. 2, 2022-06-27.Open Review, 62(1):1–62,
2022.
Li, F. F. From words to worlds: Spatial in-
telligence is ai’s next frontier, 2025. URL
https://drfeifei.substack.com/p/
from-words-to-worlds-spatial-intelligence .
Lu, C., Lu, C., Lange, R. T., Foerster, J., Clune, J., and
Ha, D. The ai scientist: Towards fully automated
open-ended scientific discovery, 2024. URL https:
//arxiv.org/abs/2408.06292.
Magnani, L. et al.Abductive cognition: The epistemological
and eco-cognitive dimensions of hypothetical reasoning,
volume 3. Springer, 2009.
mathlib Community, T. The lean mathematical library.
CoRR, abs/1910.09336, 2019. URL http://arxiv.
org/abs/1910.09336.
Norton, J. D. Einstein’s pathway to general relativity, 2020.
URL https://sites.pitt.edu/˜jdnorton/
teaching/HPS_0410/chapters/general_
relativity_pathway/index.html.
Novikov, A., V˜u, N., Eisenberger, M., Dupont, E., Huang,
P.-S., Wagner, A. Z., Shirobokov, S., Kozlovskii, B., Ruiz,
F. J. R., Mehrabian, A., Kumar, M. P., See, A., Chaudhuri,
S., Holland, G., Davies, A., Nowozin, S., Kohli, P., and
Balog, M. Alphaevolve: A coding agent for scientific and
algorithmic discovery, 2025. URL https://arxiv.
org/abs/2506.13131.
Pearl, J. and Mackenzie, D.The Book of Why: The New
Science of Cause and Effect. Basic Books, 2018.
Peirce, C. S.Collected papers of charles sanders peirce.
Harvard University Press., 1934.
Schaeffer, H. Learning partial differential equations via data
discovery and sparse optimization.Proceedings of the
Royal Society A: Mathematical, Physical and Engineer-
ing Sciences, 473(2197):20160446, 2017.
Schmidhuber, J. Driven by compression progress: A simple
principle explains essential aspects of subjective beauty,
novelty, surprise, interestingness, attention, curiosity, cre-
ativity, art, science, music, jokes. InWorkshop on antici-
patory behavior in adaptive learning systems, pp. 48–76.
Springer, 2008.
Vafa, K., Chang, P. G., Rambachan, A., and Mullainathan, S.
What has a foundation model found? using inductive bias
to probe for world models. InProceedings of the 42nd
International Conference on Machine Learning, volume
267, Vancouver, Canada, 2025. PMLR.
Wu, T. and Tegmark, M. Toward an artificial intelligence
physicist for unsupervised learning.Physical Review E,
100(3), September 2019. ISSN 2470-0053. doi: 10.1103/
physreve.100.033311. URL http://dx.doi.org/
10.1103/PhysRevE.100.033311.
Yang, Z., Ding, M., Lv, Q., Jiang, Z., He, Z., Guo, Y .,
Bai, J., and Tang, J. GPT can solve mathematical
problems without a calculator, 2024. URL https:
//openreview.net/forum?id=LojXXo2xaf.
Zahavy, T., Veeriah, V ., Hou, S., Waugh, K., Lai, M.,
Leurent, E., Tomasev, N., Schut, L., Hassabis, D., and
Singh, S. Diversifying ai: Towards creative chess with
alphazero, 2024. URL https://arxiv.org/abs/
2308.09175.
9

LLMs can’t jump
A. Einstein’s postulates of general relativity
(1) Generalized Relativity:While Special Relativity was restricted to inertial frames (those moving at constant relative
velocities), Einstein sought to extend the principle of relativity to all frames of reference, including those in non-uniform,
accelerated motion.
(2) The Equivalence Principle:Termed by Einstein as ”the happiest thought of my life,” this principle asserts that the local
effects of a homogeneous gravitational field are physically equivalent to those of uniform acceleration in gravitation-free
space. This thought experiment yielded immediate testable predictions, specifically the gravitational redshift of clocks and
the deflection of light rays by massive bodies.
(3) The Geodesic Principle:This principle posits that free-falling objects traverse ’timelike geodesics’—the straightest
possible trajectories within curved spacetime—thereby redefining gravity as a geometric phenomenon rather than a force.
This generalizes the non-relativistic notion of a geodesic (such as the shortest path across a two-dimensional surface) into
the four-dimensional framework of relativity.
(4) ”Gravity Gravitates”:By synthesizing the mass-energy equivalence (E=mc 2) with the equivalence of inertial and
gravitational mass (mi =m g), Einstein deduced that the fundamental source of gravity must be energy density. Crucially,
this implies that the energy of the gravitational field itself contributes to the field, creating a feedback loop. Mathematically,
this necessitates that the field equations must be non-linear.
(5) The Stress-Energy Tensor:Einstein identified Laue’s stress-energy tensor (Tij) as the energy density. Its components
provide a complete physical description of the source matter: T 00: The energy density (mass-energy). T 0i: The momentum
density (and energy flux).T ij: The flux of momentum, representing pressure (wherei=j ) and shear stress (wherei̸=j ).
(6) Generalized Poisson Equation:In Newtonian gravity, the potential ϕ is governed by Poisson’s equation,∇2ϕ= 4πκρ
(where∇2ϕ= 0 in a vacuum). In the relativistic framework, Einstein sought a tensor generalization of this law. He replaced
the scalar term∇ 2ϕwith the curvature tensorR ik and the mass densityρwith the stress-energy tensor term−κT ik.
(7) The Newtonian Limit:This requirement demands that under specific conditions—weak gravitational fields, slow
motion (v≪c ), and static fields—General Relativity must simplify to match Newton’s laws. In this limit, spacetime
curvature becomes negligible and geodesics reduce to Newtonian trajectories (F=ma).
10