Position: LLMs can't jump — part 1/4

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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):
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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-
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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.
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