How Far Are Large Models from “Solving Every Subject”?

Hand a challenging high school math problem to a general-purpose large model, and it will first derive the parabola equation, then construct an auxiliary line, and finally solve the system of equations to find the line expression—all within four minutes, with clear steps and a correct answer. This raises a repeatedly discussed question: how much longer will it take before large models can perfectly and thoroughly solve problems across all subjects from elementary through high school?

This article attempts to break this question into analyzable technical sub-problems. Rather than offering a vague timeline, it first clarifies what capabilities “solving every subject” actually demands and what the real state of current technology is on each of them.

1. Defining the Standard for a “Perfect Solution”

A “perfect detailed solution” is not a single metric; it involves at least four layers of constraints:

• Correct result: The final answer matches the reference answer, including values, units, and symbols.
• Verifiable process: Each reasoning step can be derived from the previous step and known conditions, with no skipped steps or “intuitive” leaps.
• Standardized expression: The solution conforms to subject-specific formats, such as factored forms in mathematics, unit annotations in physics, and balanced equations in chemistry.
• Explainability: The model can provide targeted explanations in response to student follow-up questions, rather than repeating the original answer.

These four layers are not equally difficult. Correct results are the entry-level bar; verifiable processes are the real threshold. Many models can “guess” the right answer while having logical breaks in intermediate steps, which is unacceptable in teaching scenarios.

2. Capability Breakdown: Where the Real Difficulty Lies

2.1 Semantic Understanding and Problem Modeling

A problem’s textual description must be translated into formal objects: known quantities, unknowns, constraints, and solution targets. Taking a combined parabola-and-triangle problem as an example, the model must extract three constraints simultaneously from “point P lies on the parabola in the second quadrant with x-coordinate t”: the range of the x-coordinate, the y-coordinate being determined by the function, and the sign constraint t < 0.

Natural language ambiguity is amplified here. For instance, “point F is above point C” could describe either a geometric position or a comparison of coordinate values, and the model must disambiguate using the diagram and context. Current models perform stably on single-concept problems, but once a problem contains implicit conditions or requires integrating graphical relationships, comprehension errors rise significantly.

2.2 Multi-Step Symbolic Reasoning

Mathematical problem-solving is essentially a chain of symbolic derivation. In the example above, going from solving for b and c to deriving the area function and then constructing an auxiliary line to find the line equation involves more than ten derivation steps, each of which may introduce new symbolic variables (d, e, etc.). An error at any step collapses everything downstream.

More critically, the reasoning chain is not linear. When constructing an auxiliary line, the model needs to “think backward”: to prove a certain conclusion, what intermediate relationship must first be established? This goal-directed search remains a challenge for current autoregressive-generation-based models. Models tend to advance along the most probable token path rather than systematically searching the solution space.

2.3 Diagram and Spatial Relationship Parsing

The core information in geometry problems is often hidden in the diagram: perpendicularity, parallelism, equality, collinearity. Pure text models cannot directly “see” the diagram, and while multimodal models can recognize graphical elements, they remain unstable at precise relationship extraction.

For example, to judge the condition “CF = CD and F is above C,” the model must simultaneously understand: segment equality between two points, the coordinate meaning of directional relationships, and the corresponding actual positions in the diagram. Experiments show that multimodal models’ diagram recognition often stays at the coarse level of “identifying that there is a triangle and a parabola,” still noticeably far from “extracting all geometric constraints.”

2.4 Cross-Disciplinary Knowledge Coverage

From elementary to high school, subjects include mathematics, physics, chemistry, biology, Chinese language, English, history, geography, and politics. The problem-solving paradigms differ greatly across subjects:

• STEM subjects emphasize symbolic derivation and computation;
• Humanities subjects emphasize material analysis and argument organization;
• Language subjects emphasize semantic understanding and expression.

For a unified model to achieve “perfection” across all subjects, it would need to simultaneously possess a rigorous symbolic engine, a broad knowledge base, and flexible language ability. These three exist in tension at the training-objective level—over-optimizing reasoning may harm knowledge retention, while over-optimizing language may weaken rigor.

3. Current State of Technology: What It Can and Cannot Do

Based on public evaluations and engineering practice, a rough capability profile can be drawn:

Capability Dimension	Current Performance	Main Bottleneck
Single-concept calculation problems	Good	Occasional calculation errors
Multi-step comprehensive problems	Moderate	Logical breaks in intermediate steps
Geometry proof problems	Weak	Auxiliary line construction and diagram reasoning
Humanities subjective questions	Moderate	Depth of argument and integration of materials
Cross-disciplinary comprehensive problems	Weak	Knowledge retrieval and paradigm switching

It is worth noting that models improve fastest on problems “with standard answers and fixed steps,” and slowly on problems with “open solution methods” or “requiring creative construction.” This suggests that current capability gains mainly come from covering existing solution patterns rather than genuine reasoning generalization.

4. Technical Paths Toward “Solving Every Subject”

To close the gap, scaling up model size alone is no longer sufficient; systematic design at the architecture and engineering levels is needed.

4.1 Separating Reasoning from Computation

Let the model handle understanding the problem and planning steps, and delegate symbolic computation to a deterministic computation engine. For example, the model outputs “solve the system x + y = 3, x - y = 1,” an external solver returns the result, and the model then interprets it. This division of labor can significantly reduce calculation errors while preserving natural language interaction.

# Illustration: the model generates a structured solve request
solve_request = {
    "type": "linear_system",
    "equations": ["x + y = 3", "x - y = 1"],
    "variables": ["x", "y"]
}
# Executed by a deterministic solver, returning exact results

4.2 Structured Diagram Parsing

For geometry problems, first use a vision model to convert the diagram into a structured representation: point coordinates, segment relationships, and angle constraints. Then feed this structure together with the textual conditions into the reasoning module. This decouples “seeing the diagram” from “reasoning,” allowing each to be optimized independently.

4.3 Stepwise Verification and Backtracking

Insert verification nodes into the reasoning chain: each time a key intermediate conclusion is derived, check whether it contradicts known conditions. If it does, backtrack to the previous step and reselect a path. This mechanism can reduce the accumulation of errors from “persisting down one path.”

4.4 Subject-Specific Solution Templates

Different subjects accumulate different problem-solving paradigms. Mathematics has “set unknowns—set up equations—solve—verify,” and physics has “force analysis—set up equations—substitute—discuss.” Explicitly modeling these paradigms as callable procedures is more stable than letting the model generate freely.

5. Designing Reasonable Evaluation Benchmarks

Discussing “how much longer” presupposes a trustworthy evaluation. Many current evaluations look only at final answers, which overestimates model capability. A reasonable evaluation should include:

• Step-level scoring: Score each reasoning step individually to identify logical breaks.
• Multi-solution coverage: Different correct solution methods for the same problem should all be accepted.
• Adversarial samples: Add easily confused conditions to test whether the model truly understands the problem.
• Cross-disciplinary sampling: Avoid testing only mathematics, which distorts the capability profile.

Only when evaluation can distinguish “truly capable” from “lucky guess” does progress become meaningful.

6. Conclusion: Not “Whether” but “Under What Constraints”

Returning to the original question: for large models to perfectly solve problems across all subjects from elementary to high school, the obstacle is not a single technical barrier but the superposition of four constraints—semantic understanding, symbolic reasoning, diagram parsing, and knowledge coverage.

Judging by the trend, problems in a single subject, of a single type, with clear steps will be reliably solved first; geometry proofs, open-ended investigations, and cross-disciplinary comprehensive problems will take longer. True “perfect all-subject solving” is more likely to emerge as a system of “model + tools + verification” rather than a single end-to-end model.

For developers, the pragmatic path is: first pick one subject and one problem type, make the reasoning chain solid, and then gradually expand coverage. Rather than asking “how much longer,” it is better to first answer “on which sub-problem can I now achieve verifiable reliability.”