DeepSeek Prover V2: Free Online Formal Math Proving with AI

Are you looking for a cutting-edge AI model that automates formal mathematical theorem proving—free, online, and developer-friendly? DeepSeek Prover V2 has recently made waves in the AI and mathematics communities, offering powerful Lean 4 proof generation at a scale previously unseen. In this guide, you'll learn what DeepSeek Prover V2 is, how to use it for free online via API, and see real-world proof examples. Plus, discover how modern tools like Apidog streamline the API integration process for teams.

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What is DeepSeek-Prover-V2-671B? Key Features for Developers

DeepSeek-Prover-V2-671B is a 671-billion-parameter Mixture-of-Experts (MoE) large language model created by DeepSeek, purpose-built for formal mathematical theorem proving—especially using Lean 4 syntax. Key features include:

Massive MoE Architecture: 671B parameters, with 37B active per pass, leveraging 8 of 256 dynamic experts per token for advanced reasoning.
Optimized for Formal Math: Specializes in logic-heavy tasks, automating Lean 4 proofs with high accuracy.
Long Context Support: Inherits a huge 163,840-token window from DeepSeek V3, thanks to YaRN RoPE encoding—ideal for complex proofs and rich mathematical context.
Efficient Inference: Supports FP8/BF16 precision for faster, more efficient deployments.
Open-Source & Commercial Use: MIT License on code and permissive weights license—open for research and production.

Community Feedback:
AI practitioners on X (Twitter) describe it as a “math-proof beast,” with performance outpacing other open models for formal math. Benchmarks: 63.5% on miniF2F and 25.3% on ProofNet, with a focus on mathematical logic rather than general conversation.

Distinct From General LLMs:
Unlike DeepSeek R2 (general purpose), Prover V2 is highly specialized—making it ideal for teams working on math research, automated grading, or educational platforms.

Official Model Release:
Hugging Face - DeepSeek-Prover-V2-671B

How to Use DeepSeek Prover V2 for Free Online (API Guide)

Accessing DeepSeek Prover V2 is straightforward, thanks to OpenRouter’s free tier and OpenAI-compatible API. Here’s a step-by-step guide for developers and teams:

1. Register on OpenRouter

Go to OpenRouter.ai.
Click Sign Up (top-right). Register with email, Google, or GitHub (recommended for devs).
After login, access your dashboard.

2. Locate DeepSeek Prover V2

Use the search or scroll to "Trending Models".
Select DeepSeek: DeepSeek Prover V2 (free) for zero-cost usage.

3. Generate Your API Key

On the model page, click Create API Key (under model description or in account settings).
Name your key (e.g., "ProverV2-Test") and save it somewhere safe.
OpenRouter’s API is OpenAI-compatible for drop-in integration.

4. Set Up Your Development Environment

Python is recommended for quick prototyping.
Install the OpenAI library:
```
pip install openai
```

5. Make Your API Request

Here’s a ready-to-use Python example. Replace YOUR_API_KEY_HERE with your OpenRouter key:

import openai

client = openai.OpenAI(
    base_url="https://openrouter.ai/api/v1",
    api_key="YOUR_API_KEY_HERE"
)

response = client.chat.completions.create(
    model="deepseek/deepseek-prover-v2:free",
    messages=[
        {"role": "system", "content": "You are a mathematical proof assistant specializing in formal theorem proving with Lean 4."},
        {"role": "user", "content": "Prove that the sum of two even numbers is even."}
    ]
)

print(response.choices[0].message.content)

Adjustable parameters: Tune temperature for creativity or max_tokens for longer outputs.
Tip: For API workflow design, teams can use Apidog to visually build, test, and document these endpoints—making handoff seamless for QA and backend engineers.

6. Monitor Usage and Limits

The free tier has usage limits—track consumption in your OpenRouter dashboard.
For higher volume or production use, explore paid plans or other DeepSeek models.

Developer Tips

Craft Specific Prompts: Prover V2 responds best to detailed, clear questions.
Handle Errors: Implement retries for occasional empty responses.
Secure Your Keys: Never expose API keys in public code or repos.

Example: Testing DeepSeek Prover V2 with Real Math Prompts

To evaluate DeepSeek Prover V2, let’s run a classic set theory prompt and review the actual Lean 4 proof output.

Prompt:
“Prove that for any two sets A and B, their intersection is a subset of A; that is, A ∩ B ⊆ A. Provide the complete Lean 4 proof and a one-sentence explanation of the key step.”

DeepSeek-Prover-V2 Model Response

Lean 4 Proof

theorem intersection_subset_left (A B : Type) (a : A) : A ∩ B ⊆ A := by
  intro x hx
  cases hx with
  | intro hx₁ hx₂ =>
    exact hx₁
  <;> simp_all

Explanation

The proof uses the cases tactic to split the hypothesis hx : x ∈ A ∩ B into two parts (hx₁, hx₂), then concludes x ∈ A via hx₁.

One-Sentence Key Step

Any element of A ∩ B must also be in A, so A ∩ B ⊆ A follows directly by unpacking the definition.

Model Feedback and Iterative Improvement

When submitting this proof to OpenAI’s o3 model, several refinements were suggested:

Use {α : Type*} (A B : Set α) for full generality.
Remove the unrelated parameter a : A.
Simplify the proof using hx.1 (or .left):

open Set

theorem inter_subset_left {α} (A B : Set α) : A ∩ B ⊆ A := by
  intro x hx
  exact hx.1

Or even shorter, Lean’s standard library already provides Set.inter_subset_left.

Revised Version (After Model Collaboration)

theorem intersection_subset_left {α : Type*} (A B : Set α) : A ∩ B ⊆ A := by
  intro x hx
  exact hx.1

Key Step:
Since hx : x ∈ A ∩ B is a pair ⟨hx₁, hx₂⟩, hx.1 extracts the needed membership in A.

Takeaway for Teams:
This iterative process—running prompts, reviewing AI output, and refining—mirrors how developer teams can rapidly prototype and validate proof workflows using DeepSeek models, with API tools like Apidog streamlining the iteration and collaboration.

Conclusion: The Future of AI-Powered Theorem Proving

DeepSeek Prover V2 is redefining what’s possible in formal mathematical AI. Its specialized MoE architecture, Lean 4 focus, and free API access make it an invaluable tool for research teams, edtech startups, and backend engineers automating math workflows. As more organizations adopt AI for domain-specific reasoning, tools like DeepSeek Prover V2 and platforms like Apidog empower teams to iterate faster, validate results, and integrate AI-driven solutions with confidence.

💡 Want to accelerate your API integration and documentation? Try Apidog for beautiful API documentation, seamless team handoff, and maximum productivity—all at a more affordable price than Postman.

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