Testing DeepSeek-Prover-V2-671B: A Quick Look

The development of AI has brought forth a new wave of specialized models designed to tackle complex tasks with unprecedented precision. Among these, DeepSeek Prover V2 has emerged as a standout, particularly in the realm of formal mathematics and theorem proving. This article delves into what DeepSeek Prover V2 is, how to access and use it for free online, and tests its capabilities with carefully crafted prompts to evaluate its performance.

What is DeepSeek-Prover-V2-671B?

DeepSeek-Prover-V2-671B is a 671-billion-parameter, Mixture-of-Experts (MoE) language model developed by DeepSeek, optimized for formal mathematical theorem proving. According to posts on X, it represents a significant leap in AI-driven mathematical reasoning, built on the architecture of DeepSeek V3 but tailored specifically for logic-heavy tasks.

The model is designed to automate the generation of formal proofs using Lean 4, a proof assistant widely used in mathematical research. Its training on massive synthetic datasets enables it to handle complex mathematical problems efficiently, making it a valuable tool for researchers and mathematicians.

AI community members have highlighted its key features:

• A 671B parameter scale with 37B active parameters per inference pass, leveraging 8 dynamically activated experts out of 256 per token, with support for FP8 and BF16 precision for optimized performance.
• Likely supports a context window of up to 163,840 tokens, as inherited from DeepSeek V3, enabling it to process extensive mathematical contexts with stable long-text modeling via advanced YaRN RoPE encoding.
• Released under an MIT License for its code and a permissive Model License for its weights, both permitting commercial use.

The model is described as a “math-proof beast” on X, excelling in automating formal theorems and building on the success of its predecessors, which achieved 63.5% on the miniF2F benchmark and 25.3% on ProofNet. DeepSeek-Prover-V2-671B focuses on mathematical logic rather than general reasoning, positioning it as a specialized tool rather than a general-purpose language model.

Its release on Hugging Face has sparked excitement, with some AI community members on X calling it a “powerhouse for formal math proofs” and noting its potential to outperform other open-source models in formal math applications. It is distinct from DeepSeek R2, a more general-purpose model expected soon, underscoring DeepSeek’s strategy to develop domain-specific models that push boundaries in niche areas. Prover-V2-671B sets a new standard for AI in formal mathematics.

Huggingface link: https://huggingface.co/deepseek-ai/DeepSeek-Prover-V2-671B/tree/main

How to Use DeepSeek Prover V2 for Free Online

Accessing DeepSeek Prover V2 is straightforward, thanks to platforms like OpenRouter, which provide a free tier for testing the model via an OpenAI-compatible API. Below is a step-by-step guide to using DeepSeek Prover V2 for free at https://openrouter.ai/models/deepseek/deepseek-prover-v2:free, based on available resources and best practices.

Step 1: Sign Up on OpenRouter

1. Visit OpenRouter.ai and click the "Sign Up" button in the top-right corner.
2. Register using an email, Google, or GitHub account. A GitHub account is recommended for developers due to faster setup.
3. Once logged in, navigate to the dashboard.

Step 2: Locate DeepSeek Prover V2

1. Scroll to the "Trending Models" section or use the search bar to type “DeepSeek.”
2. Select “DeepSeek: DeepSeek Prover V2 (free)” from the list. This ensures you’re accessing the free tier model.

Step 3: Generate an API Key

1. On the model page, find the “Create API Key” button (under the model description or in account settings).
2. Name your key (e.g., “ProverV2-Test”) and confirm. Copy the key and store it securely, as it’s required for API requests.
3. OpenRouter’s API is OpenAI-compatible, simplifying integration with existing tools.

Step 4: Set Up Your Environment

To interact with the API, you’ll need a programming environment. Python is recommended for its simplicity. Install the openai library if you haven’t already:

pip install openai

Step 5: Make API Requests

Use the following Python script to test DeepSeek Prover V2. Replace YOUR_API_KEY_HERE with your OpenRouter API 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)

This script sends a prompt to Prover V2 and prints the response. You can adjust parameters like temperature (for response creativity) or max_tokens (for response length) as needed.

Step 6: Monitor Usage

The free tier has usage limits, so monitor your token consumption. OpenRouter ensures reliability by routing requests to providers like “Together” for low latency. If you need more capacity, explore paid tiers or other DeepSeek models on OpenRouter.

Tips for Success

• Detailed Prompts: Prover V2 is a base model optimized for testing, requiring precise and detailed prompts for optimal results.
• Error Handling: Implement retry mechanisms, as the model may occasionally return empty responses.
• Security: Never share your API key publicly to prevent unauthorized access.

Testing DeepSeek Prover V2 with Prompts

To evaluate DeepSeek Prover V2’s capabilities, I’ve designed three test prompts that target its strengths in formal mathematical reasoning and theorem proving. These prompts range from basic to advanced, reflecting common use cases in mathematical research. Each prompt is crafted to assess the model’s ability to generate accurate, formal proofs, ideally in a format compatible with Lean 4, given its specialization.

Let's Begin with an Easy Prompt

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 Responses:

### Lean 4 Proof

```lean
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 of the Key Step

The key step in this proof is the use of the `cases` tactic to decompose the hypothesis `hx : x ∈ A ∩ B` into its two components, `hx₁ : x ∈ A` and `hx₂ : x ∈ B`, allowing us to directly use `hx₁` to conclude that `x ∈ A`. 

### One-Sentence Explanation

The intersection `A ∩ B` is a subset of `A` because by definition, any element in `A ∩ B` is also in `A`.

Out of curiosity, I asked OpenAI o3 model to make a comment on the response, and it is very interesting:

Your idea is right—​“from `x ∈ A ∩ B` extract the first conjunct”—but the statement and proof need a few fixes.

1  Type & variable header  
• `A` and `B` should be sets, not types, so write  
  `{α : Type*} (A B : Set α)`  
• The extra argument `a : A` is unrelated and should be removed.

2  Minimal idiomatic proof  
Because `hx : x ∈ A ∩ B` is literally `⟨hx₁, hx₂⟩`, you can grab the left component with `.1` (or `.left`) instead of destructuring with `cases`.  
```lean
open Set

theorem inter_subset_left {α} (A B : Set α) : A ∩ B ⊆ A := by
  intro x hx
  exact hx.1          -- or `exact hx.left`
```
Lean’s standard library already contains this lemma as `inter_subset_left`, so one line suffices:
```lean
exact Set.inter_subset_left
```

3  Unnecessary tactics  
The trailing `;<;> simp_all` doesn’t do anything here—`exact hx₁` already closes the goal.

In short, drop the extra parameter, use `Set` rather than `Type`, and shrink the body to `exact hx.1` (or just reuse the builtin lemma) for a clean, conventional proof.

I feed OpenAI o3's response to Deepseek-Prover-V3, and it says:

### Revised Lean 4 Proof

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

### One-Sentence Explanation

The key step is that `hx : x ∈ A ∩ B` is a pair `⟨hx₁, hx₂⟩` where `hx₁ : x ∈ A` and `hx₂ : x ∈ B`, so `hx.1` directly gives `x ∈ A`, proving `A ∩ B ⊆ A`.

### Additional Notes

1. The proof correctly uses `Set α` instead of `Type` to represent sets.
2. The `{α : Type*}` syntax allows the theorem to be generic over any type `α`.
3. The unnecessary parameter `a : A` and trailing tactics have been removed.
4. The `open Set` command is omitted because we use the full name `Set α`.
5. The proof leverages the fact that `hx.1` directly extracts the first component of `hx`, which is `x ∈ A`.

And o3's response to this prompt says:

Your revision is spot-on.

• Correctness and conciseness `hx.1` (alias `hx.left`) is the canonical Lean idiom for “take the first component of the conjunct,” so the proof is both valid and as short as it can be—exactly what readers should emulate.

• Generality Using `{α : Type*}` keeps the lemma polymorphic, and `Set α` is the right abstraction. Good call on deleting the stray parameter and tactics.

• Style nuance If you want to emphasise code reuse you could simply write `exact Set.inter_subset_left`—Lean already has this lemma—but showing the one-line proof is pedagogically helpful, especially for beginners learning how to unpack conjunctions.

All in all, the proof, explanation, and bullet-point commentary are clean and instructive; they would read well in your article without further edits.

It is really interesting to watch the back and forth of the 2 models and correcting each other.

Conclusion

DeepSeek Prover V2 is a groundbreaking tool for formal mathematical theorem proving, leveraging a 671B-parameter MoE architecture to automate complex proofs in Lean 4. Accessible for free via OpenRouter’s API, it offers researchers and enthusiasts a powerful platform to explore AI-driven mathematics. The test prompts provided—covering basic, intermediate, and advanced theorems—demonstrate its potential to handle diverse mathematical challenges. As AI continues to reshape academic research, Prover V2 stands out as a specialized, open-source solution driving innovation in formal mathematics.