Correct result: \sqrt(3)/3. To test the geometry question on Qwen app and the thinking mode you can get the result: Thinking mode: correct answer \sqrt(3)/3. Without thinking mode: wrong answer. Overall, the 235B model is quite powerful compared to previous SOTA model. More about the key updates in Qwen3: Hybrid reasoning model, expanded language support (100+ languages), enhanced tool calling capabilities with Qwen-Agent supporting MCP. The newly open-sourced Qwen3 is China's first "hybrid reasoning model", a concept initially proposed by Claude3.7 and recently adopted by Gemini2.5 Flash. Essentially, this allows the model to toggle reasoning processes on/off. The primary purpose is to accelerate response generation for simple queries or time-sensitive scenarios by optionally disabling the thinking process while maintaining output quality. Previous approaches struggled to directly suppress reasoning steps in LLMs without retraining, as prompt engineering offered limited control. Qwen3 introduces two control methods: 1) A hard switch via enable_thinking parameter (True/False), and 2) When enabled, secondary soft switching through appending /no_think or /think tokens. Qwen also provides recommended parameter configurations to ensure optimal performance: Think mode: Temperature=0.6, TopP=0.95, TopK=20, MinP=0 Non-think mode: Temperature=0.7, TopP=0.8, TopK=20, MinP=0 Additionally, Qwen3 features specialized training for tool invocation, with Qwen-Agent now supporting MCP.

Qwen 2.5 models have already been widely adopted on many industrial applications. And Qwen 3 release will be even more exciting and I think it will set new standard of LLM and even the large reasoning models.

Truthfully, I am a little bit surprised by the math proof ability and reasoning ability of ChatGPT. To solve the topological math problem, ChatGPT firstly gives a outline of the proof and provides more details to support the proof. The detailed response is as follows: To prove that the sum of two compact sets in a topological vector space X, X is compact, we need to show that if A and B are compact subsets of X, then A+B is also compact. Proof: 1. Recall Definitions and Properties 2. Consider the Projection Maps 3. Use the Compactness of A and B 4. Image of a Compact Set Under a Continuous Map 5. Conclusion: Thus, we have shown that if A and B are compact subsets of a topological vector space X, then A+B is also compact.