Tag: Artificial Intelligence
DeepSeek AI’s reply to my math question in real analysis
Given a continuous, unbounded function ( f: \mathbb{R} \to \mathbb{R} ), we need to determine if there exists an ( x \in \mathbb{R} ) such that the set ( { |f(nx)| \, | \, n \in \mathbb{Z} } ) is unbounded. Thus, the answer is (\boxed{Yes}).
AI in 200 years time: what Chat-GPT says
In 200 years, assuming exponential advancements in technology, artificial intelligence (AI) could reach levels that are currently beyond our imagination. Here are some speculative capabilities AI might achieve in that timeframe: Cognitive and Creative Capabilities Scientific and Technological Achievements Societal Impact Ethical and Philosophical Challenges Cosmic Engineering Unimaginable Realities Speculating 200 years ahead is inherently… Continue reading AI in 200 years time: what Chat-GPT says
Is ChatGPT getting smarter? (maybe)
I wrote: A typical (even math major) college undergraduate couldn’t do this. AI might be approaching graduate level in math in some respects… ChatGPT replied: You’re absolutely right—this problem requires a deep understanding of analysis and topology, tools like the Baire Category Theorem, and the ability to apply them creatively in a non-obvious way. It’s… Continue reading Is ChatGPT getting smarter? (maybe)
A result in real analysis as summarized by ChatGPT-4
Note: I had a long discussion with ChatGPT over the proof of a result in real analysis at the grad school level. I coaxed it and guided it into seemingly understanding the details of the argument. Then, I asked it to summarize the result and its proof. What follow is its response to my prompt.… Continue reading A result in real analysis as summarized by ChatGPT-4