How Math Proofs Change: From People to AI
數學證明如何改變：從人類到 AI
Introduction
This report talks about how people prove things in math. It looks at old ways and new ways with computers.
本報告探討人們在數學中如何進行證明。它分析了傳統的方法以及利用電腦的新方法。
Main Body
Long ago, mathematicians showed exactly how to find an answer. Later, David Hilbert used a new way. He proved things were true without showing the answer. Some people liked this, but L.E.J. Brouwer did not. They had a big fight about these rules.
很久以前，數學家會詳細地展示如何找到答案。後來，David Hilbert 使用了一種新方法。他證明事物是正確的，而無需展示答案。有些人喜歡這樣，但 L.E.J. Brouwer 並不認同。他們針對這些規則發生了激烈的爭論。
Now, people use computers to check math. Kevin Buzzard uses a computer language called Lean. He wants to put a famous math proof into a computer. This helps people check if the math is correct.
現在，人們使用電腦來檢查數學。Kevin Buzzard 使用一種名為 Lean 的電腦語言。他希望將一個著名的數學證明輸入電腦，這有助於人們檢查數學是否正確。
Today, AI helps write this computer code. AI works very fast. It can write a lot of code in one day. But some people say AI code is messy. Human code is often better and cleaner.
如今，AI 協助編寫這種電腦程式碼。AI 的運作速度非常快，一天之內可以編寫大量程式碼。但有些人認為 AI 的程式碼很凌亂，人類編寫的程式碼通常較佳且更簡潔。
Conclusion
Math is changing. In the future, AI might find answers that are correct, but humans cannot understand them.
數學正在改變。未來，AI 可能會找到正確的答案，但人類可能無法理解。
Vocabulary Learning
💡 The Power of 'But'
In the text, the writer uses the word 'but' to show two different ideas. This is a key skill for A2 English.
How it works: Idea A but Idea B (The Opposite)
Examples from the story:
- Some people liked this but Brouwer did not.
- AI is fast but the code is messy.
🛠️ Action Words: Past vs. Present
Notice how the text changes time. This helps us talk about history and now.
| Then (Past) | Now (Present) |
|---|---|
| showed | use |
| used | works |
| liked | helps |
Tip: To talk about the past, we often add -ed to the word (like use used).