對數學的靈光一閃

沒有靈光一閃這東西

誰說沒有
當你算數學算到不出來時
有一件東西吸引著你
就馬上算出來了
這不就叫做靈光一閃嗎

假如是這樣...那就是看到其他類似的題目吧!

幾年前，我曾經思考一道幾何證明題，
寫了又寫，總覺得不甚滿意，晚上睡覺時做了一個夢，夢中得到靈感。趕快起來寫，很簡潔的證明完畢。自己很滿意。

雖然只是一道小題目，事後覺得非常快樂！這樣的經驗真是美好。

腦子自己在變化

這是解決費馬定理的懷爾斯教授的親身經歷.....

懷爾斯在此期間中斷了他的工作，以處理審稿人在電子郵件中提出的問題，他自信這些問題不會給他造成很大的麻煩。尼克•凱茲負責審查第3章，1993年8月23日，他發現了證明中的一個小缺陷。數學的絕對主義要求懷爾斯無可懷疑地證明他的方法中的每一步都行得通。懷爾斯以爲這又是一個小問題，補救的辦法可能就在近旁，可是6個多月過去了，錯誤仍未改正，懷爾斯面臨絕境，他準備承認失敗。他向同事彼得•薩克說明自己的情況，薩克向他暗示困難的一部分在於他缺少一個能夠和他討論問題並且可信賴的人。經過長時間的考慮後，懷爾斯決定邀請康橋大學的講師理查德•泰勒到普林斯頓和他一起工作。
　　泰勒1994年1月份到普林斯頓，可是到了9月，依然沒有結果，他們準備放棄了。泰勒鼓勵他們再堅持一個月。懷爾斯決定在9月底作最後一次檢查。9月19日，一個星期一的早晨，懷爾斯發現了問題的答案，他敍述了這一時刻：“突然間，不可思議地，我有了一個難以置信的發現。這是我的事業中最重要的時刻，我不會再有這樣的經歷……它的美是如此地難以形容；它又是如此簡單和優美。20多分鐘的時間我呆望它不敢相信。然後白天我到系裏轉了一圈，又回到桌子旁看看它是否還在——它還在那裏。”


未曾感受到靈光乍現的人，尚未進入數學的世界。
孫文先敬上

Nov 22 2005
Famous 40-Year-Old Math Problem Solved by MU Professor
Prestigious Speaking Invitation in Spain Follows Accomplishment


COLUMBIA, Mo. - For some, spending more than three years working to solve a more than 40-year-old math problem sounds like a nightmare. For University of Missouri-Columbia mathematics professor Steve Hofmann, solving a problem posed by one of the most famous mathematicians in the second half of the 20th Century has been a dream since his college days. The major mathematical accomplishment is earning him significant recognition. Hofmann has a speaking invitation at this summer's meeting of the International Congress of Mathematicians in Madrid, Spain, which takes place only once every four years.

"It's a problem that has interested me since I was a graduate student," Hofmann said. "It was one of the biggest open problems in my field and everybody thought it was too hard and wouldn't be solved. I had toyed with it for years and then put in three years of very serious work before hitting the key breakthrough."

The problem goes back to two papers written by Tosio Kato, University of California-Berkley, in 1953 and 1961. It turned out to be quite difficult and became known as the "Kato Conjecture" in mathematical circles. The one dimensional version of the problem was solved 20 years later.

"I think I was the last person working on it," Hofmann joked. "I think everyone else had given up."

Hofmann admits explaining the problem is difficult because it is rather technical. Its solution applies to the theory of waves propagating through different media, such as a seismic wave traveling through different types of rock. Hofmann said the solution allows mathematicians to better describe the behavior of waves traveling through a medium which itself changes over time.

"To work on a problem for three years and finally crack it open feels fantastic!" Hofmann said. "It's the reason mathematicians work on problems - for moments like that."

Hofmann's work is funded by the National Science Foundation. The solution to the "Kato problem" is detailed in a series of papers published with his research collaborators Pascal Auscher, Michael Lacey, John Lewis, Alan McIntosh and Philippe Tchamitchian.

我也是有過這樣得經驗
雖然只是小題目
但心中仍充滿得意之感
睡覺真是一個好方法阿~!!!


所謂:"日也所思，夜有所夢。"