雙語暢銷書《艾倫圖靈傳》第4章:彼岸新星(87)
It was in the spring of 1939 that he gave his first Cambridge lecture course.
He started with fourteen Part III students, but 'no doubt the attendance will drop off as the term advances,' he wrote home.
他的班上有14名第三階段的學生，但他給家裏寫信說，到課的人數肯定會越來越少。He must have kept at least one, for he had to set questions on his course for the examination in June.
但他至少要留住一個學生，這樣他才能爲6月的課程考試出題。
One of these asked for a proof of the result of Computable Numbers.
其中的一道題，就是關於可計算數的證明。It must have been very pleasing to be able to set as an examination problem in 1939, the question that Newman had posed as unanswered only four years before.
能把這個問題作爲試題，是很令人愉快的，僅僅在四年前，紐曼還認爲這個問題是無法解決的呢。But at the same time, Alan joined Wittgenstein's class on Foundations of Mathematics.
與此同時，艾倫還參加了維特根斯坦的數學基礎課程。Although this had the same title as Alan's course, it was altogether different.
雖然這與艾倫的課程名稱相同，但它們的內容完全不一樣。The Turing course was one on the chess game of mathematical logic; extracting the neatest and tightest set of axioms from which to begin,
圖靈的課，是一場數學邏輯的遊戲，由最初的公理，推導出整潔而嚴密的定理，making them flower according to the exact system of rules into the structures of mathematics, and discovering the technical limitations of that procedure.
按照精密的規則系統，發展出數學體系，並發現這個過程中的侷限性。But Wittgenstein's course was on the philosophy of mathematics; what mathematics really was.
而維特根斯坦講的是數學哲學，他的問題是，數學到底是什麼東西。
