雙語暢銷書《艾倫圖靈傳》第4章:彼岸新星(61)
Its falsity would mean that the zeta-function did take the value zero at some point which was off the special line, in which case this point could be located by brute force, just by calculating enough values of the zeta-function.
This programme had already been started; indeed Riemann himself had located the first few zeroes and checked that they all lay on the special line.
這個計劃已經啓動了，黎曼親自計算了最初的一些零點，並認定它們確實都排在一條線上。In 1935-6, the Oxford mathematician E.C. Titchmarsh had used the punched-card equipment which was then used for the calculation of astronomical predictions to show that (in a certain precise sense) the first 104 zeroes of the zeta-function did all lie on the line.
1935年至1936年，牛津大學的數學家E.C.蒂施馬奇用天文預測中使用的打孔卡片設備，證明了ζ 函數的前104個零點都在一條線上。
Alan's idea was essentially to examine the next few thousand or so in the hope of finding one off the line.
艾倫的想法是，要檢驗接下來的幾千個零點，希望能找到一個不在線上的。There were two aspects to the problem.
這裏面存在兩個問題。Riemann's zeta-function was defined as the sum of an infinite number of terms, and although this sum could be re-expressed in many different ways, any attempt to evaluate it would in some way involve making an approximation.
首先，黎曼的ζ 函數的定義，是一個無限項的和式，儘管可以表示成一些其它的形式，但這些變形都要涉及到估算的問題。It was for the mathematician to find a good approximation, and to prove that it was good: that the error involved was sufficiently small.
對數學家來說，需要找到一個好的估算方法，並證明它是好的，也就是誤差足夠小。Such work did not involve computation with numbers, but required highly technical work with the calculus of complex numbers.
這個工作並不涉及算術，而是涉及到與複變函數有關的技術。Titchmarsh had employed a certain approximation which, rather romantically, had been exhumed from Riemann's own papers at Gttingen where it had lain for seventy years.
蒂施馬奇使用的估算方法，是從黎曼70年前在哥廷根的論文中挖掘出來的。But for extending the calculation to thousands of new zeroes a fresh approximation was required; and this Alan set out to find and to justify.
但是，要想計算幾千個新的零點，就需要新的估算方法。艾倫現在就要動身去尋找並證明。
