雙語暢銷書《艾倫圖靈傳》第8章:水銀延時線(5)
It was not that they were good at doing large sums, although indeed they were doing sums on desk calculators.
Their problems were roughly analogous to those that faced Alan in calculating the Riemann zeta-function in 1938.
他們遇到的問題，大體上類似於圖靈在1938年計算ζ函數時遇到的問題。When the resources of pure mathematics had been fully exploited, there might still remain a formula, or system of equations, into which actual numbers had to be substituted.
即使充分利用了純數學，但數論問題最終仍然有可能需要代入某些方程系統。
Actually doing such substitutions on desk calculators was not very interesting;
用臺式計算器來處理這種代入，是十分尷尬的。but the problem of how best to organise the work was a more abstract question, one constituting the branch of mathematics called 'numerical analysis'.
這是一個更爲抽象的問題，並形成了一個稱爲"解析數論"的數學分支注。One particular problem was that although equations and formulae would generally relate 'real numbers' of infinite precision,
有一個特別存在的問題是，方程系統是基於無窮精度的實數，practical computation would work with quantities defined only to so many decimal places, thus introducing an error into every step.
但實際的計算精度不得不是有限的，因此每一個計算步驟都會引起誤差，Deducing the effect of such errors and minimising them was an important aspect of numerical analysis.
如何評估並減小這種誤差，是解析數論的一個重要問題。The existence of such problems was partly what made Alan say that automatic computers would not make mathematicians redundant.
正是由於這個問題的存在，使得圖靈認爲，即使有了自動化的計算機器，數學家也不可能下崗。
