段尾是句柏拉图对数学在哲学的地位。如果不懂几何，就不要进入他的学园（类似现在的大学）学习了。
To Plato, as to Bertrand Russell, mathematics is therefore the indispensable prelude to philosophy, and its highest form; over the doors of his Academy Plato placed, Dantesquely, these words, "Let no man ignorant of geometry enter here."16
16 The details of the argument for the interpretation here given of the doctrine of Ideas may be followed in D.G. Ritchie's Plato, Edinburgh, 1902, especially pp.49 and 85.
对柏拉图而言，正如对伯特兰·罗素一样，数学因此是哲学的不可或缺的前提，也是哲学的最高形式；柏拉图曾以但丁式的庄严风格，在其学园（Academy）的大门上刻着这样一句话：不懂几何者，不得入内。16
16关于此处对”理念论“所作解读的论证细节，可参见D.G.里奇所著的《柏拉图》一书（爱丁堡，1902年版），尤其可参考第49页与第85页的内容。
细节解析
1、indispensable：extremely important and necessary 不可或缺的
The pandemic may have caused managers to realize who is indispensable and who isn't. 疫情也许让管理者意识到谁是必不可少的，谁是可有可无的。《经济学人（汇总）》
2、prelude：something that comes before and leads to something else — usual singular 前奏；开端
Abstraction was a necessary prelude to clarity.抽象是清晰的必要序曲。
3、Dantesquely：它是英语派生副词，遵循“从专有名词（人名）到形容词再到副词”的派生路径。
“Dante”指的就大名鼎鼎的但丁，中世纪意大利最伟大的诗人，代表作《神曲》（Divina Commedia)。这本书是西方文学与思想史的里程碑，其作品风格主要是“庄严、肃穆、带有象征意义与终极追问色彩”，它也成了“但丁专属”的风格属性。
专用名词变形容词：“-esque”。它源自法语（最终拉丁语-iscus”，在英语中属于属性类形容词后缀，核心含义是“具有……风格的、类似……特征的”，且通常用于“与特定人物（尤其是艺术家、作家）或事物相关的风格描述。如“Homeric”->“Homeresuque”荷马史诗风格的。
整段总结
开头就讲了“理念论”的难懂，“理念论”的内核就是概念，法则以及理想。毕达格拉斯说它是“数”，柏拉图将毕的“数”概念隐化更富于想象力，更富诗意，因而变得晦涩，但仍肯定几何神一样的存在。后来的斯宾塞的“实在”，也表达了柏拉图类似的想法。
所在段落
The Story of Philosophy《哲学的故事》第1章Plato第7节VI. The Psychological Solution第14段第11句：
But this famous doctrine of Ideas, embellished and obscured by the fancy and poetry of Plato, is a discouraging maze to the modern student, and must have offered another severe test to the survivors of many siftings. The Idea of thing might be the "general idea" of the class to which it belongs (the Idea of John, or Dick, or Harry, is Man); or it might be the law or laws according to which the thing operates (the Idea of John would be the reduction of all his behavior to "natural laws"); or it might be the perfect purpose and ideal towards which the thing and its class may develop (the Idea of John is the John of Utopia). Very probably the Idea is all of these — idea, law and ideal. Behind the surface phenomena and particulars which greet our senses, are generalizations, regularities, and directions of development, unperceived by sensation but conceived by reason and thought. These ideas, laws and ideals are more permanent — and therefore more "real" — than the sense-perceived particular things through which we conceive and deduce them: Man is more permanent than Tom, or Dick, or Harry; this circle is born with the movement of my pencil and dies under the attrition of my eraser, but the conception Circle goes on forever. This tree stands, and that tree falls; but the laws which determine what bodies shall fall, and when, and how, were without beginning, are now, and ever shall be, without end. There is, as the gentle Spinoza would say, a world of things perceived by sense, and a world of laws inferred by thought; we do not see the law of inverse squares but it is there, and everywhere; it was before anything began, and will survive when all the world of things is a finished tale. Here is a bridge: the sense perceives concrete and iron to a hundred million tons; but the mathematician sees, with the mind's eye, the daring and delicate adjustment of all this mass of material to the laws of mechanics and mathematics and engineering, those laws according to which all good bridges that are made must be made; if the mathematician be also a poet, he will see these laws upholding the bridge; if the laws were violated the bridge would collapse into the stream beneath; the laws are the God that holds up the bridge in the hollow of his hand. Aristotle hints something of this when he says that by Ideas Plato meant what Pythagoras meant by "number" when he taught that this is a world of numbers (meaning presumably that the world is ruled by mathematical constancies and regularities). Plutarch tells us that according to Plato "God always geometrizes"; or, as Spinoza puts the same thought, God and the universal laws of structure and operation are one and the same reality. To Plato, as to Bertrand Russell, mathematics is therefore the indispensable prelude to philosophy, and its highest form; over the doors of his Academy Plato placed, Dantesquely, these words, "Let no man ignorant of geometry enter here."16
16The details of the argument for the interpretation here given of the doctrine of Ideas may be followed in D.G. Ritchie's Plato, Edinburgh, 1902, especially pp.49 and 85.
浙江大学译本： 对柏拉图和罗素而言，数学是哲学的前提，是哲学的最高形式；在柏拉图的学院大门前，他写下这样一句有但丁风格的话：“不懂几何之人不得入内。”
上句见：Day420
