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Hippias

Hippias is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Hippias rather than just read about it. In short: Hippias of Elis (; Greek: Ἱππίας ὁ Ἠλεῖος; late 5th century BC) was a Greek sophist, and a contemporary of Socrates. With an assurance characteristic of the later sophists, he claimed to be regarded as an authority on all subjects, and lectured on poetry, grammar, history, politics, mathematics, and much else.

Key takeaways

  • Hippias belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Hippias to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Hippias from memory before moving on to harder problems.

Reference excerpt

Hippias of Elis (; Greek: Ἱππίας ὁ Ἠλεῖος; late 5th century BC) was a Greek sophist, and a contemporary of Socrates. With an assurance characteristic of the later sophists, he claimed to be regarded as an authority on all subjects, and lectured on poetry, grammar, history, politics, mathematics, and much else. Most current knowledge of him is derived from Plato, who characterizes him as vain and arrogant.

Life Hippias was born at Elis in the mid 5th-century BC (c. 460 BC) and was thus a younger contemporary of Protagoras and Socrates. He lived at least as late as Socrates (399 BC). He was a disciple of Hegesidamus. Owing to his talent and skill, his fellow-citizens availed themselves of his services in political matters, and in a diplomatic mission to Sparta. But he was in every respect like the other sophists of the time: he travelled about in various towns and districts of Greece for the purpose of teaching and public speaking. The two dialogues of Plato, the Hippias major and the Hippias minor characterize him as vain and arrogant. The Hippias major (the authorship of this work by Plato is sometimes doubted) concerns the question about the beautiful, and purposely puts the knowledge and presumption of Hippias in a ludicrous light. The Hippias minor discusses the deficiency of human knowledge, and characterizes Hippias as ridiculously vain.

Work Hippias was a man of very extensive knowledge, and he occupied himself not only with rhetorical, philosophical, and political studies, but was also well versed in poetry, music, mathematics, painting and sculpture, and he claimed some practical skill in the ordinary arts of life, for he used to boast of wearing on his body nothing that he had not made himself with his own hands, such as his seal-ring, his cloak, and shoes. He was credited with a lost work known as the Olympionikō̂n Anagraphḗ (Ὀλυμπιονικῶν Ἀναγραφή) which computed Coroebus's victory as occurring in 776 BC and became the basis of all later lists of the Olympiads and their victors. On the other hand, his knowledge always appears superficial, he does not enter into the details of any particular art or science, and is satisfied with certain generalities, which enabled him to speak on everything without a thorough knowledge of any. This arrogance, combined with ignorance, is the main cause which provoked Plato to his severe criticism of Hippias, as the sophist enjoyed a very extensive reputation, and thus had a large influence upon the education of the youths of the higher classes. Plutarch also criticized Hippias in The Life of Numa in Parallel Lives when writing about the chronology of Numa's relationship with Pythagoras, mentioning that the chronology was based on the Olympionikō̂n Anagraphḗ and stating that Hippias had no authoritative basis on his work. A mathematical discovery ascribed to Hippias is sometimes called the quadratrix of Hippias. His great skill seems to have consisted in delivering grand show speeches; and Plato has him arrogantly declaring that he would travel to Olympia, and there deliver before the assembled Greeks an oration on any subject that might be proposed to him; and Philostratus in fact speaks of several such orations delivered at Olympia, and which created great sensation. If such speeches were published by Hippias, then no specimen has come down to us. Plato claims he wrote epic poetry, tragedies, dithyrambs, and various orations, as well as works on grammar, music, rhythm, harmony, and a variety of other subjects. He seems to have been especially fond of choosing antiquarian and mythical subjects for his show speeches. Athenaeus mentions a work of Hippias under the title Synagoge which is otherwise unknown. An epigram of his is preserved in Pausanias.

Natural law Hippias is credited with originating the idea of natural law. This ideal began at first during the 5th century BC. According to Hippias, natural law was never to be superseded as it was universal. Hippias saw natural law as a habitual entity that humans take part in without pre-meditation. He regarded the elite in states as indistinguishable from one another and thus they should perceive each other as so. Because of this, he reasons, they should consider and treat each other as a society of a unanimous state. These ideas were passed on through Cynicism and Stoicism, later being the foundation for turning Roman law in legislation. Along with natural law, Hippias also wrote about self-sufficiency as a binding principle. He used this principle in his teachings as he gathered knowledge in numerous subjects, so as to be never outwitted or have his reputation questioned.

See also Cynicism (philosophy) Natural Law Quadratrix of Hippias Roman Law Self-sufficiency Stoicism

Notes

References This article incorporates text from a publication now in the public domain: Smith, William, ed. (1870). "Hippias". Dictionary of Greek and Roman Biography and Mythology. p. 479. This article incorporates text from a publication now in the public domain: Chisholm, Hugh, ed. (1911). "Hippias of Elis". Encyclopædia Britannica. Vol. 13 (11th ed.). Cambridge University Press. p. 517.

External links O'Connor, John J.; Robertson, Edmund F., "Hippias", MacTutor History of Mathematics Archive, University of St Andrews Hippias' Attempt to Trisect an Angle at Convergence

Worked examples

Example 1 — a first encounter with Hippias

Start with the simplest possible case. Write down what Hippias claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Hippias before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Hippias ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Hippias

In research
Hippias appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Hippias in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Hippias is common in secondary-school and first-year university syllabi. It links to neighbouring topics 4th-century BC deaths, 5th-century BC Greek mathematicians, 5th-century BC Greek philosophers, so understanding it makes those chapters shorter.
In everyday life
Look for Hippias outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Hippias in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Hippias means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Hippias out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hippias in simple terms?

Hippias of Elis (; Greek: Ἱππίας ὁ Ἠλεῖος; late 5th century BC) was a Greek sophist, and a contemporary of Socrates. With an assurance characteristic of the later sophists, he claimed to be regarded as an authority on all subjects, and lectured on poetry, grammar, history, politics, mathematics, an…

Why does Hippias matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Hippias?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Hippias.

Tags

  • 4th-century BC deaths
  • 5th-century BC Greek mathematicians
  • 5th-century BC Greek philosophers
  • 5th-century BC births
  • Ancient Eleans
  • Ancient Greek geometers
  • Sophists

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