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mathematics

Polymath

Polymath 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 Polymath rather than just read about it. In short: A polymath or polyhistor is an individual whose knowledge spans many different subjects, known to draw on complex bodies of knowledge to solve specific problems. Polymaths often prefer a specific context in which to explain their knowledge, but some are gifted at explaining abstractly and creatively.

Polymath — main illustration
Polymath — illustration

Key takeaways

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

Reference excerpt

A polymath or polyhistor is an individual whose knowledge spans many different subjects, known to draw on complex bodies of knowledge to solve specific problems. Polymaths often prefer a specific context in which to explain their knowledge, but some are gifted at explaining abstractly and creatively. Embodying a basic tenet of Renaissance humanism that humans are limitless in their capacity for development, the concept led to the notion that people should embrace all knowledge and develop their capacities as fully as possible. This is expressed in the term Renaissance man, often applied to the gifted people of that age who sought to develop their abilities in all areas of accomplishment: intellectually, artistically, socially, physically, and spiritually.

Etymology The word polymath derives from the Greek roots poly-, which means "many", "several" or "much", and manthanein, which means "to learn." Plutarch wrote that the Ancient Greek muse Polyhymnia was sometimes known as Polymatheia, describing her as responsible for "that faculty of the soul which inclines to attain and keep knowledge." In Western Europe, the first work to use the term polymathy in its title, De Polymathia tractatio: integri operis de studiis veterum ("A Treatise on Polymathy: The Complete Work on the Studies of the Ancients"), was published in 1603 by Johann von Wowern, a Hamburg philosopher. Von Wowern defined polymathy as "knowledge of various matters, drawn from all kinds of studies … ranging freely through all the fields of the disciplines, as far as the human mind, with unwearied industry, is able to pursue them". Von Wowern lists erudition, literature, philology, philomathy, and polyhistory as synonyms. The earliest recorded use of the term in the English language is from 1624, in the second edition of The Anatomy of Melancholy by Robert Burton; the form polymathist is slightly older, first appearing in the Diatribae upon the first part of the late History of Tithes of Richard Montagu in 1621. Use in English of the similar term polyhistor dates from the late 16th century.

Renaissance man

The term "Renaissance man" was first recorded in written English in the early 20th century. The term is used to describe a man as a dynamic being that creates and recreates himself during his life. The concept arose with the rise of capitalism. It is used to refer to great polymaths like those of the Renaissance. Leonardo da Vinci has often been described as the archetype of the Renaissance man, a man of "unquenchable curiosity" and "feverishly inventive imagination". Many notable polymaths lived during the Renaissance period, a cultural movement that spanned roughly the 14th through to the 17th century that began in Italy in the Late Middle Ages and later spread to the rest of Europe. These polymaths had a rounded approach to education that reflected the ideals of the humanists of the time. A gentleman or courtier of that era was expected to speak several languages, play a musical instrument, write poetry, and so on; thus fulfilling the Renaissance ideal. The idea of a universal education was essential to achieving polymath ability, hence the word university was used to describe a seat of learning. However, the original Latin word universitas refers in general to "a number of persons associated into one body, a society, company, community, guild, corporation, etc". At this time, universities did not specialize in specific areas, but rather trained students in a broad array of science, philosophy, and theology. This universal education gave them a grounding from which they could continue into apprenticeship toward becoming a master of a specific field. When someone is called a "Renaissance man" today, it is meant that rather than simply having broad interests or superficial knowledge in several fields, the individual possesses a more profound knowledge and a proficiency, or even an expertise, in at least some of those fields. Some dictionaries use the term "Renaissance man" to describe someone with many interests or talents, while others give a meaning restricted to the Renaissance and more closely related to Renaissance ideals.

In academia

… excerpt ends here. Continue reading the full article.

Illustrations

Polymath: Portrait of Benjamin Franklin by David Martin, 1767. Benjamin Franklin is one of the foremost polymaths in US history. Franklin was a writer, scientist, inventor, statesman, diplomat, printer and political philosopher. He further attained a legacy as one of the Founding Fathers of the United States.
Portrait of Benjamin Franklin by David Martin, 1767. Benjamin Franklin is one of the foremost polymaths in US history. Franklin was a writer, scientist, inventor, statesman, diplomat, printer and political philosopher. He further attained a legacy as one of the Founding Fathers of the United States.
Polymath: Portrait of Sir Christopher Wren by Godfrey Kneller, 1711. Best known as an architect, Christopher Wren was also an astronomer, mathematician and physicist.
Portrait of Sir Christopher Wren by Godfrey Kneller, 1711. Best known as an architect, Christopher Wren was also an astronomer, mathematician and physicist.

Worked examples

Example 1 — a first encounter with Polymath

Start with the simplest possible case. Write down what Polymath 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 Polymath 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 Polymath 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 Polymath

In research
Polymath 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 Polymath 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
Polymath is common in secondary-school and first-year university syllabi. It links to neighbouring topics Age of Enlightenment, Giftedness, Renaissance, so understanding it makes those chapters shorter.
In everyday life
Look for Polymath 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 Polymath in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Polymath 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 Polymath out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Polymath in simple terms?

A polymath or polyhistor is an individual whose knowledge spans many different subjects, known to draw on complex bodies of knowledge to solve specific problems. Polymaths often prefer a specific context in which to explain their knowledge, but some are gifted at explaining abstractly and creativel…

Why does Polymath 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 Polymath?

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 Polymath.

Tags

  • Age of Enlightenment
  • Giftedness
  • Renaissance

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