/təˈpɒlədʒi/
[noun] The branch of mathematics that studies the properties of shapes and spaces that stay the same even when they are stretched, bent, or twisted, but not torn or cut. More generally, it can refer to the way parts of something are arranged and connected to each other.
A coffee mug and a doughnut are literally the same shape — topology proved it, and mathematicians never looked at breakfast the same way again.
The word 'topology' was built from two ancient Greek roots that were combined in the 19th century to name a brand-new field of mathematics. The first part comes from the Greek word 'topos' (τόπος), meaning 'place' or 'location'. The second part comes from 'logos' (λόγος), meaning 'word', 'reason', or 'study of'. Together they form 'topology' — literally 'the study of place'. The word was coined in its modern mathematical sense by the German mathematician Johann Benedict Listing, who used the Latin equivalent 'Topologie' in a letter in 1836 and later published a foundational paper called 'Vorstudien zur Topologie' in 1847.
The Greek root 'topos' had a rich life long before mathematics borrowed it. In ancient Greek, it referred simply to a physical place or position, but it also carried a more abstract meaning in rhetoric and philosophy. Greek orators used 'topos' — often translated as 'commonplace' — to describe a standard argument or theme that could be applied across many different speeches. This rhetorical meaning passed into Latin as 'locus' (its direct Latin translation), giving rise to 'locus communis', and then into English as 'commonplace'. Meanwhile, 'topos' itself travelled directly into English through academic language, giving us the literary and philosophical term 'topos' still used today to mean a recurring theme or motif.
The '-logy' suffix, derived from Greek 'logos' via the combining form '-logia', has been one of the most productive building blocks in the history of English scientific vocabulary. Ancient Greek 'logos' → Latin '-logia' → Old French '-logie' → English '-logy'. This chain gave English dozens of words: 'biology', 'geology', 'psychology', 'sociology', and many more, all following the same pattern of 'subject + logy = the study of that subject'. By the 19th century, European scientists — especially German and British scholars — were freely coining new '-logy' words as entire new fields of enquiry opened up.
Topology as a formal discipline grew slowly through the 19th century and exploded in the early 20th century. Leonhard Euler's famous 1736 solution to the Königsberg Bridge Problem is now considered a founding moment of topological thinking, though Euler did not use the word. The core insight of topology is that it asks not 'how big is this shape?' or 'what angle does this have?' but rather 'how is this shape connected?' A square and a circle are topologically identical because you can reshape one into the other without cutting. But a sphere and a doughnut are topologically different, because you cannot transform one into the other without tearing a hole — which topology strictly forbids.
The word entered broader English usage in the early 20th century as the mathematics of topology was formalised by figures such as Henri Poincaré and later Felix Hausdorff, whose 1914 book 'Grundzüge der Mengenlehre' laid out many foundational concepts. By the mid-20th century, 'topology' had begun to escape the mathematics classroom and enter the language of computer networking, where it describes the layout of a network — how devices are connected to each other. A 'star topology' has all devices connecting to a central hub; a 'ring topology' connects each device to two others in a circle. In this technical but everyday sense, millions of people now use the word without realising they are speaking the language of ancient Greek geometry.