To students who are new to Hindi, terms such as विद्यार्थी (vidyārthī = student) or अध्यापक (adhyāpaka = teacher) might seem a bit daunting and, without doubt, not only a bit too complicated for what they describe. That native speakers are, to a certain extent, equally puzzled by the shape of these words, is probably the reason why in today’s language the English words teacher and student are on the good way to replace the original Hindi words. Puzzlement arises essentially from one source: failure to see that these words are speaking words, i.e. that they very simply describe what a teacher and a student usually do, what their characteristic features are. Once one turns to Sanskrit, the source of these two words, their meaning becomes as crystal-clear as the word railway in English.
विद्यार्थी is constructed from two roots: विद्, (vid) to know (reflecting the same Indo-European root as found in the English words wit, wise and wisdom) and अर्थ् (arth), to wish, desire, seek. These are the essential building blocks of the word विद्यार्थी. In order to end of with the word in question we first have to make two nouns from these roots. From विद् we make a feminine noun विद्या (vidyā), science, learning, scholarship. From अर्थ् we make अर्थ (artha), that which is desired or sought, hence aim, intention or goal. To the latter we add the adjectival suffix -इन् (in), which in the nominative, the form used in Hindi, is -ई (-ī), resulting in अर्थी (arthī), having an aim, intending, desiring. In this case the aim is विद्या, making विद्यार्थी, the one who has learning as his aim, i.e. a student.
The noun अध्यापक is only made of from one root: ई (ī), to go. This is used with the verbal prefix अधि (adhi), unto, upon. The two together result in अधी (adhī), to direct the mind upon, to concentrate or focus. When the causative is formed from this root it takes on the shape अध्याप् (adhyāp), which is used to make all sorts of forms having the basic meaning: to cause to concentrate or focus. The last part of the word अध्यापक is the agentive suffix -क (-ka), which gives the entire noun the meaning: the one who causes to concentrate or focus, i.e. a teacher.
teacher for ancient languages