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In most of the science textbooks I read, I observed that most of them contain the terms, definitions and etymology too.

But nowadays, the mathematics textbooks are becoming more formal and contain only the relevant terms and their corresponding definitions.

Consider the following scenario:

The probability mass function is a function from the powerset of a sample space to [0,1].

The probability density function is a positive function that integrates to 1 on totality.

Both are formal definitions. Needs to be remembered.

There is some intuitive explanation regarding why we call mass function and density function. First, one tells about the value directly and hence called mass and the second one gives information about probability or area under it as probability and hence it is called a density function.

Do the textbooks covering all these aspects in historical etymology view exist for major fields of mathematics?

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  • $\begingroup$ "all etymological aspects" is a bit broad. For example, in "probability mass function," do you also want the etymology for "probability" and "function"? $\endgroup$ – Joel Reyes Noche May 12 at 13:37
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    $\begingroup$ jeff560.tripod.com/mathword.html $\endgroup$ – Paracosmiste May 12 at 18:27
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    $\begingroup$ Your question remains unclear. In your title you ask for a textbook/reference "that cover most etymological aspects of mathematics". If that's your question, than you've received an excellent link in the comments, and an answer. In the body of your question you address, particularly, the probability mass function and the probability density function, and indicate in your comment to JoelReyesNoche that you "need the etymology for probability or function if there is any reason behind them like mass and density." So it seems you are asking for a probability text that includes... $\endgroup$ – Namaste May 17 at 14:20
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    $\begingroup$ ... references to the historical development of the field of probability, which accompanies the introduction of each major new term with an "aside" that shares the origin of the term? $\endgroup$ – Namaste May 17 at 14:22
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    $\begingroup$ One book I’ve found which blends actual mathematics and a relatively large amount of history/context is Remmert’s Theory of Complex Functions. As you might imagine, it’s about complex analysis, and it is focused on teaching analysis, rather than discussing etymology — but when it touches on history/etymology/motivation, it does so quite well in my opinion. $\endgroup$ – pjs36 Jun 7 at 3:53
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There are already some books dedicated to etymological aspects of mathematics. Here are two of them:

For mass:

  • Bello: mass The Latin noun massa means a lump.
  • Schwartzman: mass (noun): from Greek maza "kneaded dough." The Indo-European root is mag - "to knead, fashion, fit," as seen in native English make. A related borrowing from Greek is magma, a fiery mass of molten rock. The nontechnical sense of mass is "stuff, substance." In physics, mass is defined as a measure of a body's tendency to resist changes in velocity.

For density:

  • Bello: From the Latin adjective densus meaning thick, close was formed the noun densitas by the addition of the suffix -itas to the stem of the adjective. This noun entered French as densité and from there came into English as density.
  • Schwartzman: dense (adjective), density (noun): from Latin densus "having its particles close together, crowded, thick." The word is used with its meaning virtually unchanged in English. In topology a set S is said to be dense in a space P if every point in P is a point or a limit point of S. In physical applications, density is defined as mass of matter per unit of volume.
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