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I've seen adjectives like "Guassian" (e.g., Guassian elimination) or "Bayesian" (e.g., Bayesian networks) which derive from people's names. In the previous examples, "Guassian" derives from "Gauss" and "Bayesian" derives from "Bayes".

I've always wondered if I had always to start these kinds of adjectives with an uppercase letter (because of obvious reasons), or if I should just use them in the same way a "normal" adjective is used, i.e., starting with an uppercase letter only whenever the same adjective is the first word of a sentence.

I would appreciate an explanation of why should we use one variant rather than the opposite.

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    Once the "adjectival" usage becomes so common we associate it directly with a specific meaning rather than with the actual namesake, we usually forget about capitalising (which is only really there to help the reader when a usage is new and relatively unfamiliar). Consider, for example, a platonic relationship. – FumbleFingers Jan 9 '17 at 14:37
  • ...that hasn't happened yet with a Gaussian distribution, but people are more likely to notice your inconsistent spelling than care whether you capitalised it or not. – FumbleFingers Jan 9 '17 at 14:40
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Yes, but only until it becomes so common that people consider it a part of "standard" English and not based on a proper noun. Some other examples:

cesarean (Julius Caesar)
chauvinistic (Nicholas Chauvin)
lilliputian (based on characters from the novel "Gulliver's Travels)
quixotic (based on Don Quixote from Cervantes' novel)

and many others. Meanwhile some remain capitalized despite the passing of centuries or even millennia:

Darwinian (Charles Darwin)
Freudian (Sigmund Freud)
Socratic (Socrates)

A more complete list

An example of a word in the middle of this process is the modern verb, "to google" something (meaning to search on the internet, whether using Google's actual search engine, or something else). When used as a verb, it is rarely capitalized, since the use is informal and does not relate directly to the company.

I'm afraid you'll have to evaluate each of these on a case-by-case basis. Fortunately you can always look in a dictionary to check if they have it capitalized or not.

  • Related note: The British write it capitalised while (or whilst) Americans write it capiltalized with a Zee / Zed. Each might insist the other spelling is incorrect, but there's nothing to do be done about that. – Andrew Jan 9 '17 at 19:05
  • One should be certain to check for typographical errors in comments when one is being specific about regional spellings. – T.J.L. Jan 11 '17 at 4:43

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