Is more than 1 PhD a waste of time?

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Pursuing a second PhD in computer science after obtaining a PhD in pure mathematics is generally considered unnecessary. While there are specific professional scenarios, such as in medical physics, where individuals with PhDs in other fields may pursue additional qualifications, it is rare to see someone obtain a second PhD. Typically, professionals opt for post-PhD certificates or master's degrees to gain the necessary credentials. The primary value of a PhD lies in developing independent research skills, which are not significantly enhanced by pursuing another PhD. For those seeking in-depth knowledge in a new field, more efficient alternatives exist beyond obtaining a second doctoral degree.
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Say you have a PhD in pure mathematics but want credentials for computer science for some reason where it might be necessary (is there such a situation?). Is it a waste of time to also get another PhD in computer science?
 
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Generally speaking, yes.

An exception might be for professional cases. In medical physics it's not uncommon for people with PhDs in other branches of physics to go through a medical physics graduate program, but I've never seen anyone go through with a second PhD. Usually they either get a post-PhD certificate or a master's degree - enough so that they can go on to enter the profession.

A PhD is largely about learning the skills to research independently. Once you have those, repeating that training is just an excercise in futility. The other thing you get is an in-depth knowledge of a particular field, but there are more efficient ways to get that if that's all you're lacking.
 

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