Gödel had his doctorate at 23, completing all his university studies in about 5 years. In the U.S., for example, if one goes through the usual path of four years of undergraduate studies (after being admitted to a university at 18), a 23-year-old student would likely be a first-year graduate student (assuming he or she does not take any break after the undergraduate years) in the midst of taking several core classes, which might demand enough time of study that even the most dedicated student might not be able to think of other mathematical questions not related to those classes. After taking those core classes, which might take two years, the prepared student is told to take more classes from different areas for a broad mathematical knowledge, which might take an additional year or more, before he or she is allowed to focus on some research. Hence, getting a doctorate at twenty-three is rather an exception. But, are all those classes really needed to become a mathematician?

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