*The three pillars of learning; seeing much, suffering much, and studying much*.* *(Welsh triad; later attributed to Benjamin Disraeli)

It is a very good idea to do your graduate study at a different institution as your undergraduate study, and to take a postdoctoral position at a different place from where you did your graduate study.

Even the best mathematics departments do not have strengths in every field, so being at several mathematics departments will broaden your education and expose you to a variety of mathematical cultures, including interesting tools and parts of mathematics outside of your existing fields of expertise. Furthermore, you will be able to interact over time with a greater number of mathematicians in your area if you study and work at different places, than if you stay at a single institution; given that a significant portion of one’s career advancement in a field is based in part on the recognition you and your work receive from your peers in that field, this can thus be quite beneficial to your future career in a mathematical area.

Furthermore, the act of moving will help you make the (substantial) psychological transition from an undergraduate student to a graduate student (in which you have to go beyond rigour and proofs), or from a graduate student to a postdoctoral researcher (in which one has to take the initiative rather than rely purely on your advisor). Staying in the same institution for these transitions may feel comforting and convenient, but it can slow down one’s mathematical development.

See also “Continually aim just beyond your current range“.

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5 June, 2009 at 4:53 am

Essential Career Lessons[...] 4. Diversify your experience Even the best mathematics departments do not have strengths in every field, so being at several mathematics departments will broaden your education and expose you to a variety of mathematical cultures. (source) [...]

23 March, 2010 at 9:04 am

Which universities should one apply to? by Terence Tao « Press4ward: faith, hope and love[...] do however strongly urge that you study at different places; it’s good to move a little bit out of your own “comfort zone” and broaden your education. [...]

22 July, 2010 at 7:51 am

在不同的地方学习 | 一桶天下[...] 原作者：来源Study at different places译者kayachristina The three pillars of learning; seeing much, suffering much, and studying much. (Welsh triad; later attributed to Benjamin Disraeli） It is a very good idea to do your graduate study at a different institution as your undergraduate study, and to take a postdoctoral position at a different place from where you did your graduate study. Even the best mathematics departments do not have strengths in every field, so being at several mathematics departments will broaden your education and expose you to a variety of mathematical cultures, including interesting tools and parts of mathematics outside of your existing fields of expertise. [...]

17 April, 2014 at 1:40 pm

AnonymousA general question that is not directly related to the topic at hand: coming from a university in Norway, where all public education is free, it came as a shock to see the tuiton fees of public universities in the US, even for graduate students. Will a graduate student in the US at a somewhat respectable university be able to finance his studies exclusively on the financial support offered to him by the university/other sources of funding, given that no other financial support (family, etc.) is available?