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<p>However, math PhD programs may expect PhD students to have a reading knowledge of one or more foreign languages in which math research papers are published (French, German, or Russian are common options).</p>
<p><a href=“https://math.mit.edu/academics/grad/timeline/language.php”>https://math.mit.edu/academics/grad/timeline/language.php</a>
<a href=“http://web.math.princeton.edu/~templier/language-exam.txt”>http://web.math.princeton.edu/~templier/language-exam.txt</a>
<a href=“Harvard Mathematics Department Graduate Information”>http://www.math.harvard.edu/graduate/</a>
<a href=“http://math.berkeley.edu/programs/graduate/phd-program”>http://math.berkeley.edu/programs/graduate/phd-program</a></p>