The source for most references is the excellent site http://www-history.mcs.st-andrews.ac.uk/history/BiogIndex.html
Visit also the main page http://www-history.mcs.st-andrews.ac.uk/history/
and the following pages there:
History Topics Index and A Time Line of Mathematicians
Abel, Niels Henrik (Norwegian; 1802-1829)
Banach, Stefan (Polish; 1892-1945) [born in Kraków, then Austria-Hungary now Poland]
Bernstein, Felix (German; 1878-1956)
Bolyai, Farkas (Wolfgang) (Hungarian; 1775-1856) [father of János Bolyai 1802-1860]
Borel, Émile (French; 1871-1956) [Félix Édouard Justin Émile Borel]
Cantor, Georg (born in St. Petersburg, Russia but lived in Germany; 1845-1918) [Georg Ferdinand Ludwig Philipp Cantor]
Cauchy, Augustin (French; 1789-1857) [Augustin Louis Cauchy]
Dehn, Max (German; 1878-1952) [Max Wilhelm Dehn]
Euler, Leonhard (Swiss; 1707-1783) [He mostly worked in St. Petersburg, Russia, and in Berlin, Prussia]
Fermat, Pierre de (French; 1601-1665)
Gerwien, P???. (Prussian; 18??-18??)
Hilbert, David (German; 1862-1943) [born in Königsberg, Prussia, now Kaliningrad, Russia]
König, Dénes (Hungarian; 1884-1944)
Laczkovich, Miklós (Hungarian; 1948-)
Lagrange, Joseph-Louis (Italian; 1736-1813) [born as Giuseppe Lodovico Lagrangia]
Schröder, Ernst (German; 1841-1902) [Friedrich Wilhelm Karl Ernst Schröder]
Tarski, Alfred (Polish; 1902-1983) [born in Warsaw, then Russia now Poland]
Tychonov, Andrei Nikolaevich (Russian; 1906-1993)
Wilson, John (English; 1741-1793)
Zermelo, Ernst (German; 1871-1953) [pron. Tsermelo] [Ernst Friedrich Ferdinand Zermelo]
Zorn, Max (German; 1906-1993) [pron. Tsorn]