The twenty-fifth meeting was held October 8-9, 2010, at Xavier University. We read Zur Theorie der complexen Zahlen (On the theory of complex numbers), J. Reine Angew. Math. 35 (1847) 319-326 [Collected Papers, A. Weil (ed.), pp. 203-210], in its English translation as found in Smith, A Source Book in Mathematics, 119-126. The paper presents Ernst Kummer's first description of his invention of ideal complex numbers, famously used to illustrate that unique factorization of integers into primes is not always available in certain rings of algebraic integers.