[1] After early exhibiting a talent for drawing and painting, he went to study at the Academy of Fine Arts in Munich, where his teachers were Ludwig von Loeffts and the history painter Wilhelm Lindenschmidt.
He is especially known for his paintings of men in cluttered offices filled with business furnishings or laboratory equipment, such as his several paintings of the mineralogist Thomas Price.
He left San Francisco for New York City on April 15, 1887, in order to be at the center of the art world, but he suffered from money troubles and alcoholism.
Alexander's work attracted enough notice that the New York Herald described him as one of the creators of the modern school of art.
[2] On May 15, 1894, his money troubles led him to commit suicide by swallowing oxalic acid in the Oriental Hotel at Broadway and Thirty-Ninth Street.