The correct answer is John Quincy Adams. John Quincy Adams (July 11, 1767 – February 23, 1848) was an American statesman who served as the 6th President of the US (1825-1829). According to the Metropolitan Museum of Art web site, this image is a copy of a lost daguerreotype of Adams taken by Philip Haas ca. 1843. However, Beard, Charles A., Mary R. Beard, and William Beard, New Basic History of the United States, Garden City: Doubleday, 1944, 1960, says it was taken 1847, a year before Adams's death.

The photograph is not of his father John Adams because the elder Adams died before the invention of photography. It is also not Andrew Johnson, who became President of the US after the assassination of Abraham Lincoln in 1865. There are well-known photographs of him - look it up if in doubt. As Charles Darwin was not even American, he should have been eliminated first.

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