Update: I’ve been working on expanding this timeline into a book. I’m currently in the research phase, but you can read my notes here. They are generally more up-to-date and correct than this timeline.
Any corrections, additions, or additional information would be much appreciated – please add comments below.
Updates and corrections will be noted in the comments. (I haven’t been keeping up with this, I’ve just been making corrections and not noting them)
1844 – Vestiges of the Natural History of Creation by Robert Chambers. Best seller, popularized evolutionary theory after Lamarckian theory discredited.
1853 – First volume of An Essay on the Inequality of the Human Races by Joseph Arthur Comte de Gobineau. “One of the earliest examples of scientific racism”
1871 – The Coming RaceNarrators speculates that the Vril-ya are decedents of the Aryan race that will replace humanity, but a character tells him they are actually evolved from frogs. Some suggest this is parody of Darwinism, it could also be seen as a parody of Gobineau’s writings about the Aryan race (or both). More research is needed regarding the intent. Also, some have speculated that this is non-fiction. Clearly an influence on Blavasky, but to what extent? Still, the Vril-ya can be seen as the first speculation as to a race of humanoid replacing humans and may be the first mutants.
1881 – The Great Romance by The Inhabitant. A man puts himself into a suspended state and wakes up in the year 2143 to find that humans have evolved to have telepathic powers.
1884 – “The Artificial Man. A Semi-Scientific Story” by Don Quichotte, published in The Argonaut on August 16, 1884. The anonymous narrator of the story meets a sickly old man who turns out to be an 18 year old raised in a bell jar and fed chemicals through his stomach. The Artificial Man claims to be the next evolution of being that will replace humans, and that his race will in turn be replaced by more vigorous beings. Summary 1, Summary 2 Update: I no longer see this as particularly relevant, it’s likely a response to both Frankenstein and “Darwin among the Machines)
1883-87 “The Past and Future of the Human Race,” a paper presented by H.G Wells to his college debate society. Exact date unknown, cited variously as 1883, 1885, or 1887. Lost, but thought to have been revised into the later essay “The Man of the Year 1,000,000.” [1 2 3]
1888 Ernest G. Harmer, “Professor Bommsenn’s Germs” – a scientist uses electricity to evolve a germ into an evolved human. The mutant human has no teeth or hair and possesses some sort of mesmeric ability. A “spoof of current biology.”
1889 – 10,000 Years in a Block of Ice by Louis Boussenard. A man wakes up 10,000 years in the future to find a race of people with small bodies, large heads, and telekinetic powers. Audiobook.
Boussenard was a Spiritualist and is said to have predicted his own death and composed his own obituary. 
1891 Meda: A Tale of the Future by Kenneth Folingsby. A novel about a future populated by evolved humans with huge heads who are nourished by atmospheric electricity instead of food, and, thanks to their abnormally large brains, can control electricity and magnetism with their minds. Note: a “private circulation” edition was published in 1891, followed by a public release in 1892. The 1891 edition has a preface claiming the book was written in 1888, and the title page of the 1892 edition says “Written in 1888, Published in 1892.” Excerpts here.
1892 or 1893 – HG Wells publishes the essay “The Man of the Year 1,000,000,” in which he speculates humans will evolve to use their brains more than their bodies and would look something like the above illustration from the December 23 1893 edition of the Ottawa Journal.
1893 – Camille Flammarion, La fin du Monde (published in English as Omega: The Last Days of the World in 1897). Predicts a future in which humans have evolved to have smaller bodies and larger heads.
1896 – Henri Becquerel discovers radiation.
1912 – The Night Land by William Hope Hodgson
1924 – The Last of My Race: A Dream of the Future by John Lionel Tayler. Coins the term “Homo ignorans” – proto-Stapledon.
1927 – “The Machine Man of Ardathia” by Francis Flagg. “A modern American is unexpectedly visited by a creature encased in a glass cylinder and sustained by an intricate system of tubes. It arrived from a distant future in which artificial systems have taken over all physiological functions. The evolutionary link that connected such fully ‘mechanical’ Ardathians with still ‘natural’ humans were the Bi-Chanics.” Strong echoes of “The Artificial Man” here.
1928 – “The Metal Man” by Jack Williamson.Perhaps the first sci-fi story to deal with radiation creating a mutant race. Synopsis. The Metal Man and Others, The Collected Stories of Jack Williamson, Volume One on Amazon.
1930 – Last and First Men by Olaf Stapledon. Stapledon speculates as to human evolution of a span of 2 billion years. Includes genetic engineering, and a telepathic hive mind.
1930 – Gladiator by Philip Gordon Wylie. In this novel, a mutant is deliberately engineered by a scientist who injects a serum into his wife, creating a super human offspring. Full text. Site dedicated to the novel, including covers. Kindle book.
1931 – “The Man Who Evolved” by Edmond Hamilton. First story portraying the use of “cosmic rays” in creating super human mutants? Story appears in Before the Golden Age: A Science Fiction Anthology of the 1930s (Book 1).
1945 – First atomic bomb detonated.
1951 – Strange Adventures # 9 by writer John Broome and artist Carmine Infantino. First appearance of Captain Comet, the first (?) mutant super hero in comic books. May also be the first time a mutant appears as a hero rather than antihero.
1952 “The Weird Woman” – By artist Joe Sinnott (writer unknown). First known Marvel (known as Atlas at the time) comic book appearance of mutants. Tells the story of a mutant woman who has heard rumors of the existence of a male mutant, whom she seeks to find. At the end, a super powered male appears, presumably the mutant she sought. The mutants in this story appear to be amoral.
1959 “The Man With The Atomic Brain!” by artist Steve Ditko (writer unknown). First appearance in Marvel Universe of a mutant organization, which is located on an island (reminds me of the colony in Odd John)
1959 “The Mutants and Me!” Hints at the existence of an underground network of mutants in the Marvel Universe.
1960 Village of the Damned film debuts – an adaptation of Midwich Cuckoos, important early (first?) cinematic of mutants.
1961 – “The Man in the Sky!” by Stan Lee and Steve Ditko, in Amazing Adult Fantasy # 14. Similar to “The Man With The Atomic Brain!” The character Tad Carter appeared much later in X-Men: Hidden Years
1961 Fantastic Four # 1 by Stan Lee and Jack Kirby. The FF are not generally considered mutants, since they were not born with their powers. They apparently mutated by radiation, however, like “The Man Who Evolved” and, later, the Ninja Turtles. reprints the first 10 issues of FF.
1963 Outer Limits episode “The Sixth Finger.” Clearly based on “The Man Who Evolved.” Early (first?) appearance of a mutant on television.
1963 X-Men # 1. First appearance of the X-Men. Amazon link. Can be seen as a re-envisioning of the The Man With The Atomic Brain!” and “The Man in the Sky!” – with a bald telepath bringing mutants together. This series made a deliberate effort to explore social issues through the metaphore of the mutant.
1964 Outer Limits episode “The Mutant” – At least one mutant had been seen on Outer Limits by this point, but this episode specifically uses the term “mutant.”
1975 Giant Sized X-Men # 1 by . Introduces new version of the X-Men, including the existing character Wolverine. This version would prove to be much more popular. Marvel Masterworks: Uncanny X-Men, Vol. 1 reprints Giant Sized X-Men # 1 plus Unccany X-Men #94-100.
1981 Spiderman and His Amazing Friends debuts, which features Iceman (from the X-Men) and original character Firestar, who are both mutants and said to have been X-Men members. The X-Men occasionally appear in the series.
1987 Teenage Mutant Ninja Turtles animated series begins.
What was the first use of the term “mutant” in a science fiction context?
What was the first deliberate use of the concept of the mutant to explore the issue of racism?
Where does the bald headed mutant archetype come from? Kuttner? Update: I’m now guessing this came from Folingsby and Wells, via various “alien” fiction. See: Media History of Grey Aliens.
Namor is considered to be the Marvel’s first mutant, but he was not identified as such until X-Men # 6 in July 1964.
Works referenced but not linked above
Science Fact and Science Fiction By Brian Stableford
Sci-Fi to Comics blog comments
Superhuman on Wikipedia
Mutant (Marvel Comics) on Wikipedia