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Cut and pasted from Wikipedia:
Mycroft Holmes is a character in the stories written by Arthur Conan Doyle. He is the elder brother (by seven years) of the famous detective Sherlock Holmes.
Possessing deductive powers exceeding even those of his younger brother, Mycroft is nevertheless incapable of performing detective work similar to that of Sherlock as he is unwilling to put in the physical effort necessary to bring cases to their conclusions.
... he has no ambition and no energy. He will not even go out of his way to verify his own solutions, and would rather be considered wrong than take the trouble to prove himself right. Again and again I have taken a problem to him, and have received an explanation which has afterwards proved to be the correct one. And yet he was absolutely incapable of working out the practical points ...
— Sherlock Holmes, speaking of his brother in "The Adventure of the Greek Interpreter"
Though Sherlock initially tells Watson that Mycroft audits books for some government departments, he later reveals that Mycroft's true role is more substantial. While Conan Doyle's stories leave unclear what Mycroft Holmes' exact position is in the British government, Sherlock Holmes says that "Occasionally he is the British government":
“You are right in thinking that he is under the British Government. You would also be right in a sense if you said that occasionally he is the British Government … Mycroft draws four hundred and fifty pounds a year, remains a subordinate, has no ambitions of any kind, will receive neither honour nor title, but remains the most indispensable man in the country. … His position is unique. He has made it for himself. There has never been anything like it before, nor will be again. He has the tidiest and most orderly brain, with the greatest capacity for storing facts, of any man living. The same great powers which I have turned to the detection of crime he has used for this particular business. The conclusions of every department are passed to him, and he is the central exchange, the clearinghouse, which makes out the balance. All other men are specialists, but his specialism is omniscience. … They began by using him as a short-cut, a convenience; now he has made himself an essential. In that great brain of his everything is pigeon-holed and can be handed out in an instant. Again and again his word has decided the national policy.”
— "The Bruce-Partington Plans"
Mycroft has appeared or been mentioned in four stories by Doyle: "The Greek Interpreter", "The Final Problem", "The Empty House" and "The Bruce-Partington Plans". While he does occasionally exert himself in these stories on behalf of his brother, he on the whole remains a sedentary problem-solver, providing solutions based on seemingly no evidence and trusting Sherlock to handle any of the practical details. In fact, Mycroft's own lack of practicality is a severe handicap despite his inductive talents: in "The Greek Interpreter", his blundering approach to the case nearly costs the client his life.
Mycroft resembles Sherlock, but is described in "The Greek Interpreter" as being "a much larger and stouter man". In "The Bruce-Partington Plans", the following description is given:
Heavily built and massive, there was a suggestion of uncouth physical inertia in the figure, but above this unwieldy frame there was perched a head so masterful in its brow, so alert in its steel-gray, deep-set eyes, so firm in its lips, and so subtle in its play of expression, that after the first glance one forgot the gross body and remembered only the dominant mind.
Mycroft spends most of his time at the Diogenes Club, which he co-founded.