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At the last point of his life, he noted that he slept 15 minutes extra every night then he calculated that he would die on the day that the extra 15 minutes a night accumulated to 24 hours. That day was November 27, 1754, the actual day of his death. He died in London and was buried at St. Martin-in-the-Fields.
Is this claim true? Is there any more information on similar predictions by mathematicians?
This is a common claim which has been repeated enough times that one can find many sources claiming it to be true. However, this doesn't seem to be corroborated by accounts of the time or serious biographies. Indeed, Helen M. Walker, in her 1934 biography of De Moivre in Scripta Mathematica Volume II, Number 4, August 1934, (reproduced here freely on Google Books as an afterward) explicitly states the following:
It is often related that De Moivre, always interested in number series, had foretold that each day he should need 15 minutes more sleep than on the preceding day, and that his death would occur when the total reached 24 hours. The story, passed on as an interesting fiction by several writers, has some basis in fact, but the arithmetic progression and De Moivre's prophetic statement are purely apocryphal, and are not to be found in any of the accounts written by men living at the time of his death.
Therein, she cites a number of biographies of De Moivre, including by Fouchy (original available through Gallica) and by Maty (available translated through Arxiv). These are the only two major biographies to have appeared soon after his death. They're quite similar (see the annotations to Maty's biography for more details). Neither has any mention of this story. I have not checked every other biography cited therein, only those two linked above, but Walker extensively documents her sources and it can be reasonably safely assumed that none of them have anything related to this story or she would have noted it.
The story isn't completely false. It is true that De Moivre was, towards the end of his life, in an increasingly frail state. He required in excess of 20 hours per day of sleep, and his condition only worsened. However, the story about predicting his own death has no reliable source, and can reasonably be assumed to be at least partly apocryphal.
I have not traced this back to its origin. Wikipedia cites Cajori's 1893 text A History of Mathematics. This contains a slightly different version of the story without citation. It should be noted that this was intended as a popular presentation of an abbreviated history of mathematics, not an extensive scholarly work, so the lack of references is not surprising. There may be earlier sources for this claim (in fact, I suspect this is likely, as Cajori probably didn't just make it up), but none by any of De Moivre's biographers who knew him personally.
I could not find any direct sources to confirm and support this claim. W.W. Rouse Ball (1850 – 1825), writes in A Short Account of the History of Mathematics first published in 1908, pages 383-384:
The manner of his death has a certain interest for psychologists. Shortly before it he declared that it was necessary for him to sleep some ten minutes or a quarter of an hour longer each day than the preceding one. The day after he had thus reached a total of something over twenty-three hours he slept up to the limit of twenty-four hours, and then died in his sleep.
However, no source is added to support this claim made by Rouse Ball.
I have read through Matthew Maty's (1718 - 1776) biography on de Moivre published 1755 in Journal britannique, in which nothing of the sort is mentioned as far as I could tell. What Maty mentions about de Moivre is that he required much sleep.
He suffered partial loss of sight and hearing; his body required more rest and his mind, greater respite. Although he came to need twenty hours sleep, he spent the remaining three or four hours taking his only meal of the day and talking with his friends.
And,
In a letter to Mr. De Mairan which he found the energy to dictate and sign, he expressed his commitment and gratitude with enthusiasm. However, he overestimated the time that he probably had left to live and underestimated the difficulty of recovering the manuscripts that he had lent when he promised to repay the honor bestowed upon him through some scholarly tribute. He was to enjoy this recognition for a few months only. His health grew steadily worse and he needed to sleep longer and often. After being confined to bed for seven or eight days, he died in his sleep on November 27, 1754.
Abraham de Moivre was a great statistician, but one of his greatest achievements may very well have been predicting his own death.
From this pdf:
W.W. Rouse Ball wrote of de Moivre’s final days:
The Manner of de Moivre’s death has a certain interest for psychologists. Shortly before it, he declared that it was necessary for him to sleep some ten minutes or a quarter of an hour longer each day than the preceding one: the day after he had thus reached a total of something over twenty-three hours he slept up to the limit of twenty-four hours, and then died in his sleep.
From here,
He noted that he was sleeping 15 minutes extra every night, and calculated that he would die on the day that the extra 15 minutes a night accumulated to 24 hours. That day was November 27, 1754, the actual day of his death. He died in London and was buried at St. Martin-in-the-Fields.
Note, though, that the source for that is Wikipedia, so perhaps we should throw that source out.
Finally, from Erich Friedman's Periodic Table of Mathematicians page:
De Moivre, like Cardan, is famed for predicting the day of his own death. He found that he was sleeping 15 minutes longer each night and summing the arithmetic progression, calculated that he would die on the day that he slept for 24 hours. He was right!
This answers your last question
Any more information on similar predictions by mathematicians?
“Cardan” appears to be Gerolamo Cardano, another famous mathematician.
By the way, this page has the exact same text.
Although this story is frequently repeated, if you think about it you will realise that it is highly implausible. Let us start off with him sleeping eight hours a night. We will see him sinking from a normal sleep pattern to oblivion in just 4 x 16 = 64 days, or just over two months. Is such a thing possible?
