“Often the hands will solve a mystery that the intellect has struggled with in vain.”

Source: Social Problems (1883), Ch. 1 : The Increasing Importance of Social Questions
Context: The intelligence required for the solving of social problems is not a thing of the mere intellect. It must be animated with the religious sentiment and warm with sympathy for human suffering. It must stretch out beyond self-interest, whether it be the self-interest of the few or of the many. It must seek justice. For at the bottom of every social problem we will find a social wrong.

Source: Big Stone Gap

Source: Black Blood

Attributed to Merton in a number of sources, the earliest located being Studia mystica, Volumes 5-6 (1982), p. 76 http://books.google.com/books?id=59EYAAAAIAAJ&q=%22problem+to+be+solved%22#search_anchor. This does not attribute a direct quote to Merton, but says "To use another of Merton's favorite distinctions, for Furlong Merton's life is seen principally as a problem to be solved, which it was, in the final analysis, successfully, rather than a mystery to be lived". The next-earliest source located is the 1998 book The Artist's Way at Work: Riding the Dragon by Mark Bryan and Julia Cameron, which attributes the exact quote to Merton on p. 152 http://books.google.com/books?id=CghAQDPahhcC&lpg=PP1&pg=PA152#v=onepage&q&f=false. In reality this seems to be a slightly altered version of the quote "The mystery of life is not a problem to be solved; it is a reality to be experienced" which appeared in the 1928 book The Conquest of Illusion by Jacobus Johannes Leeuw, p. 9 http://books.google.com/books?id=OFdVAAAAMAAJ&q=%22not+a+problem+to+be+solved%22#search_anchor.
Misattributed

The Nature of Time (1961) as quoted by Douglas Martin, "Gerald J. Whitrow, 87, Author Of Philosophic Tomes on Time" The New York Times (June 27, 2000)

Variants:
Science cannot solve the ultimate mystery of nature. And that is because, in the last analysis, we ourselves are a part of the mystery that we are trying to solve.
Science cannot solve the ultimate mystery of nature, for in the final analysis we ourselves are part of the mystery we are trying to solve.
Source: Where is Science Going? (1932)

Gegen die Langeweile kämpfen Götter selbst vergebens.
Sec. 48
The Antichrist (1888)
Source: The Anti-Christ

As quoted in Report on the Activities of the Council of People’s Commissars, Collected Works, Vol. 26, pages 459-61.
Attributions

Source: Dune