I have a vague memory of some prominent scientist in the time just before quantum mechanics got going bragging that physics was solved except for a few edge cases and some slightly more precise measurements. I am trying to find the original wording and source of the quote, but I can't remember the exact wording well enough for simple Googling to be effective.
“In this field, almost everything is already discovered, and all that remains is to fill a few unimportant holes." -Philipp von Jolly, 1878.
He said it to Max Planck, who was his student at the time, advising Planck not to go into physics. Ironically, Planck would go on to do work which opened up the field of quantum mechanics.
“While it is never safe to affirm that the future of Physical Science has no marvels in store even more astonishing than those of the past, it seems probable that most of the grand underlying principles have been firmly established and that further advances are to be sought chiefly in the rigorous application of these principles to all the phenomena which come under our notice. It is here that the science of measurement shows its importance — where quantitative work is more to be desired than qualitative work. An eminent physicist remarked that the future truths of physical science are to be looked for in the sixth place of decimals.” - Albert A. Michelson, 1894
I also had some trouble finding it , did not remember it was Lord Kelvin. Here is the quote :
"There is nothing new to be discovered in physics now, All that remains is more and more precise measurement."
Kelvin is also known for an address to an assemblage of physicists at the British Association for the advancement of Science in 1900 in which he stated, "There is nothing new to be discovered in physics now. All that remains is more and more precise measurement." A similar statement is attributed to the American physicist Albert Michelson.