TITLE: What are some examples of when Mathematics 'accidentally' discovered something about the world?
QUESTION [242 upvotes]: I do not remember precisely what the equations or who the relevant mathematicians and physicists were, but I recall being told the following story. I apologise in advance if I have misunderstood anything, or just have it plain wrong. The story is as follows.

A quantum physicist created some equations to
  model what we already know about sub-atomic particles. His equations
  and models are amazingly accurate, but they only seem to be
  able to hold true if a mysterious particle,
  currently unknown to humanity, exists. 
More experiments are run and lo and
  behold, that 'mysterious particle' in actual fact exists! It was found to be a quark/dark-matter/anti-matter, or something of the sort.

What similar occurrences in history have occurred, where the mathematical model was so accurate/good, that it 'accidentally' led to the discovery of something previously unknown? 
If you have an answer, could you please provide the specific equation(s), or the name of the equation(s), that directly led to this?
I can recall one other example.

Maxwell's equations predicted the existence of radio waves, which were
  then found by Hertz.

REPLY [4 votes]: During World War 2,  a Hungarian mathematician by the name of Abraham Wald was called upon to provide advice on how to minimize bomber losses to enemy fire. There was an inclination within the military to consider providing greater protection to parts that received more damage but Wald made the assumption that damage must be more uniformly distributed and that the aircraft that did return or show up in the samples were hit in the less vulnerable parts.
However, Wald noted that the study only considered the aircraft that had survived their missions—the bombers that had been shot down were not present for the damage assessment. The holes in the returning aircraft, then, represented areas where a bomber could take damage and still return home safely. 
Wald proposed that the Navy instead reinforce the areas where the returning aircraft were unscathed since those were the areas that, if hit, would cause the plane to be lost. His work is considered seminal in the then-fledgling discipline of operational research.
Source - Abraham Wald