It isn’t often that physics produces news that diverts the mainstream media from politics, crime and sports. But, now, in the space of four years’ time, physicists have twice elevated the intellectual content of Google News listings: with the discovery of the Higgs boson in 2012, and now the detection of the spacetime vibrations known as gravitational waves.

Finding the Higgs shored up the standard model of particle physics, the mathematical framework for understanding the science of the ultrasmall. Gravitational waves cemented the exalted status of Albert Einstein’s general theory of relativity, the math that rules the cosmos at large.

Physicists regard both discoveries as grand accomplishments. Verifying the existence of the Higgs confirmed science’s favored explanation for why nature’s basic particles have mass. Gravitational (or just gravity) waves verified the existence of black holes, in particular confirming that black holes sometimes pair up, twirl around each other and then merge in a cataclysmic explosion. Such a cosmic blast provided the first direct detection of gravity waves, recorded last September by the twin Advanced LIGO observatories in Louisiana and Washington state. Over a brief blip of time, that explosion produced more than 50 times the power of all the stars in the universe put together, as Caltech physicist Kip Thorne explained during the news conference on February 11 announcing the discovery.

In a way, both the Higgs and gravity waves should not have been especially surprising. Almost all physicists believed strongly that the Higgs had to exist (or else they’d spent their careers believing bogus mathematics). And nobody seriously doubted that Einstein was right about gravity waves (or more precisely, that his general theory of relativity was correct in forecasting their existence — there was a time when Einstein had his doubts). But there’s a deeper sense in which both discoveries have something in common that reflects an even more astounding realization: the power of the human mind to discern deeply hidden features of physical reality.

For both the Higgs particle and gravity waves, the actual discovery required enormous physical apparatus, constructed at great cost. But in both cases the idea that such exotic phenomena existed at all came from human brainpower — deciphering the physical meaning of mathematical symbols manipulated with pencil and paper. There was no chance that random experimentation could have stumbled upon these phenomena; detecting them required an explicit search. Experimentalists knew where (and how) to search only because of roadmaps created by the minds of humans who could see the meaning hidden in their math.

Think about it. Peter Higgs deduced the existence of a new particle by contemplating the consequences of some complicated equations. He wasn’t even thinking about the particle possibility. But his paper presenting the equations was rejected (the reviewers said it was just math without much physics). So Higgs looked at the equations again and noticed that they implied the existence of the particle now named for him. Somehow, his math knew something about the universe that nobody else had previously suspected.

Einstein, in a similar way, found there was much more physics in the math of general relativity than he initially knew. After years of struggle, he pieced together the equations describing gravity, accounting for the odd orbit of Mercury and accurately predicting the bending of starlight passing near the sun. But then a little later he looked at his equations anew and realized that they contained a surprise: ripples in the fabric of spacetime that would carry messages across the universe. But too feebly, he thought, for humans to ever detect them.

Later, Einstein lost faith in his own math. In the 1930s, he attempted to show that gravitational waves did not really exist after all. With a collaborator he prepared a paper attempting to show they were phantoms in the math, not real phenomena with physical effects. But errors in the analysis turned up, scuttling that paper. Gravity waves remained an implication of general relativity. They exist in the math, and they exist in the universe.

Surveying the history of physics turns up many more examples of the power of math to reveal secrets of reality. (I once wrote a whole book about them.) General relativity provided more surprises than just gravity waves, for instance. Black holes, gravitational lensing and even, in a way, the expansion of the universe emerged from Einstein’s equations before any astronomer observed them. Quarks, the constituents of protons and neutrons, showed up in Murray Gell-Mann’s math before evidence for their existence showed up in particle accelerators. And antimatter, the fuel of science fiction’s future, became science fact in Paul Dirac’s mathematical mind before experimentalists noticed antiparticles in cosmic rays.

Perhaps the closest analog to gravity waves, though, is the appearance of radio waves in James Clerk Maxwell’s math describing electromagnetism. In the 1860s, Maxwell worked out the math of electricity and magnetism and discovered within it the surprise that light itself is an electromagnetic wave. Maxwell almost instantly realized that other electromagnetic waves of different frequencies could exist. A couple of decades later the German physicist Heinrich Hertz sought, and found, the new waves Maxwell had predicted. Those radio waves both verified Maxwell’s theory and handed science (and humankind) a powerful new tool.

It’s doubtful that gravity waves will revolutionize society in quite the way that radio has. But they certainly will open a new realm for exploring the cosmos in much the way that radio telescopes have. Either way, regardless of their eventual scientific (or practical) uses, gravity waves will forever stand as a sign that the math conceived in the human mind coexists, in some sense, in the fabric of reality.

Hertz embarked on his search for Maxwell’s waves because he had faith in that notion. Hertz fully realized that exploring the implications of the equations in electromagnetic theory had enabled Maxwell to perceive unseen features of reality.

“It is impossible to study this wonderful theory,” Hertz wrote, “without feeling as if the mathematical equations had an independent life and an intelligence of their own, as if they were wiser than ourselves, indeed wiser than their discoverer, as if they gave forth more than he had put into them.”

*Follow me on Twitter: **@tom_siegfried*