Antea came from a small town in southern Italy.
She possessed remarkable artistic, as well as mathematical talents. She stared at the clear night sky through a large eastward window of the Albert Einstein Institute in Golm, near Potsdam. The Institute had been set up at the end of the 20th century, in proximity to where Einstein had once owned a holiday cottage. A good part of the research at the Institute was concerned with the problematical issue of "quantum gravity", which attempts to unify the principles underlying Einstein' general relativity with those of quantum mechanics --a mystery at the very basis of the laws of the world.
This was the direction of Antea's own research. But she was a newcomer; and she had some unorthodox, not yet fully formed ideas as to how to proceed, some of which were fundamentally at variance with those of her colleagues.
That night she had continued to work well into the small hours, in the Institute's upper library, at a time when all the others had long left for their beds. She had been studying some old research pertaining to gigantic energy emissions taking place at the centers of some galaxies. It is indeed fortunate, she thought to herself, that the Earth and the solar system are nowhere close to any of these, else they would be, in entirety, almost instantly vaporized. The established explanation of these stupendous explosions is that each is powered by a black hole of immense proportions.
Antea knew that a black hole is a spacetime region within whose interiors lies a structure known as a "spacetime singularity" -- whose scientific description is still profoundly elusive, and which depends upon the still missing theory of quantum gravity. But Antea's real interest was not so much galactic black holes as even more monstrous explosions. The explosion to end all explosions; or rather the one that began them all. The Big Bang. She mused that It was the origin of all things good, as well as of all things bad. Yet the spacetime singularity in the Big Bang provided mysteries even greater than those in black holes. Antea knew that at the root of these mysteries lay the secret of how to unite Einstein's large-scale theory of spacetime, and gravity, with the quantum-mechanical principles of physics.
It was a cold, yet peaceful, night; and the stars were unmistakably clear. For a while, Antea stood in a pensive state, her arms folded, resting on the balustrade over the staircase, and staring at the patterns of the stars through the large window -- she did not know for how long. She always felt awe as she contemplated, in that vast -- seeming hemispherical dome, the great distance of those tiny pinpricks of light, though it counted but little compared to the greater enormity of cosmological scales. Yet, she thought, if some cosmic explosion were to become visible to her now, no matter how far away, its little photons would have experienced no time at all in reaching her. The same could apply to the tiny gravitons produced in the explosion, which would be felt by the Institute's gravitational wave detector, some 250km away. She felt moved, chilled, by the thought that she would in effect be in immediate, direct contact with the explosive event.
As she stood there looking to the east, she was startled by a momentary and unexpected streak of green light, just as the dawn was about to come upon her, whereupon the deep red of the Sun broke through. While she knew the phenomenon of the "green flash" and its well-established physical explanation, she had never actually witnessed it before; and it created in her a strange emotional effect. This experience mingled with some puzzling mathematical concepts that had been troubling her throughout the night.
Then an odd thought overtook her:
"The most important single insight that has emerged from our journey is that there is a deep unity between certain areas of mathematics and the workings of the physical world. If the 'road to reality' eventually reaches its goal, then there will have to be a deep, underlying simplicity about that end point.
"There are two powerful driving forces that have strongly influenced technology yet usually go unmentioned in serious discussion, for fear, no doubt, that their influences may seem to have drifted too far from the strict rules of proper procedure. The first of these is beauty, or elegance. The second is something that can arise in development of technology and has a much more powerful impact than mere mathematical elegance, something referred to as a 'miracle'.
"The two are not unconnected, yet beauty is the most easily accepted. There is undoubtedly beauty in Euclidean geometry, which forms the basis of the most profoundly accurate physical theory, namely the theory of space as formulated by the ancient Greeks. Fifteen hundred years later came the extraordinary elegance of Newtonian dynamics, with its deep and beautiful underlying simplistic geometry structure.
"Yet miracles are doubted, as their inexplicable origins leave room, by definition, for disbelief. Numbers that previously seemed to have little to do with one another were found to be the same, as was the case when Candelas solved the equations leading to 317206375. It may be that Dirac's discovery that his relativistic wave equation automatically incorporated the electron's spin seemed like a miracle; as had Boer's use of angular momentum quantization to obtain the correct atomic spectrum of hydrogen; and likewise Einstein's realization that his approach to gravity through the curved space of general relativity actually gave the correct answer for the perihelion motion of Mercury.
"One thing is certain, however." she thought. "What's really going on is beautiful."
While Antea watched the Sun rise, she realized that a great many questions that had been profoundly puzzling and sometimes terrifying, even in modern times, had found answers.
She returned and covered her latest computations and notes with the large printed words, "beautiful miracles," then vowed to continue her work with a slightly shifted goal: understanding the crucial underlying factors that govern the mysterious relation between mathematics and the physical world.
It is within the discovered answers that we are now required to ask innovative questions. We need new, powerful ideas that will take us in directions significantly different than those currently being pursued. A slight shift is all that's required.
Beautiful miracles.