Mathematics has a way of finding pleasure in the beauty that many of us fail to see. Nature, on the other hand, is a wonderful place where one can observe the beauty generated by mathematical relations.
The natural world presents countless patterns based on numbers, if only we are able to recognize them. Building on this notion, a team of researchers has recently discovered another astounding similarity between mathematics and nature. This connection lies between one of the purest forms of mathematics, the theory of numbers, and the mechanisms governing the evolution of life at the molecular level: genetics.
The theory of numbers, although abstract, is one of the most familiar forms of mathematics for many people. It encompasses the operations of multiplication, subtraction, division, and addition of integers.
An example that highlights the connection between mathematics and nature is the famous Fibonacci sequence, where each number in the sequence is the sum of the previous two numbers. Remarkably, the patterns found in this sequence can also be observed in nature, such as in the arrangement of cones, pineapples, and sunflower seeds.
Dr. Ard Louis, a mathematician from the University of Oxford and the senior author of a new study, emphasizes that, “The beauty of the theory of numbers lies not only in the abstract relations between integers, but also in the deep mathematical structures that it encompasses in our natural world.”
In their research, Louis and his colleagues focused on mutations, which are genetic errors that accumulate over time in an organism’s body and drive its evolution.
Specifically, the researchers investigated how a unique genetic sequence, known as the genotype, corresponds to a specific phenotype or observable trait in an organism.
Using numerical modeling, they calculated various possibilities and demonstrated that mutation stability can be maximized in naturally occurring proteins and RNA structures. Surprisingly, the maximum stability followed a self-related fractal pattern known as the Blancmange curve, and it was proportional to a fundamental concept in the theory of numbers called the number of numbers.
Vaibhav Mohanty, a researcher from Harvard Medical School, explains, “We have found clear evidence of sequences displaying secondary RNA structures that, in some cases, reach the upper boundary of stability.”
The findings of this study were published in the journal “Interface” of the Royal Society. To learn more, you can refer to the