Link Between Math & Genes

Researchers have discovered an unexpected link between number theory in mathematics and genetics, providing critical insight into the nature of neutral mutations and the evolution of organisms. The team found the maximal robustness of mutations—mutations that can occur without changing an organism’s characteristics—is proportional to the logarithm of all possible sequences that map to a phenotype, with a correction provided by the sums-of-digits function from number theory.


An interdisciplinary team of mathematicians, engineers, physicists, and medical scientists has discovered a surprising connection between pure mathematics and genetics. ThAnd yet, again and again, number theory finds unexpected applications in science and engineering, from leaf angles that (almost) universally follow the Fibonacci sequence, to modern encryption techniques based on factoring prime numbers. Now, researchers have demonstrated an unexpected link between number theory and evolutionary genetics.

Specifically, the team of researchers (from Oxford, Harvard, Cambridge, GUST, MIT, Imperial, and the Alan Turing Institute) have discovered a deep connection between the sums-of-digits function from number theory and a key quantity in genetics, the phenotype mutational robustness. This quality is defined as the average probability that a point mutation does not change a phenotype (a characteristic of an organism).

The discovery may have important implications for evolutionary genetics. Many genetic mutations are neutral, meaning that they can slowly accumulate over time without affecting the viability of the phenotype. These neutral mutations cause genome sequences to change at a steady rate over time. Because this rate is known, scientists can compare the percentage difference in the sequence between two organisms and infer when their latest common ancestor lived.is connection sheds light on the structure of neutral mutations and the evolution of organisms.

Number theory, the study of the properties of positive integers, is perhaps the purest form of mathematics. At first sight, it may seem far too abstract to apply to the natural world. In fact, the influential American number theorist Leonard Dickson wrote “Thank God that number theory is unsullied by any application.”     READ MORE...

Quantum Physics & Truth

I first learnt about Plato’s allegory of the cave when I was in senior high school. A mathematics and English nerd – a strange combination – I played cello and wrote short stories in my spare time. I knew a bit about philosophy and was taking a survey class in the humanities, but Plato’s theory of ideal forms arrived as a revelation: this notion that we could experience a shadow-play of a reality that was nonetheless eternal and immutable. 

Somewhere out there was a perfect circle; all the other circles we could see were pale copies of this single Circle, dust and ashes compared with its ethereal unity.  Chasing after this ideal as a young man, I studied mathematics. I could prove the number of primes to be infinite, and the square root of two to be irrational (a real number that cannot be made by dividing two whole numbers). 

These statements, I was told, were true at the beginning of time and would be true at its end, long after the last mathematician vanished from the cosmos. Yet, as I churned out proofs for my doctoral coursework, the human element of mathematics began to discomfit me. My proofs seemed more like arguments than irrefutable calculations. Each rested on self-evident axioms that, while apparently true, seemed to be based on little more than consensus among mathematicians.

These problems with mathematics turned out to be well known. The mathematician and philosopher Bertrand Russell spent much of his career trying to shore up this house built on sand. His attempt was published, with his collaborator Alfred North Whitehead, in the loftily titled Principia Mathematica (1910-13) – a dense three-volume tome, in which Russell introduces the extended proof of 1 + 1 = 2 with the witticism that ‘The above proposition is occasionally useful.’ Published at the authors’ considerable expense, their work set off a chain reaction that, by the 1930s, showed mathematics to be teetering on a precipice of inconsistency and incompleteness.  READ MORE...

Math and Machine Learning

Machine learning makes it possible to generate more data than mathematician can in a lifetime

For the first time, mathematicians have partnered with artificial intelligence to suggest and prove new mathematical theorems. While computers have long been used to generate data for mathematicians, the task of identifying interesting patterns has relied mainly on the intuition of the mathematicians themselves. However, it’s now possible to generate more data than any mathematician can reasonably expect to study in a lifetime. Which is where machine learning comes in.

Two separate groups of mathematicians worked alongside DeepMind, a branch of Alphabet, Google’s parent company, dedicated to the development of advanced artificial intelligence systems. András Juhász and Marc Lackenby of the University of Oxford taught DeepMind’s machine learning models to look for patterns in geometric objects called knots. The models detected connections that Juhász and Lackenby elaborated to bridge two areas of knot theory that mathematicians had long speculated should be related. In separate work, Williamson used machine learning to refine an old conjecture that connects graphs and polynomials.

András Juhász and Marc Lackenby of the University of Oxford taught DeepMind’s machine learning models to look for patterns in geometric objects called knots. The models detected connections that Juhász and Lackenby elaborated to bridge two areas of knot theory that mathematicians had long speculated should be related. In separate work, Williamson used machine learning to refine an old conjecture that connects graphs and polynomials.

“The most amazing thing about this work and it really is a big breakthrough is the fact that all the pieces came together and that these people worked as a team,” said Radmila Sazdanovic of North Carolina State University.

Some observers, however, view the collaboration as less of a sea change in the way mathematical research is conducted. While the computers pointed the mathematicians toward a range of possible relationships, the mathematicians themselves needed to identify the ones worth exploring.

Math Is A Fundamental Part of Nature

Nature is an unstoppable force, and a beautiful one at that. Everywhere you look, the natural world is laced with stunning patterns that can be described with mathematics. From bees to blood vessels, ferns to fangs, math can explain how such beauty emerges.

Math is often described this way, as a language or a tool that humans created to describe the world around them, with precision.

But there's another school of thought which suggests math is actually what the world is made of; that nature follows the same simple rules, time and time again, because mathematics underpins the fundamental laws of the physical world.

This would mean math existed in nature long before humans invented it, according to philosopher Sam Baron of the Australian Catholic University.

"If mathematics explains so many things we see around us, then it is unlikely that mathematics is something we've created," Baron writes.

Instead, if we think of math as an essential component of nature that gives structure to the physical world, as Baron and others suggest, it might prompt us to reconsider our place in it rather than reveling in our own creativity.

(Westend61/Getty Images)

A world made of math
This thinking dates back to Greek philosopher Pythagoras (around 575-475 BCE), who was the first to identify mathematics as one of two languages that can explain the architecture of nature; the other being music. He thought all things were made of numbers; that the Universe was 'made' of mathematics, as Baron puts it.

More than two millennia later, scientists are still going to great lengths to uncover where and how mathematical patterns emerge in nature, to answer some big questions – like why cauliflowers look oddly perfect.

TO READ MORE ABOUT THE FUNDAMENTAL PART OF NATURE, CLICK HERE...

STEM Education in the USA

VISION STATEMENT

“All citizens can contribute to our nation’s progress and vibrancy. To be prepared for the STEM careers of the future, all learners must have an equitable opportunity to acquire foundational STEM knowledge. The STEM Education of the Future brings together our advanced understanding of how people learn with modern technology to create more personalized learning experiences, to inspire learning, and to foster creativity from an early age. It will unleash and harness the curiosity of young people and adult learners across the United States, cultivating a culture of innovation and inquiry, and ensuring our nation remains the global leader in science and technology discovery and competitiveness.”

Rapid technological advancements and societal changes are our daily reality. While the future of work, the economy, and society is uncertain, one thing is not: To maintain the nation’s leadership in science and technology discovery, we must create an approach to science, technology, engineering, and math (STEM) education that prepares and advances the U.S. for this future.

Experts agree that science, technology, engineering and math will drive new innovations across disciplines, making use of computational power to accelerate discoveries and finding creative ways to work across disciplinary silos to solve big challenges. To remain competitive going forward, our nation must continue to design and build a thriving innovation economy, supported by a citizenry that is invested in the STEM enterprise. To succeed, the nation must invest in new research and innovation infrastructures that include all people, regardless of their background.

HOW DO WE ACHIEVE THIS VISION?

We instill creativity, innovation, and a passion for STEM from an early age, and we maintain that engagement and enthusiasm throughout their lives. Doing so will unleash an innovation culture, teaching learners of all ages to take risks, be creative, and problem-solve. Today, we are far from this goal. 

Many Americans are entering the workforce without a basic grasp of STEM facts and approaches. Equally worrisome, amid the stagnant or dipping numbers of U.S.-born STEM workers, there is a critical lack of women, people with disabilities and African Americans, Hispanic Americans, and Native Americans who remain underrepresented in STEM. This underrepresentation is especially evident in several strategic areas critical for U.S. progress and security, including computer science, mathematics, and engineering. 

We are in dire need of STEM role models and leaders for the future. By 2060,1 Black and Hispanic youth will comprise nearly half of all U.S. school-age children. However, STEM faculty from these backgrounds are currently scarce, and trends among the number of domestic students who pursue advanced research degrees in STEM disciplines—particularly computer science, mathematics, and engineering...  READ MORE...

Three "D" Printing

A strange shape described by mathematician Lord Kelvin in 1871 and predicted to behave unusually in a fluid has finally been fully studied in the real world thanks to 3D printing – and it seems Kelvin may have been wrong. The behaviour of the shape, called an isotropic helicoid, has been described in fluid dynamics textbooks, but it hadn’t been directly measured until now.

An isotropic helicoid must experience the same amount of drag from a fluid regardless of its orientation, like a sphere, but also rotate as it moves through the fluid. So if you dropped an isotropic helicoid into a tank of a viscous liquid, it should spin as it sinks, similar to the way a propeller turns.

Greg Voth at Wesleyan University in Middletown, Connecticut, and his colleagues 3D printed five different shapes that should be isotropic helicoids, each a little more than a centimetre across, and dropped them into a tank of silicone oil. They were unable to detect rotation in any of them, meaning the predictions for an isotropic helicoid may be wrong.

“You’ve got to guess that somebody else has tried this in 150 years – in Kelvin’s original paper, it even sounds like he tried it,” says Voth. “I suspect that people have tried to fabricate these particles, but they were limited by defects in the fabrication so they simply didn’t publish, so the hypothesis of this behaviour has stayed with us.”

Upon delving into the hydrodynamic effects in play, the researchers calculated that there was almost certainly a link, or coupling, between the movement and rotation of their particles, meaning they fulfilled Kelvin’s criteria. But this was far too small to have any detectable effect.

“The coupling is tiny, but it still exists,” says Voth. He and his team are now working on building an isotropic helicoid where that coupling could be measurable, which would finally vindicate Lord Kelvin’s idea.  READ MORE

Planet Vulcan

In 1846, astronomer and mathematician Urbain Le Verrier sat down and attempted to locate a planet that had never been seen before by humans. Uranus (grow up) had been moving in unexpected ways, as predicted by the Newtonian theory of gravity.

Though the discrepancies were small, there was a difference between the observed orbit of Uranus and the way Newtonian physics predicted its orbit to be. In July, Le Verrier proposed that the difference could be explained by another planet beyond Uranus, and made predictions as to the orbit of this previously unknown body.

Being a mathematician first and an astronomer second, he wasn't really interested in finding it with a telescope now that he'd found it in maths, and the task of searching for it was left to German astronomer Johann Gottfried Galle. On September 23, 1846, Galle looked at the spot Le Verrier had predicted the planet would be, and found to within 1 degree of the spot... the planet Neptune.

So, having discovered a new planet by looking at the orbit of another, Le Verrier was called upon to take a look at a planet whose name doesn't also mean butt hole: Mercury. Mercury, being so close to the Sun, is the most difficult planet in our Solar System to observe (assuming there is no Planet Nine out there). Le Verrier was tasked with plotting Mercury's orbit using Newtonian physics.

But he couldn't. No matter how much he tried, Mercury's eccentric orbit didn't make any sense. According to Newtonian theory, the planets move in elliptical orbits around the Sun, but observations showed that Mercury's orbit wobbles more than could be accounted for by the gravity exerted by the other known planets.  TO READ MORE, CLICK HERE...