India: The Land Of Human Computers?

With a recent warts-and-all Bollywood biopic of Shakuntala Devi, is India the land of “human computers” – i.e. people who can do incredible mathematical feats without the aid of a calculator?

By: Ringo Bones

For much of the 20^th Century, India has become a go-to country for those in the search of people who can do amazing mathematical feats without the aid of a pocket calculator or even a slide rule. From the number theories of Srinivasa Ramanujan to scores of others who can recite the value of pi to several decimal places that necessitate the use of an electronic device much more advanced than a battery-operated electronic pocket calculator, India seems to be the go to place to find them.

Recently, Indian math wizard Shakuntala Devi, often described as a “human computer”, became the subject of a new film that premiers on the online streaming giant Amazon Prime Video on Friday, July 31, 2020. Born in November 4, 1929 in Bengaluru, India, and in her interviews, Shakuntala Devi said she was “doing mathematical calculations from the age of 3 in my head” and that her father, a circus artist, discovered her felicity with numbers while playing cards with her when he discovered that she was beating him not by cheating – but by memorizing the cards.

At the age of 6, Shakuntala Devi first displayed her extraordinary mathematical skills in a public performance in the city of Mysore in Karnataka the southern state where she was born. She taught herself reading and writing and for decades travelled around the world doing impossibly complex mental calculations before audiences in universities and theaters and in radio and television studios.

In 1950, when Shakuntala Devi participated in a BBC television show, her answer to a problem differed from the host’s. That was because, as she pointed out, there was a flaw in the question. She was proved right when experts re-examined the numbers. In 1977 in the American city of Dallas, she beat Univac, one of the fastest supercomputers ever built during that time. And for her 1982 Guinness Book of World Records recognition s the fastest human computer, she multiplied two 13-digit numbers, randomly picked by a computer, in front of an audience of 1,000 at the Imperial College of Science and Technology in London. It took her 28 seconds, including the time to recite the 26-digit answer. For much of her professional life, she strove to simplify mathematics for students before passing away back in April 21, 2013 in the Bangalore Hospital, Bengaluru, India.

Johann Daniel Titius: Original Author Of Bode’s Law?

Even though he’s not a well known household name like Newton, did the astronomer and mathematician Johann Daniel Titius the original author of Bode’s Law?

By: Ringo Bones

It has since been rechristened as the Titius-Bode Law and in his honor, an asteroid – 1998 Titius -  and a crater on the Moon was named after him, the 18^th Century German mathematician and astronomer Johann Daniel Titius never became a well-known household name like the Englishman Isaac Newton. But nonetheless, Titius did make some important contributions to mathematics, physics, astronomy and biology during his lifetime.

Johann Daniel Titius (1729 – 1796) was born on January 2, 1729 in Konitz Royal Prussia – a fiefdom of the Crown of Poland – to Jakob Tietz, a merchant and council member from Konitz, and Maria Dorothea, née Hanow. His original name was Johann Tietz, but as was customary in the 18^th Century, when he became a university professor, he Latinized his surname to Titius. Teitz attended school in Danzig (Gdansk) and studied at the University of Leipzig (1749-1752). He died in Wittenberg, Electorate of Saxony on December 16, 1796.

Titius proposed his law of planetary distances in an unsigned interpolation in his German translation of the Swiss philosopher Charles Bonnet’s Contemplation de la nature (“Contemplation of Nature”). Titius fixed the scale by assigning 100 to the distance of the planet Saturn from the Sun. On this scale, planet Mercury’s distance from the Sun is approximately 4. Titius therefore proposed that the sequence of planetary distances (starting from Mercury and moving outward) has the form:  4,4 + 3,4 + 6,4 + 12,4 + 24,4 + 48,4 + 96,…

There was an empty place at distance 28, or 4 + 24 (between the planets Mars and Jupiter), which Bode asserted, the Founder of the Universe surely has not left unoccupied. Titius’ sequence stopped with the planet Saturn, the most distant planet then known. His law was reprinted, without his credit, by Johann Elert Bode in the second edition of his Deutliche Anleitung zur Kenntniss des gestirnten Himmels (Clear Guide to Knowledge of the Starry Heaven) in 1772. In later editions, Bode did credit Titius, but this mostly escaped notice and during the 19^th Century the law was usually associated with Bode’s name.

Titius published a number of works on other areas in physics, such as a set of conditions and rules for performing experiments and he was particularly focused in thermometry. In 1765, he presented a survey of thermometry up to that date. He wrote about the metallic thermometer constructed by Hans Loeser. In his treatises on both theoretical and experimental physics, he incorporated the findings of other scientists, such as the descriptions of experiments written by Georg Wolfgang Kraft in 1738.

As a confirmed polymath, Titius was also active in biology, particularly in classification of organisms and minerals. His biological work was influenced by Carolus Linnaeus. Lehrbegriff der Naturgeschichte Zum ersten Unterrichte, his most extensive publication in biology, was on the systematic classification of plants, animals and minerals, as well as the elemental substances: ether, fire, air, water and earth. The standard author abbreviation Titius is used to indicate Johann Daniel Titius as the author when citing a botanical name.

The Mysterious Mathematics Behind Bode’s Law: The Most Puzzling Law Of Science?

Often cited as the most productive – and most puzzling – scientific law at the same time, are there any “mathematical” mysteries behind Bode’s Law?

By: Ringo Bones

This rather “curious” scientific law was named after an 18^th Century German astronomer and mathematician named Johann Elert Bode, but contrary to popular belief, it was actually discovered by Johann Daniel Titius – a German mathematician – back in 1766. However, the empirical relation that gives the approximate distances of the planets from the Sun did not attract attention to the 18^th Century astronomical community until it was publicized by Johann Elert Bode – whose name has since then associated with it – back in 1772.

To the uninitiated, Johann Elert Bode (1747-1826) was an 18^th Century era German astronomer and mathematician who popularized an empirical law that was later named after him, which gives the approximate distances of the planets from the Sun. Bode was also famous for naming the planet Uranus that ended the confusion in the astronomical community at the start of the 19^th Century when the British astronomer William Herschel desired to name the then newly discovered planet as Georgium Sidius after King George III of England.

After examining the work of fellow German mathematician, Johann Daniel Titius, Bode noted that the distances of the various planets from the Sun fell into a curious mathematical sequence. Bode then published a paper which arbitrarily assigned numbers to the planets: 0, 3, 6, 12, 24, 48, 96, and 192. Thus the planet Mercury was numbered 0, planet Venus 3, planet Earth 6, planet Mars 12, and so on, each number being double the last one. When 4 was added to each of these numbers and the result is divided by 10, figures emerged which almost exactly equaled the planets’ distances from the Sun, measured in astronomical units. By the way, an astronomical unit is a unit of distance between the planet Earth and the Sun – which is around 93-million miles or 150-million kilometers.

The only trouble with the law was that back in the time when Bode published it in 1772, there were no planets found at positions 24 or 192. But astronomers searching in position 24 located the asteroids – around the start of the Nineteenth Century – i.e. the discovery of asteroid Ceres in 1801. The planet Uranus, which was discovered back in 1781, occurs at position 192 and conforms almost exactly to Bode’s calculations. Only the outermost planets – Neptune and the dwarf planet Pluto – failed to obey Bode’s Law. Although many attempts have been made to derive a physical explanation for the law, none has completely succeeded.  Today, many astronomers dismiss Bode’s Law as a coincidence and that Bode’s Law is not a rule governing planetary systems. Yet it remains one of the most mysterious statements of natural law formulated by man with the help of mathematics.

Did A 13 Year Old Girl’s Mathematical Skills Help Design The Spitfire’s Weapons System?

It would also have been much of a dream job for boys within her age but did a 13 year old girl helped design the weapons system of the iconic Supermarine Spitfire?

By: Ringo Bones

Now, 80 years after the start of the Battle of Britain on July 10, 1940, the RAF has finally recognized the role of an unseemly inventor and mathematical genius. In 1934, Hazel Hill, a teenage girl from north London, carried out the calculations that proved the new generation of fighter planes – i.e. Spitfires and Hurricanes – should carry eight fifty caliber machine guns, instead of just four. In a documentary researched by her granddaughter, Felicity Baker, a journalist, Hazel Hill’s contribution that allowed the Spitfire to dominate the Battle of Britain and denied the Nazi’s their British conquest finally got the recognition it deserve. Yet – until now – the compelling story of the schoolgirl who helped to win a war has been sadly untold. Hazel Hill’s only recognition was in a memoir written by her father’s superior officer in the UK Air Ministry.

Fortunately for Hazel Hill and her dad, the historic mathematical collaboration happened way before Number 10 declared that the Supermarine Spitfire’s design details were part of the UK’s Official Secrets Act or she could certainly have been denied access to it. In the summer of 1934, Hazel Hill, a 13 year old girl from north London, was approached by her father, Captain Fred Hill, a scientific officer in the UK Air Ministry who was trying to make the case for the new generation of fighter planes. Despite her youth, Captain Hill drew upon his daughter’s mathematical intellect and discussed plans with her as to how it could be possible to arm Spitfires with eight 50 caliber machine guns, as opposed to the four which had been originally suggested. Along with her father, she worked through the night on complex calculations that would shape the future of fighter planes like the Spitfire and the Hurricane. The work was done by lamplight over a kitchen table in north London. Night after night throughout the early months of 1934, Captain Fred Hill and his 13 year old daughter burned the midnight oil plotting graphs and laboring over complex algorithms.

When they got access to the new “calculating machines” of the time – which to our eyes today, resemble very rudimentary vacuum tube based computers – father and daughter worked long into the night analyzing the data that was previously obtained at their kitchen table. Their complicated calculations showed conclusively that each Spitfire needed to be capable of firing 1,000 rounds a minute – per gun. They also calculated the exact distance the Spitfire – whose top speed was about 360 mph – had to be from the enemy to hit them, just 755 feet.  The biggest thing was the huge increase in speed of the new fighters, which was way beyond anything people had experienced before – says mathematician Niall MacKay, the current head of the Department of Mathematics at the University of New York.

  It was tiring, unrewarding work but they both sensed how vital it would prove to be. And their instincts would before long be ratified by history because their intricate calculations would go on to help the RAF secure victory in the Battle of Britain – a triumph that many historians now believe changed the course of World War II. Bent together over their graphs, father and daughter concluded that the new generation of aircraft being built by the UK government to prepare for future war should be armed not with four powerful machine guns but eight – an idea was seen as deeply radical, even improbable at the time. Yet only then, the Hills had come to believe, would a new generation of Spitfires and Hurricanes have sufficient firepower to bring down enemy aircraft. A scientific officer in the UK Air Ministry, Captain Hill managed to convince his superior officers of the importance of his and Hazel’s findings – and six years later, in 1940, their calculations were put to the test in the skies above Britain as the RAF fought Adolf Hitler’s much feared Luftwaffe in a four month battle that has been described as the most important military campaign ever fought. The Battle of Britain is often referred to as the first major military battle which was fought entirely by air forces. Who knew that Reginald Joseph Mitchell’s iconic design could still be improved by a 13 year old girl from north London?

Can Mathematical Modeling Be Used To Stop The Spread of COVID 19?

Can mathematical modeling help us in keeping the individual spread – or basic reproduction number - of COVID 19 to less than 1?

By: Ringo Bones

Since COVID 19 transmission started in late January 2020, the use of mathematical modeling has been at the forefront of shaping the decisions around different non-pharmaceutical interventions to confine the spread of the virus. Mathematical modeling can be used to understand how a virus spreads within a population. The essence of mathematical modeling lies in writing down a set of mathematical equations that mimic reality. These are then solved for certain values of the parameters within the equations.

 The solutions of the mathematical model can be refined when we use information that we already know about the virus spread, for example, available data on reported number of infections, the reported number of hospitalizations or the confirmed number of deaths due to the infection. This process of model refinement – or calibration – can be done a number of times until the solutions of the mathematical equations agree with what we already know about the virus spread. The calibrated model can then be used to tell us more about the future behavior of the virus spread.

One outcome of mathematical models is the predicted epidemic curve representing the number of infections caused by the virus over time. Using different parameters in the model, which may illustrate different interventions, or calibrating the model against different data, can change the predicted epidemic curve.

Mathematical modeling is a powerful tool for understanding transmission of COVID 19 and exploring different scenarios. But, instead of focusing on which model is correct, we should accept that “one model can’t answer it all” and that we need more models that answer complementary separate questions that can piece together the jigsaw and halt the COVID 19 spread.

Farewell Katherine Johnson

Could the United States have won the so-called space race against the then Soviet Union without the help of NASA's African-American mathematician Katherine Johnson?

By Ringo Bones

Fortunately, she got her due credit while still alive given that her most important mathematical works were done during Jim Crow era America. As of February 24, 2020, former NASA mathematician Katherine Johnson, also known as Katherine Goble passed away in Newport News, Virginia. Born in August 25, 1918 in White Sulphur Springs, West Virginia, USA became well known as America’s NASA mathematician whose calculations of orbital mechanics during her employment at NASA were critical to the success of the first and subsequent manned spaceflights.

Katherine Johnson was better known to the generation born after the Apollo moon missions as the NASA African-American mathematician portrayed by Taraji P. Henson in the 2016 movie Hidden Figures about a group of trailblazing African American women mathematicians employed by NASA during the start of America’s Civil Rights movement at the start of the 1960s. Although Katherine Johnson’s mathematical work began earlier in the National Advisory Committee for Aeronautics / NACA – the predecessor of NASA – back in 1953. Before being made famous by the movie Hidden Figures in 2016, Katherine Johnson was awarded with the Presidential Medal of freedom – America’s highest civilian honor – by President Barack Obama in 2015.

During the early days of programmable digital computers – whose active components of which were still largely made with subminiature vacuum tubes first manufactured during 1947 – astronauts were not exactly keen on putting their lives in the care of these early electronic calculating machines, which were prone to hiccups and blackouts according to NASA. So pioneering astronaut John Glenn asked the NASA engineers to “get the girl” – referring to Katherine Johnson to run the computer equations by hand for improved reliability. Johnson and her team of African American women mathematicians did vital work for NASA that eventually made the United States won the space race by successfully landing the first men on the moon and  taking them back safely to earth before President John F. Kennedy’s end of the 1960s deadline.

Jeffrey Epstein Was A Mathematics Professor?

While his tenure at the esteemed Manhattan prep school was only a brief one, historically speaking, Jeffrey Epstein is not the only mathematics professor with an “iffy” sexuality by today’s standards?

By: Ringo Bones

When it comes to mathematics professors who had dabbled in “paedophilia”, it seems that only the most scholarly can attest that there are already two of them – i.e. Charles Lutwidge Dodgson, also known as Lewis Carroll and the disgraced billionaire financier who had recently allegedly committed suicide in prison named Jeffrey Epstein. But is there any truth to the “alleged paedophilia” to both math professors?

Even though US President Donald Trump seems to have got off Scott-free when it comes to his “paedophile adventures” with Jeffrey Epstein, it was Prince Andrew who got a grilling by public opinion after an ill-advised interview at the BBC Panorama program. But does the “mathematical profession” really attract some “perverts”?

Dalton – the esteemed Manhattan prep school  where Jeffrey Epstein became a mathematics professor back in the 1970s has long been known for its rigorous academics, repeatedly ranking among the United States’ best private schools while drawing the sons and daughters of New York’s titans of finance, media and art. And students who are enrolled in Epstein’s class vividly remembered the then mathematics professor dressing in furs with open chest revealing chest hairs and blingy gold jewelry. Many say that the only reason Epstein got the job is that a number of New York’s upper crust acquired millions via Epstein’s financial advised backed by his mathematical acumen – although Epstein eventually quit after getting richer off the New York Stock Exchange.

Even though Victorian era mathematician Charles Dodgson – aka Lewis Carroll – who wrote Alice’s Adventures In Wonderland had an extensive collection of photos of naked girls aged 8 to 11. Though Charles Dodgson signed his real name to only his “serious” mathematical works, mathematicians for decades have been intrigued by the rich skein of symbolic logic that is woven into fantasies like in Alice’s Adventures In Wonderland and Through The Looking Glass.

The Mathematical Merits of Jeopardy’s 69 Ban?

I thought it was the premise of the upcoming third Bill and Ted movie, but is there any so-called “mathematical merits” of Jeopardy’s 69 ban?

By: Ringo Bones

I have no idea when it started, but it still surprises me that middle-school kids still giggle whenever the number 69 is uttered in an unguarded moment. But during the last week of April 2019, a new ruling on the iconic TV game-show Jeopardy has been divulged preventing contestants from betting $69 on the Final Jeopardy stage of the game citing the awkward sexual nature of the number.

It is not only the number 69 that got the axe on Jeopardy – it also includes the so-called “Number of the Beast” – i.e. 666 as in $666 Final Jeopardy bets. The betting ban also includes numbers of Neo-Nazism significance, like the number 88, the number 14, and the number 1488 – odd since before the Obama Administration era episodes of Glenn Beck’s show on Fox News, the only “Nazi significance” I know of the number 88 was the 88 millimeter shell used by Nazi era Germany. Outside of joining Richard Butler’s Aryan Nation, it was probably Glenn Beck who made Neo-Nazi numerology more or less common knowledge. Fortunately, a $420 Final Jeopardy bet is still valid.

Ernest William Brown: More Mathematician Than Astronomer?

Despite being more well-known for his astronomical work in lunar theory, Is Ernest William Brown more of a mathematician than an astronomer?

By Ringo Bones 

Born in November 29, 1 in Kingston upon Hull, UK, Earnest William Brown FRS was an English mathematician and astronomer, who spent the majority of his career working in the United States and thus became a naturalized American citizen in 1923. In 1907, he was appointed Professor of Mathematics at Yale University. 

His life’s work was the study of the Moon’s motion (lunar theory) and the compilation of extremely accurate lunar tables. Brown also studied the motion of the planets and calculated the orbits of Trojan asteroids. During the height of his professorship at Yale, Brown was also an active member of the American Mathematical Society as its president from 1915 to 1916. 

Since 1923, the Lunar Tables of Ernest William Brown have reduced the Moon’s complicated motion to a numerical theory that yielded serviceable tables, which only proves that his mathematical skills are way better than his mathematical skills. Brown’s Tables were adopted by nearly all of the national ephemerides in 1923 for their calculations of the Moon’s position and continued to be used with some modification until 1983. With the advent of programmable digital computers, Brown’s original trigonometric expressions, given in the introduction to his 1919 tables (and from which the tables had been compiled), began to be used for direct computation instead of the tables themselves. This also gained some improvement precision, since the tables had embodied some minor approximations, in a trade-off between accuracy and the amount of labor needed for computations in those days of manual calculation. 

By the middle of 20^th Century, the difference between Universal and Ephemeris Time had been recognized and evaluated and the troublesome empirical terms were removed. Further adjustments to Brown’s theory were made, arising from improved observational values of the fundamental astronomical constants used in the theory and from reworking Brown’s original analytical expansions to gain more precise versions of the coefficients used in the theory. Eventually in 1984, Brown’s work was replaced by results gained from more modern observational data – including data from lunar laser ranging - and altogether new computational methods for calculating the Moon’s ephemeris. 

A heavy smoker, Brown suffered from bronchial trouble for much of his life. He was afflicted by ill-health during most of the six years of his retirement and died in New Haven, Connecticut in 1938. 

Largest Known Prime Number Discovered in a University of Central Missouri Computer

It may be seen only as a mathematical curiosity to most of us, but did you know that very large prime numbers are indispensable in maintaining effective cyber security?

By: Ringo Bones 

Previously seen as a mere mathematical curiosity – and it still is by most of the population – but prime numbers – such as two, three, five and seven – numbers that are divisible only by themselves and one, play a vital role in computer data encryption. The latest prime number discovered so far back in January 20, 2016 is more than 22-million digits long – 22,338,618 digits long to be exact - five million digits longer than the previously discovered largest known prime number. Prime numbers this large could prove useful to computing in the future – which is sooner than you might think given the current rapidity of advances in hardware and software. 

The new prime number was found as part of the “endless mathematical quest” called the Great Internet Mersenne Prime Search or GIMPS, a global quest to find a particular type of large prime numbers. Mersenne Primes are named after a French monk, Marin Mersenne, who studied them in the 17^th Century during his spare time. Given that modern programmable digital computers processes data in binary code, they can be configured to hunt for Mersenne Prime Numbers by multiplying two by itself a large number of times, then taking away one. It is a relatively manageable calculation for today’s computers, but not every result is a prime number. This year’s newly discovered prime number is written as 2^74,207,281-1, which denotes the number two, multiplied by itself 74,207,280 times with one subtracted afterwards. Since it began 29 years ago, the GIMPS project has calculated the 15 largest Mersenne Prime Numbers and it is possible that there could still be an infinite number of them to discover.  

Very large prime numbers are important in computer encryption and help make sure that online banking, shopping and private messaging services are secure, but current encryption typically use prime numbers that are only hundreds of digits long – not millions. But given our increasing reliance on computers for online commerce and private messaging, the search for very large prime numbers can be very important to maintain encryption with ever increasing processing power – although mathematicians involved in the GIMPS project admitted in a statement that this year’s newly discovered prime number is “too large to currently be of practical value”. 

However, searching for large prime numbers is intensive work for computer processors and can have unexpected benefits. “One prime project discovered that there was a problem in some computer processors that only showed up in certain circumstances.” said Dr. Steven Murdoch, cybersecurity expert at University College London. This year’s new large prime number – the 49^th known Mersenne Prime Number, was discovered by Dr. Curtis Cooper at the University of Central Missouri. Although computers do most of the hard work, very large prime numbers are said to be discovered only after when a human operator takes note of the result. 

Ancient Babylonians: First To Use Sophisticated Geometry?

Previously known for starting an order of astrologer-priests, are the Ancient Babylonians are also the first ones to use sophisticated geometry? 

By: Ringo Bones

Before the recent research findings were published back in January 29, 2016, Ancient Babylonians were more famous for establishing the first order of astrologer-priests that would later evolve into what we know as the science of astronomy. But that all changed when evidence were uncovered that Ancient Babylonians were using a branch of geometry that only got widespread use in the 14^th Century. The new study is published in the journal Science. Its author, Prof. Mathieu Ossendrijver from the Humboldt University of Berlin, Germany said: “I wasn’t expecting this. It is completely fundamental to physics and all branches of science use this method.” The study suggests that sophisticated geometry – the branch of mathematics that deals with shapes – was being used at least 1,400 years earlier than previously thought. 

The possibility that Ancient Babylonians were using geometrical calculations to track the planet Jupiter across the night sky entered the realm of plausibility after Prof. Ossendrijver examined five Babylonian tablets that were excavated in the 19^th Century and which are now held in the British Museum’s archives. The script reveals that the Babylonians were using four-sided shapes, called trapezoids, to calculate when Jupiter would appear in the night sky and also the speed and distance that it traveled. “This figure – a rectangle with a slanted top – describes how the velocity of a planet, which is Jupiter, changes with time,” he said. “We have a figure where one axis, the horizontal side, represents time, and the other axis, the vertical side, represents velocity.” “The area of the trapezoid gives you the distance traveled by Jupiter along its orbit.” “What is so special is that this type of graph is unknown from antiquity – so making figures of motion in this rather abstract space of velocity against time – this is something very, very new.” It has been previously thought that complex geometry was first used by scholars in Oxford and Paris in Medieval times.    

The Ancient Babylonians once lived in what is now Iraq and Syria. The civilization emerged in about 1,800 BC. Clay tablets engraved in their Cuneiform writing system have already shown these people were advanced in astronomy. “They wrote reports about what they saw in the sky,” Prof. Ossendrijver told the BBC World Service’s Science In Action programme. “And they did this over a very long period of time, over centuries,” he says.  

Farewell Dr. John Nash....

As the world mourns of his recent tragic car crash, will the world be a sadder place without mathematician Dr. John Nash?

By: Ringo Bones

He’s probably more famous to the world at large via the 2001 movie A Beautiful Mind as he’s portrayed by actor Russell Crowe than by his works on game theory during the height of the Cold War and his being a 1994 Nobel Economics Prize laureate, but back in Saturday, May 23, 2015, mathematician Dr. John Nash together with his wife Alicia tragically dies in a car crash in the New Jersey Turnpike. The whole world – and not just the mathematicians’ corner – will be a sadder place without him. 

His work on noncooperative games, published in 1950 and known as the Nash equilibrium is considered as his most influential work of the 20^th Century. It provided a conceptually simple but powerful mathematical tool for analyzing a wide range of competitive situations, from cooperative rivalries to legislative decision making. His theories are used in economics, computing, evolutionary biology, artificial intelligence, accounting, politics and military theory. Dr. Nash also made contributions to pure mathematics that many mathematicians view as more significant than his Nobel-winning work on game theory, including solving an intractable problem in differential geometry derived from the work of the 19^th century mathematician G.F.B. Riemann. His achievements were more remarkable, colleagues say, for being contained in a small handful of papers published before he was 30.  

Given his lifelong struggle with depression and paranoid schizophrenia, it is quite remarkable feat indeed that Dr. Nash managed to communicate his mathematical brilliance to the whole world and managed to get recognition for it. Looks like Russell Crowe’s Tweet back in Sunday, May 24, 2015 is indeed both a touching and fitting tribute of Dr. Nash’s mathematical legacy.

Homer Simpson: Mathematical Genius?

Even though the world-renowned patriarch of The Simpsons is a well-known bumbling oaf, but did you know that Homer Simpson, at one time, exhibited his “mathematical genius”?

By: Ringo Bones

Though he is more well-known as a dunce and a bumbling oaf, Homer Simpson – a world-renown animated character often used by its creators to assess the prevailing zeitgeist – once displayed his mathematical genius and even predicted the mass of the Higgs Boson to within more than 90-percent accuracy 14 years before it was confirmed by a team of particle physicists operating CERN’s Large Hadron Collider. To the curious, this was from an episode titled “The Wizard of Evergreen Terrace” where Homer Simpson got envious of Thomas Alva Edison and tries to out-invent the “Wizard of Menlo Park”.

The episode would have been forgotten and would have languished in some obscure footnote of 20^th Century history if not for Dr. Simon Singh who wrote a book back in 2013 titled “The Simpsons And Their Mathematical Secrets” that included a spotlight on the 1998 episode “The Wizard of Evergreen Terrace” when Homer becomes “obsessed” with Thomas Alva Edison and decides to become an inventor. A scene in that particular The Simpsons episode script required a reading glasses-clad Homer to be placed in front of a chalkboard with complex mathematical equations. One of the writers on staff had a physicist friend who was researching the then-theoretical Higgs Boson particle and needed a “scientifically believable” illustration of Homer dabbling with a complex mathematical equation predicting the mass of the Higgs Boson particle – which is also known as the “God Particle”.

“That particular equation - as shown on TV on that particular 1998 The Simpsons episode – predicts the mass of the Higgs Boson” says Dr. Simon Singh. “If you work it out, you get the mass of the Higgs Boson that’s only a bit larger than the nano-mass of a Higgs Boson actually is. It is kind of amazing as Homer makes the prediction 14 years before it was discovered” (in the CERN’s Large Hadron Collider). For those super interested, the Higgs Boson particle was discovered to have a mass of 126 GeV.

The Higgs Boson particle is the “visible” that interacts with the Higgs Field – just like gravitons do with the gravitational field. The Higgs Field is an energy force that permeates across the universe that gives baryonic matter mass and allows the weak nuclear force and the electromagnetic force to co-exist in the “Standard Model” of how we think, so far, on how universal molecular physics work.

Even though Homer’s mathematical musings on the Higgs Boson somewhat reminds me of 1984 Nobel Physics Prize winner Carlo Rubbia’s mathematical musings that was pictured on a 1990 era Time magazine, the field of particle physics / quantum mechanics, mathematics can be a very useful tool in discovering and describing an “unknown particle” with better than 90-percent accuracy. Back in 1962, a then 32 year old Caltech physicist named Murray Gell-Mann proposed a search for a then theoretical particle called the Omega Minus. The particle’s existence was mathematically predicted by the Standard Model, Gell-Mann argued by a theory he formulated himself and by another physicist – a then 37 year old former Israeli Army officer named Yuval Ne’eman.

This theory which Gell-Mann called “The Eightfold Way” was based on an obscure mathematical system invented in the 19^th Century in order to manipulate numbers in groups of eight since each interacting nuclear particle had eight quantum numbers how subatomic baryons and mesons are organized into octets. Independently, Ne’eman did the same. Eventually, Gell-Mann was awarded the 1969 Nobel Physics Prize for his work on elementary particles and by 1971 began work in search for a then unknown family of particles called “quarks” using "The Eightfold Way".

Career Mathematicians: America’s Most Lucrative Profession?

Given that in a 2013 survey shows that they now earn about the same as - or slightly higher than - a typical Beverly Hills plastic surgeon, are mathematicians now America’s most lucrative profession? 

By: Ringo Bones

An overwhelming majority of the American public view career mathematicians as lone researchers into the most abstruse of matters, but frequently, America’s career mathematicians frequently work with other scientists. A survey conducted back in 2013 has shown that the median annual salary of a career mathematician in the United States was about U.S. $101,360 – comparable to that of a typical Beverly Hills plastic surgeon. Given that career tenured mathematicians in the United States could turn out to be one of the best-paid jobs, could there be any prevailing trends that lead to this rather fortunate outcome? Though, if you ask me, one should not put a cheap price on brain power.  

Since the internet boom of the latter half of the 1990s, “big data” and the analytical mathematical models describing them had become a hot commodity for the top commercial internet firms. Remember how career statistician Nate Silver (full name Nathaniel Read Silver) who used mathematics to show an uncannily accurate Obama victory prediction for the 2012 U.S. Presidential Race weeks before the November election via the use of big data is a powerful proof of the power of mathematics. Though years before, Nate Silver’s powerful analytic mathematical contribution to Major League Baseball has been immortalized in the movie Money Ball. 

Will – if favorable trends continue – career mathematicians will soon be earning more money than investment bankers? Could be, given that the leading internet firms had been inexplicably quick in commoditizing and monetizing big data and are also very keen on using analytical mathematics to describe and predict trends via big data – or to use higher mathematics to manipulate big data for commercial gain.