Keyword: mathematics

Mathieu Ossendrijver of Humboldt University in Berlin found the tablet while combing through the collections at the British Museum. The written record gives instructions for estimating the area under a curve by finding the area of trapezoids drawn underneath. Using those calculations, the tablet shows how to find the distance Jupiter has traveled in a given interval of time. Until now, this kind of use of trapezoids wasn't known to exist before the 14th century. ... By 400 B.C. Babylonian astronomers had worked out a coordinate system using the ecliptic, the region of the sky the sun and planets move...

Two pages from the book "Arithmetica Infinitorum," by John Wallis. In the table on the left page, the square that appears repeatedly denotes 4/pi, or the ratio of the area of a square to the area of the circumscribed circle. Wallis used the table to obtain the inequalities shown at the top of the page on the right that led to his formula. Credit: Digitized by Google ============================================================================================================= In 1655 the English mathematician John Wallis published a book in which he derived a formula for pi as the product of an infinite series of ratios. Now researchers from the University...

A new trend in math at elementary schools around the country has parents pulling out their hair. Mainly because it is the opposite of how most of today's adults were taught to do simple multiplication in the first place. According to a Common Core math worksheet that's gone viral, an elementary child today cannot just say, "5 x 3 = 15." Instead they have to change the multiplication problem to addition before solving the equation. However, if the child says, "5 + 5 + 5 = 15," they will still lose points because the problem must be written as it...

Here's a "repeated addition" Common Core problem that's taught in third grade in US schools: Use the repeatedaddition strategy to solve: 5x3 If you answer the question with "5+5+5=15,” you would be wrong. The correct answer is "3+3+3+3+3.” Mathematically, both are correct. But under Common Core, you're supposed to read "5x3" as "five groups of three." So "three groups of five" is wrong. According to Common Core defenders, this method will be useful when students do more advanced math. This way of reading things, for instance, can be used when students learn matrices in multivariable calculus in high school. But...

A Life in Games John Horton Conway claims to have never worked a day in his life. This adaptation from the biography Genius at Play shows how serious advances such as the surreal numbers can spring out of fun and games. Princeton University, Office of Communications, Denise ApplewhiteJohn Horton Conway at Princeton University in 2009. By: Siobhan RobertsAugust 28, 2015 Comments (6) Gnawing on his left index finger with his chipped old British teeth, temporal veins bulging and brow pensively squinched beneath the daybeforeyesterdayÂ’s hair, the mathematician John Horton Conway unapologetically whiles away his hours tinkering and thinkering Â— which...

Steven A. Camarota is the Director of Research and Karen Zeigler is a demographer at the Center for Immigration Studies. While employers argue that there are not enough workers with technical skills, most prior research has found little evidence that such workers are in short supply. This report uses the latest Census Bureau data available to examine the science, technology, engineering, and math (STEM) fields. Consistent with other research, the findings show that the country has more than twice as many workers with STEM degrees as there are STEM jobs. Also consistent with other research, we find only modest levels...

John Forbes Nash Jr. was a mathematical genius who had his life chronicled in the movie A Beautiful Mind. One of Nash’s colleagues says that just days before he died in a New York taxi cab accident, he had discussed his latest and possibly most brilliant discovery to date. Mathematician Cédric Villan says that Nash told him that he had replaced Einstein’s Theory of Relativity and that the new equation would further explain quantum gravity. The Daily Mail reports that on May 20, 2015, just three days before the tax cab accident that would take his life, Nash spoke to...

Sir Isaac Newton...came to the realization that the math that had been used thus far to describe physical motion of massive bodies, simply would not suffice... Newton developed the Calculus in which this way of approaching moving bodies, he was able to accurately model the motion of not only Halley’s comet, but also any other heavenly body that moved across the sky. ... Newton recognized that Kepler’s mathematical equation for planetary motion, Kepler’s 3rd Law ( P2=A3 ), was purely based on empirical observation, and was only meant to measure what we observed within our solar system. Newton’s mathematical brilliance...

John F. Nash Jr. is widely known as the subject of the Oscarwinning film “A Beautiful Mind,” but his contributions to the advancement of human knowledge are far greater. Nash paved the way for game theory to spread from a collection of toy cases in mathematics to a generalizable theory applicable to virtually anything — board games, economics, politics, international relations — to the point where now it’s practically a mode of critical thinking in its own right. On Saturday, the 86yearold mathematician and his wife, Alicia, were killed in a car crash in New Jersey. There have been...

Mathematicians Chase Moonshine’s Shadow Researchers are on the trail of a mysterious connection between number theory, algebra and string theory. In 1978, the mathematician John McKay noticed what seemed like an odd coincidence. He had been studying the different ways of representing the structure of a mysterious entity called the monster group, a gargantuan algebraic object that, mathematicians believed, captured a new kind of symmetry. Mathematicians weren’t sure that the monster group actually existed, but they knew that if it did exist, it acted in special ways in particular dimensions, the first two of which were 1 and 196,883.McKay, of...

Infinity Is a Beautiful Concept Â– And ItÂ’s Ruining Physics By Max Tegmark  February 20, 2015 9:00 am I was seduced by infinity at an early age. Georg CantorÂ’s diagonality proof that some infinities are bigger than others mesmerized me, and his infinite hierarchy of infinities blew my mind. The assumption that something truly infinite exists in nature underlies every physics course IÂ’ve ever taught at MITÂ—and, indeed, all of modern physics. But itÂ’s an untested assumption, which begs the question: Is it actually true?A Crisis in Physics There are in fact two separate assumptions: Â“infinitely bigÂ” and Â“infinitely...

Of all the numerals, "0"  alone in green on the roulette wheel  is most significant. Unique in representing absolute nothingness, its role as a placeholder gives our number system its power. It enables the numerals to cycle, acquiring different meanings in different locations (compare 3,000,000 and 30). With the exception of the Mayan system, whose zero glyph never left the Americas, ours is the only one known to have a numeral for zero. Babylonians had a mark for nothingness, say some accounts, but treated it primarily as punctuation. Romans and Egyptians had no such numeral either... Found on...

On the last day of the 2014 campaign, Democrats knew they were in trouble.

DENVER — Results for a new standardized test for science and social studies came in on Monday and they likely put frowns on educators and parents. ... Just 17 percent of Colorado fourth and seventhgraders scored “strong” or “distinguished” on social studies tests. Those are the scores necessary to for students to be considered on track to be ready for college and a career, ... Achievement gaps still persisted between white and students of color. For example, in fourthgrade social studies, 6 percent of Hispanic/Latino students and 7 percent of AfricanAmerican students have “strong” or “distinguished command” of the subject....

Among the 34 OECD countries, the US performed below average in mathematics and is ranked 27th ... While the U.S. spends more per student than most countries, this does not translate into better performance (e.g. the Slovak Republic, which spends around $53k per student, performs at the same level as the US, which spends over $115k per student).

Thousands of children in swaths of wartorn Syria, now controlled by dreaded Islamic State militants, can no longer study math or social studies under new diktats issued by the jihadists. While sports is banned, the children will not be allowed to learn about elections and democracy. Instead, the children will be subjected to the teachings of the radical Islamist group. And any teacher who dares to break the rules "will be punished." ... The Sunni militant group has captured a slew of Syrian and Iraqi cities in recent months as it tries to establish a caliphate, or Islamic state, spanning...

I home school a young girl. In years past, we have gone to the local air show and done such things as measure the tops and bottom of wings and rotos and figure the ratio or difference between the area of the top of the wing versus the bottom and estimated which wings had more lift than others. We measure how much area the wheels occupied on the ground and consulted with the crew chief what the tire pressure was and calculated the weight of the plane. In years past we were able to see F18s form a vapor cone...

by Gina Cassini  Top Right NewsOne student got tired of being dumbeddown by Common Core's convoluted "standards" to do basic arithmetic. "Standards" like how to add two numbers, which the student was told to do like THIS: WHAT? It's enough to make you pull your hair out. So when he was given his next basic arithmetic assignment, to find the difference between 180 and 158 (180158), this 5th grade student just did it his own way  the right way  and dissed Common Core with single, awesome word:

Robert Krulwich/NPRPoor Johannes Kepler. One of the greatest astronomers ever, the man who figured out the laws of planetary motion, a genius, scholar and mathematician — in 1611, he needed a wife. The previous Mrs. Kepler had died of Hungarian spotted fever, so, with kids to raise and a household to manage, he decided to line up some candidates — but it wasn't going very well.Being an orderly man, he decided to interview 11 women. As Alex Bellos describes it in his new book The Grapes of Math, Kepler kept notes as he wooed. It's a catalog of small...

Nearly 90 years after Werner Heisenberg pioneered his uncertainty principle, a group of researchers from three countries has provided substantial new insight into this fundamental tenet of quantum physics with the first rigorous formulation supporting the uncertainty principle as Heisenberg envisioned it. In the Journal of Mathematical Physics, the researchers reports a new way of defining measurement errors that is applicable in the quantum domain and enables a precise characterization of the fundamental limits of the information accessible in quantum experiments. Quantum mechanics requires that we devise approximate joint measurements because the theory itself prohibits simultaneous ideal measurements of position...

For a new study ranking the best jobs of 2014, jobs website CareerCast.com did some numbercrunching and found Â— perhaps not surprisingly Â— that crunching numbers is a pretty good gig.With a median income of $101,360 and a 23% projected job growth rate by 2022, mathematician topped the siteâ€™s roundup of the most desirable jobs. CareerCast points to the â€śexponentially growing popularity of mathematicsâ€ť in everything from healthcare and technology to sports and politics.Â“Mathematicians are employed in every sector of the economyâ€¦ from Wall Street brokerages to energy exploration companies to IT R&D labs to university classrooms,Â” CareerCast publisher Tony...

The Silicon Valley touts itself as a meritocracy where people climb the economic ladder based on the power of their ideas. But many people of color can't even find that ladder, let alone climb it. They're not part of the valley's whitemaledominated "bro culture," advocates say, and aren't connected to the social and educational networks where companies recruit talent.

Mathematics has been called the language of the universe. Scientists and engineers often speak of the elegance of mathematics when describing physical reality, citing examples such as Ď€, E=mc2, and even something as simple as using abstract integers to count realworld objects. Yet while these examples demonstrate how useful math can be for us, does it mean that the physical world naturally follows the rules of mathematics as its "mother tongue," and that this mathematics has its own existence that is out there waiting to be discovered? This point of view on the nature of the relationship between mathematics and...

It is one the oldest mathematical problems in the world. Several centuries ago, the twin primes conjecture was formulated. As its name indicates, this hypothesis, which many science historians have attributed to the Greek mathematician Euclid, deals with prime numbers, those divisible only by themselves and by one (2, 3, 5, 7, 11, etc.). Under this assumption, there exists an infinite number of pairs of prime numbers whose difference is two, called twin primes (e.g., 3 and 5), but nobody has been able to confirm this so far.

A Jewel at the Heart of Quantum Physics Artist’s rendering of the amplituhedron, a newly discovered mathematical object resembling a multifaceted jewel in higher dimensions. Encoded in its volume are the most basic features of reality that can be calculated — the probabilities of outcomes of particle interactions. Physicists have discovered a jewellike geometric object that dramatically simplifies calculations of particle interactions and challenges the notion that space and time are fundamental components of reality.“This is completely new and very much simpler than anything that has been done before,” said Andrew Hodges, a mathematical physicist at Oxford University who has...

It is impossible that Christianity is not God's revelation of truth to man. Simply impossible. The math proves it beyond question. It doesn't take faith to believe that one plus one equals two, and it doesn't take faith to identify the religion which has mathematical certainty in its corner. God didn't have to give us mathematical proof of His existence, but He did it anyway. God didn't have to give us proof of Christianity, but He chose to do so. And God didn't have to give us proof of His love for us, but that is exactly what He did....

Every pure mathematician has experienced that awkward moment when asked, “So what’s your research good for?” There are standard responses: a proud “Nothing!”; an explanation that mathematical research is an art form like, say, Olympic gymnastics (with a much smaller audience); or a stammered response that so much of pure math has ended up finding application that maybe, perhaps, someday, it will turn out to be useful. That last possibility is now proving itself to be dramatically true in the case of category theory, perhaps the most abstract area in all of mathematics. Where math is an abstraction of the...

Most people have heard of “evolutionary biology.” But the term “evolution” is often applied in a broader sense (gradual, naturalistic changes over long ages) to other fields of study. Some people study geology or astronomy from an evolutionary perspective. But has anyone ever studied “evolutionary mathematics”? What would an evolutionist mathematician study? Can the existence of numbers and mathematical laws be explained by a timeandchance naturalistic origin? To answer these questions, let us first consider some background material and definitions. Mathematics is the study of the relationships and properties of numbers. What, then, are numbers? That may seem like an...

Certain measures of brain anatomy were even better at judging learning potential than traditional measures of ability such as IQ and standardized test results, says study author Kaustubh Supekar of Stanford University. These signatures include the size of the hippocampus — a string bean–shaped structure involved in making memories — and how connected the area was with other parts of the brain. The findings suggest that kids struggling with their math homework aren’t necessarily slacking off, says cognitive scientist David Geary of the University of Missouri in Columbia. “They just may not have as much brain region devoted to memory...

A fifth of adults are so bad at math that they struggle to perform basic mental arithmetic, a survey has revealed. More than a third can only manage sums that total less than 100 and have to use a calculator for anything larger. One in 50 people were stumped by adding or subtracting in their head if the total was more than ten. And one in three parents believed their children’s ability exceeded their own. …

An Indian teen has recently proposed a solution to an unsolved problem in mathematics. The 17yearold young achiever, Rutvik Oza, a student of The H. B. Kapadia New High School, from Ahmedabad, Gujarat has now put a full stop to another open problem in the field of maths by providing a closed formula for the problem called Reve's Puzzle (also popularly known as the 4peg Tower of Hanoi Problem). When asked about how was he feeling, "Thrilled! I really didn't realize at first that the problem that I had solved was an open problem in mathematics. It was only later...

HetchingerEd is offering a rather radical proposal to increase the number of American students who graduate college: dump math. Specifically, the argument is that since many college students, a disproportionately large number of them of an AfricanAmerican or Hispanic descent, are unprepared to tackle collegelevel mathematics courses, they might be stymied by a requirement that all those receiving a degree from a particular institution must pass the freshman version of the course. A fifth of students entering a fouryear college don’t have the needed math skills to pass the course and are forced into remediation. Nearly half of community college...

Bill Thurston, who made fundamental contributions to our understanding of lowdimensional manifolds and related structures, died on Tuesday, aged 65.

A TYPICAL American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high school and college, all too many students are expected to fail. Why do we subject American students to this ordeal? I’ve found myself moving toward the strong view that we shouldn’t. My question extends beyond algebra and applies more broadly to the usual mathematics sequence, from geometry through calculus. State regents and legislators — and much of the public — take it as selfevident that every young person should be made to master polynomial functions and parametric...

How to Win a ThreeWay Gunfight Truels are things guaranteed to make any Western fifty percent better — by adding a third person to a duel. Each person can choose his or her target, and the worst person might very well be the winner — provided they play it smart. Learn how to win yourself a truel, gunslingerstyle. Game theorists have thought about the problem of duels for a long time. As much as the Old West was depicted as a lawless place where anything might happen, it was also known for hanging its criminals high — which meant that...

A 16yearold schoolboy has solved a mathematical problem which has stumped mathematicians for centuries, a newspaper report said. The boy put the historical breakthrough down to “schoolboy naivety.” Shouryya Ray, who moved to Germany from India with his family at the age of 12, has baffled scientists and mathematicians by solving two fundamental particle dynamics problems posed by Sir Isaac Newton over 350 years ago, Die Welt newspaper reported on Monday. Ray’s solutions make it possible to now calculate not only the flight path of a ball, but also predict how it will hit and bounce off a wall. Previously...

If one manages to graduate from high school without the rudiments of algebra, geometry and trigonometry, there are certain relatively highpaying careers probably offlimits for life  such as careers in architecture, chemistry, computer programming, engineering, medicine and certain technical fields. For example, one might meet all of the physical requirements to be a fighter pilot, but he's grounded if he doesn't have enough math to understand physics, aerodynamics and navigation. Mathematical ability helps provide the disciplined structure that helps people to think, speak and write more clearly. In general, mathematics is an excellent foundation and prerequisite for study in...

Enlarge Image Laserinduced switching. Experimental images showing two small domains with magnetic orientation up (white) and down (black). Each laser pulse reverses the direction repeatedly. Credit: Johan Mentink; Richard Evans (inset) An ultrashort heat pulse can predictably flip a bit in a magnetic memory like the one in your hard drive. The surprising effect could ultimately lead to magnetic memories hundreds of times faster and more energy efficient than today's hard drives. It also provides a way to control the direction in which a bit is magnetized without applying something else that has a direction, such as a magnetic...

LAST FALL, President Obama threw what was billed as the first White House Science Fair, a photo op in the giltmirrored State Dining Room. He tested a steering wheel designed by middle schoolers to detect distracted driving and peeked inside a robot that plays soccer. It was meant as an inspirational moment: children, science is fun; work harder. Politicians and educators have been wringing their hands for years over test scores showing American students falling behind their counterparts in Slovenia and Singapore. How will the United States stack up against global rivals in innovation? The president and industry groups have...

We all know the standard drill for a math class. The teacher delivers lectures on a new concept, students do some homework problems, and after a few weeks they take an exam. Some do well, some do poorly, and then it's on to the next topic.

Finite formula found for partition numbersFor centuries, some of the greatest names in math have tried to make sense of partition numbers, the basis for adding and counting. Many mathematicians added major pieces to the puzzle, but all of them fell short of a full theory to explain partitions. Instead, their work raised more questions about this fundamental area of math. On Friday, Emory mathematician Ken Ono will unveil new theories that answer these famous old questions. Ono and his research team have discovered that partition numbers behave like fractals. They have unlocked the divisibility properties of partitions, and developed...

Benoît B. Mandelbrot, a maverick mathematician who developed an innovative theory of roughness and applied it to physics, biology, finance and many other fields, died Thursday in Cambridge, Mass. He was 85...Dr. Mandelbrot coined the term “fractal” to refer to a new class of mathematical shapes whose uneven contours could mimic the irregularities found in nature...In a seminal 1982 book, “The Fractal Geometry of Nature,” Dr. Mandelbrot defended mathematical objects that he said others had dismissed as “monstrous” and “pathological.” Using fractal geometry, he argued, the complex outlines of clouds and coastlines, once considered unmeasurable, could now “be approached in...

Benoit B. Mandelbrot, a maverick mathematician who developed an innovative theory of roughness and applied it to physics, biology, finance and many other fields, died on Thursday in Cambridge, Mass. He was 85. His death, at a hospice, was caused by pancreatic cancer, his wife, Aliette, said. He had lived in Cambridge. Dr. Mandelbrot coined the term “fractal” to refer to a new class of mathematical shapes whose uneven contours could mimic the irregularities found in nature. “Applied mathematics had been concentrating for a century on phenomena which were smooth, but many things were not like that: the more you...


Those who most loudly proclaim the need for qualified math and science teachers are literally being challenged on how much they value science, technology, engineering, and mathematics. “Despite the fact that Washington’s Legislature and Governor last session passed a law (House Bill 2621) intending to accelerate the teaching and learning of math and science, the system is hardwired to do the opposite,” the Center for Reinventing Public Education found. “In a new analysis from the University of Washington’s Center on Reinventing Public Education (CRPE), researchers demonstrate that the average pay for math and science teachers in Washington state lags behind...

Walter Rudin, a preeminent mathematician who taught at UWMadison for 32 years, died Thursday at the age of 89 after suffering from Parkinson’s disease. Rudin’s advanced work on mathematical analysis may have been of interest to only a small worldwide audience, but his three textbooks were translated into multiple languages and used by generations of college students. “Especially because of his textbooks, he was known universally among undergraduates and graduates studying mathematics,” said Alexander Nagel, a colleague in the UWMadison math department. Rudin was born in Vienna, Austria, on May 2, 1921, to a prosperous Jewish family. His family fled...

At least 25 people are reported to have been killed in an explosion on the Metro system in central Moscow, with a second blast coming shortly afterwards. The first blast happened at the city's central Lubyanka station, reports quoting security sources said. A second explosion happened at the Park Kultury station, Russian news agency Tass reported. Ten people were injured in the first blast, Tass said, quoting the emergencies ministry. The number of casualties at the second blast is not yet clear.

The forecasts of global warming are based on the mathematical solutions of equations in models of the weather. But all of these solutions are inaccurate. Therefore no valid scientific conclusions can be made concerning global warming. The false claim for the effectiveness of mathematics is an unreported scandal at least as important as the recent climate data fraud. Why is the math important? And why don't the climatologists use it correctly? Mathematics has a fundamental role in the development of all physical sciences. First the researchers strive to understand the laws of nature determining the behavior of what they are...

boom in affordable housing in the 1950s was helped by the invention of a distinctive multifunctional piece of equipment: the backhoe. Its strong yet relatively slender articulated arm allowed precise yet rapid placement for digging or lifting. The manipulative device is trim and fast, since hoses transfer power to it from a powerful hydraulic pump within the main chassis. The "arm" of the backhoe makes many people think the equipment design is similar to a human arm, but what makes it so versatile is that it is actually more like a giant human finger. If a valuable piece of equipment...

Enlarge ImageObviously. The area of this triangle is 13, a congruent number. Credit: L. Blizard/Science Quick! What do the numbers 5, 6, 7, 13, 14, 15, 20, 21, 22, and 23 have in common? If you said they're all "congruent" numbersnumbers related to the areas of certain trianglesthen you may be one of those folks who scored an 800 on your math SAT. Even if that answer didn't leap to mind, you may be intrigued to know that mathematicians have now cataloged the congruent numberswhich are easy to define but not so easy to spotup to a trillion. A...


