Christopher Hacon, a mathematician at the University of Utah, and James McKernan, a physicist at the University of California at San Diego, won this year's Breakthrough Prize in Mathematics for proving a long-standing conjecture about how many types of solutions a polynomial equation can have. Polynomial equations are mainstays of high-school algebra — expressions like `x^2+5x+6 = 1` — in which variables are raised to the whole number exponents and added, subtracted and multiplied. The mathematicians showed that even very complicated polynomials have just a finite number of solutions.
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Wednesday, December 06, 2017
Thursday, August 24, 2017
Mathematical Secrets of Ancient Tablet Unlocked After Nearly a Century of Study
Dating from 1,000 years before Pythagoras’s theorem, the Babylonian clay tablet is a trigonometric table more accurate than any today, say researchers.
At least 1,000 years before the Greek mathematician Pythagoras looked at a right angled triangle and worked out that the square of the longest side is always equal to the sum of the squares of the other two, an unknown Babylonian genius took a clay tablet and a reed pen and marked out not just the same theorem, but a series of trigonometry tables which scientists claim are more accurate than any available today.
The 3,700-year-old broken clay tablet survives in the collections of Columbia University, and scientists now believe they have cracked its secrets.
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At least 1,000 years before the Greek mathematician Pythagoras looked at a right angled triangle and worked out that the square of the longest side is always equal to the sum of the squares of the other two, an unknown Babylonian genius took a clay tablet and a reed pen and marked out not just the same theorem, but a series of trigonometry tables which scientists claim are more accurate than any available today.
The 3,700-year-old broken clay tablet survives in the collections of Columbia University, and scientists now believe they have cracked its secrets.
Click here for more information.
Thursday, August 17, 2017
The Formula That Plots (Almost) Everything
Hold onto your logic hats! In this article we're going to explore one of the most amazing formulas in maths: Tupper's self-referential formula.
The protagonist of our story is the following inequality:
`1/2<\floor{mod(\floor{\frac{y}{17}}2^(-17\floor{x}-mod(\floor{y},17)),2))`
The plot works by either coloring a square or not coloring it: a square with coordinates (x, y) is colored if the inequality is true for x and y. If not the square is left blank.
If you plot the plot for many values of and , the outcome is the following:
I'll let that sink in a moment. No, your eyes are not deceiving you, the formula plots a bitmap picture of itself! Hence the name Tupper's self-referential formula (though Tupper never called this function that himself in his 2001 paper).
There is one missing detail, however. I haven’t told you the value of the number N on the y-axis.
Click here to read more information and see where Euler's equation appears.
The protagonist of our story is the following inequality:
`1/2<\floor{mod(\floor{\frac{y}{17}}2^(-17\floor{x}-mod(\floor{y},17)),2))`
The plot works by either coloring a square or not coloring it: a square with coordinates (x, y) is colored if the inequality is true for x and y. If not the square is left blank.
If you plot the plot for many values of and , the outcome is the following:
I'll let that sink in a moment. No, your eyes are not deceiving you, the formula plots a bitmap picture of itself! Hence the name Tupper's self-referential formula (though Tupper never called this function that himself in his 2001 paper).
There is one missing detail, however. I haven’t told you the value of the number N on the y-axis.
Click here to read more information and see where Euler's equation appears.
Sunday, July 16, 2017
Math 'Genius' Maryam Mirzakhani Dies At Age 40
Maryam Mirzakhani, an Iranian-born mathematician who was the first woman to win the coveted Fields Medal, died Saturday in a US hospital after a battle with cancer. She was 40.
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Friday, June 30, 2017
Mathematicians Deliver Formal Proof Of Kepler Conjecture
A team led by mathematician Thomas Hales has delivered a formal proof of the Kepler Conjecture, which is the definitive resolution of a problem that had gone unsolved for more than 300 years. The paper is now available online through Forum of Mathematics, Pi, an open access journal published by Cambridge University Press. This paper not only settles a centuries-old mathematical problem, but is also a major advance in computer verification of complex mathematical proofs.
The Kepler Conjecture was a famous problem in discrete geometry, which asked for the most efficient way to cram spheres into a given space. The answer, while not difficult to guess (it's exactly how oranges are stacked in a supermarket), had been remarkably difficult to prove. Hales and Ferguson originally announced a proof in 1998, but the solution was so long and complicated that a team of a dozen referees spent years working on checking it before giving up..
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The Kepler Conjecture was a famous problem in discrete geometry, which asked for the most efficient way to cram spheres into a given space. The answer, while not difficult to guess (it's exactly how oranges are stacked in a supermarket), had been remarkably difficult to prove. Hales and Ferguson originally announced a proof in 1998, but the solution was so long and complicated that a team of a dozen referees spent years working on checking it before giving up..
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Thursday, June 22, 2017
Monday, May 22, 2017
Eccentric French maths genius's 'scribblings' go online
Nearly 18,000 pages of notes by eccentric French maths genius Alexandre Grothendieck were posted online Wednesday by his alma mater, Montpellier University in southern France.
Grothendieck, who died aged 86 in 2014, "revolutionised an entire area of mathematics, algebraic geometry," said Jean-Michel Marin, head of an institute that bears the mathematician's name at the university.
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Grothendieck, who died aged 86 in 2014, "revolutionised an entire area of mathematics, algebraic geometry," said Jean-Michel Marin, head of an institute that bears the mathematician's name at the university.
Click here for more information.
Math Champion Wins With Answer About Pecking Chicks
A 13-year-old boy from Texas won a national math competition on Monday with an answer rooted in probabilities — and a dash of farming.
The boy, Luke Robitaille, took less than a second to buzz in at the Raytheon Mathcounts National Competition with the correct answer.
The question: In a barn, 100 chicks sit peacefully in a circle. Suddenly, each chick randomly pecks the chick immediately to its left or right. What is the expected number of unpecked chicks?
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The boy, Luke Robitaille, took less than a second to buzz in at the Raytheon Mathcounts National Competition with the correct answer.
The question: In a barn, 100 chicks sit peacefully in a circle. Suddenly, each chick randomly pecks the chick immediately to its left or right. What is the expected number of unpecked chicks?
Click here for more information.
Sunday, March 26, 2017
New Twist on Sofa Problem that Stumped Mathematicians and Furniture Movers
The Moving Sofa problem asks, what is the largest shape that can move around a right-angled turn? UC Davis mathematician Dan Romik has extended this problem to a hallway with two turns, and shows that a 'bikini top' shaped sofa is the largest so far found that can move down such a hallway.
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French Mathematician Yves Meyer Wins Top Prize for 'Wavelet Theory'
A French mathematician known for his pioneering work on a theory used for applications ranging from image compression to the detection of gravitational waves from the merging of black holes has earned one of the world's top prizes in mathematics.
Yves Meyer, a professor emeritus in mathematics at the École normale supérieure Paris-Saclay in France, will receive the Abel Prize, the Norwegian Academy of Sciences and Letters (which awards the prize) announced today (March 21) in Oslo. The prize, which comes with a cash award of 6 million Norwegian krone ($710,000), will be bestowed by King Harald V of Norway on May 23.
Meyer was honored largely "for his pivotal role in the development of the mathematical theory of wavelets," the academy said. His work on wavelets began in the mid-1980s.
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Yves Meyer, a professor emeritus in mathematics at the École normale supérieure Paris-Saclay in France, will receive the Abel Prize, the Norwegian Academy of Sciences and Letters (which awards the prize) announced today (March 21) in Oslo. The prize, which comes with a cash award of 6 million Norwegian krone ($710,000), will be bestowed by King Harald V of Norway on May 23.
Meyer was honored largely "for his pivotal role in the development of the mathematical theory of wavelets," the academy said. His work on wavelets began in the mid-1980s.
Click here for more information.
Thursday, January 19, 2017
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