Friday, January 05, 2018

50th Known Mersenne Prime Found!

Persistence pays off. Jonathan Pace, a GIMPS volunteer for over 14 years, discovered the 50th known Mersenne prime, 277,232,917-1 on December 26, 2017. The prime number is calculated by multiplying together 77,232,917 twos, and then subtracting one. It weighs in at 23,249,425 digits, becoming the largest prime number known to mankind. It bests the previous record prime, also discovered by GIMPS, by 910,807 digits.

Click here for more information.

Wednesday, December 06, 2017

Mathematicians Awarded $3 Million for Cracking Century-Old Problem

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.

Click here for more information.

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.

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.

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.

Click here for more information.

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..

Click here for more information.