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NEWS: 13532385396179

Recently, James Davis found a counterexample to John H. Conway’s ‘Climb to a Prime’ conjecture, for which Conway was offering $1,000 for a solution.

The conjecture states the following:

Let n be a positive integer. Write the prime factorisation in the usual way, where the primes are written in ascending order and exponents of 1 are omitted. Then bring the exponents down to the line, omit the multiplication signs, giving a number f(n). Now repeat.”

For example, f(60) = f(2^2 x 3 x 5) = 2235. As 2235 = 3 x 5 x 149, f(2235) = 35149. Since 35149 is prime, we stop there.

Davis had a feeling that the counterexample would be of the form

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where p is the largest prime factor of n. This motivated him to look for x of the form

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The number Davis found was 13532385396179 = 13 x 53^2 x 3853 x 96179, which maps to itself under f (i.e. its a fixed point). So, f will never map this composite number to a prime, hence disproving the conjecture.

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NEWS: Abel Prize 2017

The Abel Prize 2017 has been awarded to Yves Meyer of the École normale supérieure Paris-Saclay in France due to his “pivotal role in the development of the mathematical theory of wavelets”, which has applications in data compression, medical imagery and the detection of gravitational waves.

Yves Meyer, en 2010, recevant le prix Gauss.

Meyer, aged 77, will receive 6 million Norwegian krone (around £600,000) for the prize, which aims to recognise outstanding contributions to mathematics. It is often called the ‘Nobel Prize’ of mathematics.

The Abel Prize was previously won by Andrew Wiles in 2016, who solved Fermat’s Last Theorem.

Biography

Yves Meyer, born on the 19th July 1939, grew up in Tunis in the North of Africa. After graduating from École normale supérieure de la rue d’Ulm in Paris and completing a PhD in 1966 at the University of Strasbourg, he became a professor of mathematics at the Université Paris-Sud, then the École Polytechnique and then Université Paris-Dauphine. He then moved to École normale supérieure Paris-Saclay in 1995, until formally retiring in 2008, although he still remains an associate member of the research centre.

To read a full biography of Meyer, click here.

Video of the Ceremony

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Sublime Symmetry

The De Morgan Foundation organised a one day synopsium called ‘Sublime Symmetry’ on the 13th January, which explored the mathematics behind William De Morgan’s ceramic designs.

William De Morgan was a ceramic designer in the late Victorian period.

“His conjuring of fantastical beasts to wrap themselves around the contours of ceramic hollowware and his manipulation of fanciful flora and fauna to meander across tile panels fascinated his contemporaries and still captivates today.

The ‘Sublime Symmetry’ exhibition highlights the influence of geometry in William De Morgan’s work, and particularly the use of symmetry to create his designs. This application of geometry naturally produces beautiful and visually striking images. Below are some images of his work:

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symmetries

Source: auckboro.wordpress.com

I find it fascinating how mathematics is so naturally interlaced in art and beauty, and so I really wanted to share this with you. Hopefully you found it interesting as well! The ‘Sublime Symmetry’ exhibition will be at the New Walk Gallery in Leicester until the 4th March, after which it will be displayed at the William Morris Gallery in Walthamstow on the 12th March until the 3rd September. [Source]

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NEWS: Vera Rubin

Vera Rubin died on 25th December 2016, aged 88. Rubin was an American astronomer who pioneered work on galaxy rotation rates.

In the 1960s and 70s, Rubin and her collogue Kent Ford noted a discrepancy between the predicted angular motion of galaxies and their observed motion, whilst studying galactic rotation curves.

Galactic Rotation Curve | Source: en.citizendium.org

This led Rubin to conclude that some unseen mass must be influencing the rotation of galaxies. As a result, in an attempt to explain the galaxy rotation problem, the theory of dark matter was created. The existence of this ‘invisible mass’ was first theorised by Fritz Zwicky in the 1930s but until Rubin and Ford’s work it had not been proven to exist.

Although initially it was met with skepticism from the scientific community, Rubin’s results have been confirmed over the subsequent decades.

Emily Levesque from the University of Washington said in an interview with Astronomy magazine:

This discovery “utterly revolutionised our concept of the universe and our entire field.”

It is considered one of the most significant results of the 20th century.

However, Rubin never received the Nobel Prize for Physics, although she was frequently mentioned as a candidate for it. It has been 53 years since a women has won a Nobel Prize in Physics, and now that Vera Rubin has passed away, she is no longer eligible. But, we can take some consolation in the fact that Rubin was indifferent to not being nominated for the Nobel Prize.

“Fame is fleeting,” Rubin said in 1990 to Discover magazine. “My numbers mean more to me than my name. If astronomers are still using my data years from now, that’s my greatest compliment.”

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NEWS: 2017 Breakthrough Prize in Mathematics

The Breakthrough Prizes is awarded in three categories: Life Sciences, Fundamental Physics and Mathematics, in recognition of great scientific advance.

This year, the Breakthrough Prize in Mathematics was awarded to Belgian mathematician Jean Bourgain, for his “multiple transformative contributions to analysis, combinatorics, partial differential equations, high-dimensional geometry and number theory”.

He has published, on average, 10 papers a year tackling some of the most challenging problems in a range of mathematical fields. For example, his most recent work is on the decoupling theorem: whilst Pythagoras showed that the length of the two shorter sides of a right-hand triangle are related to the hypotenuse, the decoupling theorem, proven by Bourgain and Ciprian Demeter, shows a similar relationship in the superposition of waves.

“It is of course an immense honour for me to be awarded the Breakthrough Prize and also an occasion to thank all those who helped me along my career. Over the years I have been fortunate to interact with several truly exceptional individuals who introduced me to different subjects and from whom I learned a lot. Collaborations on all levels played an important part in my work and are greatly valued. Appointments at research institutions such as the Institut des Hautes Études Scientifiques in Bures/Yvette (France) and the Institute for Advanced Study in Princeton provided ideal conditions for a full dedication to mathematics. I am most grateful for their trust. Last but not least, thanks to my family for their love and continuous support over the years.” – Jean Bourgain

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NEWS: New Twin Primes Found

PrimeGrid is a collaborative website with the aim to search for prime numbers. It is similar to GIMPS, which only searches for Mersenne Primes specifically. It works by allowing anyone to download their software and donate their “unused CPU time” to search for primes. PrimeGrid is responsible for many of the recent prime numbers that have been found, which includes “several in the last few months which rank in the top 160 largest known primes“.

On the 14th of September they announced their most recent discovery made by the user Tom Greer who discovered a new pair of twin primes. (Note that twin primes are prime numbers that differ by two.)

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The primes are “388,342 digits long, eclipsing the previous record of 200,700 digits”. These primes have been entered in the database for The Largest Known Primes, which is maintained by Chris Caldwell and are currently ranked 1st for twins and each are ranked 4180th overall.

Source

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NEWS: Hitchin wins Shaw Prize

This years Shaw Prize in mathematics was awarded to Professor Nigel Hitchin, from the University of Oxford. This award was honoured to him due to “his far reaching contributions to geometry, representation theory and theoretical physics. The fundamental and elegant concepts and techniques that he has introduced have had wide impact and are of lasting importance.”

File:Nigel Hitchin 2004.jpg

Hitchin’s innovative work has had a profound impact on a variety of areas in Mathematics, including algebraic geometry, differential geometry, complex analysis, topology, integrable systems, mathematical and theoretical physics.

One of his most notable achievements was deriving the self-duality equations, which are a “special class of solutions of the self-dual Yang-Mills equations“. He discovered that when described on a compact Riemann surface – a surface that can be covered by a finite collection of planes –  a “surprisingly rich space of solutions” is produced.

A typical feature of Hitchin’s work is as follows: he proves that objects in theoretical physics define new concepts in algebraic or differential geometry, and then uses rigorous mathematics to produce powerful and elegant results.

Marta Mazzocco describes how

… Hitchin defies the stereotype that mathematicians need to be in their early thirties to produce great results. When already in his sixties, Hitchin introduced the notion of co-Higgs bundle …“.

An apt winner of the Shaw Prize, I hope to hear of his work for many years to come.

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