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Saturday, February 23, 2019

Mathematician finds balance and beauty in math | Mathematics - MIT News

Jennifer Chu, covers mechanical engineering, mathematics, physics, aeronautics, astronautics, and earth, atmospheric, and planetary sciences as a writer for the MIT News Office inform, Zhiwei Yun seeks to connect seemingly disparate fields in mathematics.

On mentoring graduate students, Yun says that “every student has their own taste, and finds problems that interest themselves, and I encourage this. That should make the transition from student to researcher more smooth.”
Photo: Bryce Vickmark

Since he was a child growing up in Changzhou, China, Zhiwei Yun’s appetite for mathematics was nothing but linear, growing with each year as he absorbed lessons and solved increasingly difficult problems, both in the classroom and on his own time, with a zeal that can only come from finding one’s true passion.  

But when Yun was a graduate student, he felt his trajectory come up short. In his third year, he was in a panic as he faced for the first time the difference between learning established mathematics and discovering new math as a researcher.

But his advisor Bob MacPherson, a professor at the Institute for Advanced Study, kept encouraging him to find his own way, saying “only a problem found by yourself can really interest and drive you to the final solution.”..

After graduation, Yun headed to Princeton University to pursue a PhD in pure mathematics. When he did eventually land on a thesis topic, it was in representation theory, a branch of mathematics that seeks to represent abstract algebraic structures in concrete terms such as matrices or symmetries of shapes.

Representation theory plays a crucial role in the Langlands program, a series of associated conjectures devised by mathematician Robert Langlands, that seeks to connect the seemingly disparate fields of number theory and geometry. The Langlands program is considered one of the biggest projects in modern mathematical research, and Yun continues to work in the field of representation theory, with a focus on the Langlands program.
Read more...

Source: MIT News


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A philosopher argues that an AI can’t be an artist | Intelligent Machines - MIT Technology Review

Creativity is, and always will be, a human endeavor, insist Sean Dorrance Kelly, philosophy professor at Harvard. 

Photo: COURTESY OF THE ARTISTS

On March 31, 1913, in the Great Hall of the Musikverein concert house in Vienna, a riot broke out in the middle of a performance of an orchestral song by Alban Berg. Chaos descended. Furniture was broken. Police arrested the concert’s organizer for punching Oscar Straus, a little-remembered composer of operettas. Later, at the trial, Straus quipped about the audience’s frustration. The punch, he insisted, was the most harmonious sound of the entire evening. History has rendered a different verdict: the concert’s conductor, Arnold Schoenberg, has gone down as perhaps the most creative and influential composer of the 20th century.

You may not enjoy Schoenberg’s dissonant music, which rejects conventional tonality to arrange the 12 notes of the scale according to rules that don’t let any predominate. But he changed what humans understand music to be. This is what makes him a genuinely creative and innovative artist. Schoenberg’s techniques are now integrated seamlessly into everything from film scores and Broadway musicals to the jazz solos of Miles Davis and Ornette Coleman.

Creativity is among the most mysterious and impressive achievements of human existence. But what is it?...

Some mathematicians are like musical virtuosos: they are distinguished by their fluency in an existing idiom. But geniuses like Srinivasa Ramanujan, Emmy Noether, and Alexander Grothendieck arguably reshaped mathematics just as Schoenberg reshaped music. Their achievements were not simply proofs of long-standing hypotheses but new and unexpected forms of reasoning, which took hold not only on the strength of their logic but also on their ability to convince other mathematicians of the significance of their innovations. A notional AI that comes up with a clever proof to a problem that has long befuddled human mathematicians is akin to AlphaGo and its variants: impressive, but nothing like Schoenberg.
Read more...

Source: MIT Technology Review


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This Perpetual Calendar Hidden in an Italian Chapel Is a Mathematical Marvel | Stories - Atlas Obscura

The 19th-century device accurately tracks 4,000 years with nine cylinders and a crank, as Atlas Obscura reports.
 

The Perpetual Calendar tracks 4,000 years with nine rolls and a hand-operated crank.
Photo: Ranna Utida


A very early computer, quite unlike any other, is discreetly hanging in the sacristy of a small chapel in the heart of Turin, the beautiful Italian city at the foot of the Alps. Thousands of people pass by every day along Via Garibaldi, one of the main shopping thoroughfares in town, but hardly anyone knows it is there. That is because the tiny baroque jewel that owns the artifact is hidden in plain sight, and the church only opens on Saturday afternoons and Sunday mornings for mass. Still, anyone in-the-know or curious enough to find it will be awestruck by the Perpetual Calendar of Giovanni Antonio Amedeo Plana.

Built by the astronomer and mathematician in 1831, the Perpetual Calendar took 10 years to complete, from planning to assembly. The device, which resides in the Chapel of Bankers and Merchants, operates via a simple wooden crank under the adorned golden frame, a crank that hides a stunningly accurate universal mechanical calculator spanning the years 1 to 4,000. Want to know the day of the week that the Western Roman Empire fell to the barbarians, on September 4, 476? The calendar will tell you that it was a Monday. Or maybe the phase of the moon on the day you were born? Or the date of Easter a thousand years from now (April 18, 3019)? All of this information can be accessed by a pre-internet machine made of fragile wood and paper, and communicated through 46,000 little numbers carefully arranged around nine cylinders. Each of these is linked to a central one—the only adjustable part of the device—where the user can input the year. That cylinder synchronously regulates all the others through gears and chains...

Details of how the device actually works were more or less a secret until very recently. Plana, for all his assiduousness, did not leave any written material describing the mechanism inside. So in 2015 the prestigious Polytechnic University of Turin challenged its students to parse the algorithm that governs the machine. Four teams responded to the call. “This challenge has shown itself a useful way of valorizing the territory, proposing the use of engineering disciplines to improve the fruition of cultural goods,” the university’s vice dean of research, Enrico Macii, said in a statement at the time.

Source: Atlas Obscura


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Inside mathematician Cédric Villani’s plan to make France an AI leader | Siliconrepublic.com

Celebrated mathematician Cédric Villani has been tasked by the French government to create a national AI strategy, notes Ellen Tannam is a writer covering all manner of business and tech subjects.

Cédric Villani.
Photo: J Barande/Ecole polytechnique/Flickr (CC BY-SA 2.0)

AI is a competitive field and various global regions are competing to be at the very edge of innovation in the space. French president Emmanuel Macron is keen for the country and Europe to be leaders in artificial intelligence (AI) and he has appointed mathematician Cédric Villani to lead the charge.

Discussing his role with Bloomberg, Villani explained: “There is a deficit of contact between science and politics. It’s part of my job to reinforce that link. It will be France’s role to lead the rest of Europe.”

An accomplished academic 
Villani has a storied academic career, having taught at institutions such as Georgia Tech, the University of California Berkeley and Princeton University. In 2010, he received the Fields Medal for his work on Landau damping and the Boltzmann equation.

In a 150-page report published in 2018, the mathematician outlined a series of sectors to work on to secure a place for France as an AI leader: healthcare, security, transport and defence...

According to Wired, the French government is implementing about 95pc of his recommendations, but Villani said there is still a lot to do to make the lofty ambitions a reality. He said: “We’re currently very far from these goals. It’s going to take very voluntarist actions.”
Read more... 

Source: Siliconrepublic.com


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Thursday, February 21, 2019

Big data is being reshaped thanks to 100-year-old ideas about geometry | Science + Technology - The Conversation - UK

Photo: Ittay Weiss
Techniques from topology can help us understand DNA and improve drug development, explains Ittay Weiss,  Lecturer in Mathematics at the University of Portsmouth.
 
Photo: Elesey/Shutterstock

Your brain is made up of billions of neurons connected by trillions of synapses. And how they’re arranged gives rise to the brain’s functionality and to your personality. That’s why scientists in Switzerland recently produced the first-ever digital 3D brain cell atlas, a complete mapping of the brain of a mouse. While this is a colossal achievement, the great challenge now lies in learning to decipher the atlas. And it’s a huge one.

Science is full of this kind of problem: how to turn large amounts of information into useful insight. For many years, researchers relied on mathematics and statistics to explore data. The explosion of large datasets created by digital storage, the internet, and cheap sensors has led to the development of new techniques designed specifically to deal with this “big data”.

And now there is an emerging new approach based on century-old ideas that’s producing superior tools for understanding certain types of big data. Using the mouse’s brain as an example, its physical shape determines its functionality. But a precise description of this shape, which we now have, doesn’t automatically reveal everything about how the brain works. 

Behind the physical shape lies a more abstract shape formed by the interconnections within the brain. Capturing aspects of this shape by applying techniques from the study of what’s known as “topology” can help reveal a deeper understanding of the brain’s functioning. This same guiding principle of using topological techniques on big data also has applications in drug development and other cutting-edge endeavours...

Millions of years ago, evolution was confronted with a similar problem. DNA in cells is a molecule composed of two coiled up chains. Each chain is a very long wire, built up from a sequence of small molecules called nucleobases. When a cell divides, these wires unwind, replicate and then coil up again. But just like wires in a bag, the strands of DNA can become tangled, which prevents the cell from dividing and causes it to die.
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Source: The Conversation - UK 


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A mathematical formula for sharing fair and square | Science - The Irish Times

Photo: Peter Lynch

That’s Maths: Even the naming of the Thue-Morse sequence is about fair play, says Peter Lynch, emeritus professor at UCD School of Mathematics & Statistics – he blogs at thatsmaths.com.

Sequencing is important in sports: penalty shoot-outs in football, service order in tennis tie-breaks and choice of colour in chess matches.
Photo: Clive Rose/Getty Images

It is common practice in science to name important advances after the first discoverer or inventor. However, this process often goes awry. A humorous principle called Stigler’s Law holds that no scientific result is named after its original discoverer.

This law was formulated by Prof Stephen Stigler of the University of Chicago in his publication “Stigler’s law of eponymy”. He pointed out that his “law” had been proposed by others before him so it was, in a sense, self-verifying. 

The Calculus Wars
Occasionally, mathematical inventions are made simultaneously by more than one person. Perhaps the greatest example is the formulation of calculus by Isaac Newton and Gottfried Wilhelm Leibniz. Jason Bardi, The Calculus Wars. The conflict between British and European mathematicians raged for decades before joint credit for independent discovery was accepted.

The Calculus Wars
The ensuing controversy over priority was described in a book by Jason Bardi, The Calculus Wars. The conflict between British and European mathematicians raged for decades before joint credit for independent discovery was accepted.
 
Axel Thue (1863-1922) and Marston Morse (1892-1977)
A remarkable numerical sequence that has been discovered several times by different mathematicians in different circumstances illustrates Stigler’s Law. It was originally called the Morse sequence when, in 1921, it was popularised by the American mathematician Marston Morse, who applied it in differential geometry. Today, it is usually called the Thue-Morse sequence: the Norwegian mathematician Axel Thue discovered the sequence while studying “combinatorics” on words; this was in 1906, well before Morse. But, more recently, the name Prouhet has been prefixed to the title of the sequence, which was first studied by Eugène Prouhet in 1851...

But what use is the Thue-Morse sequence? It arises in a remarkably wide variety of contexts. It is valuable in number theory, combinatorics, computer graphics, fractal geometry and equitable sharing. Let’s look at the last of these.

Source: The Irish Times  


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Top 10 Greatest Mathematicians Of All Time: Check Them Out | Science - ValueWalk

Here are Vikas Shukla, technology reporter at Value Walk's list of top 10 Greatest Mathematicians Of All Time below.
 

Photo: geralt / Pixabay

Mathematics has been around for thousands of years, and several mathematics geniuses have contributed to the field with their revolutionary discoveries that changed the world. It is at the core of almost every aspect of our lives including satellites, computers, medicines, astronomy, and advanced technologies. Here we are going to take a look at the top 10 greatest mathematicians of all time based on their contributions to the field.

Top 10 greatest mathematicians Dozens of mathematicians have made revolutionary contributions to the field of mathematics. So, it’s pretty tricky to pick the top 10 and leave many other legends out. Muhammad Al-Khowarizmi invented algebra; Aryabhatta discovered zero; John Von Neumann gave the Von Neumann architecture; and Paul Erdos published about 1,500 papers. We believe these are the top 10 greatest mathematicians.
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Source: ValueWalk


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Wednesday, February 20, 2019

Stories of African-American STEM Societies: Part 2 — From Psychologists to Mathematicians | Absolutely Maybe - PLoS Blogs

After the slow first wave of African-American STEM societies from 1895 to 1947 (part 1), a new wave swept in at the end of the 1960s. So there have been a few golden jubilees, and more coming, inform Hilda Bastian, Absolutely Maybe - PLoS Blogs.

At the Conference for African American Researchers in the Mathematical Sciences (CAARMS) in Berkeley, 1995
Lenore Blum, via Wikimedia Commons
The new organizations in the ’60s and early ’70s were fueled by the energy of the Black Power, student, and civil rights movements in a tumultuous time for society and universities. The organizations they created, in turn, empowered them, changing their professions, and sometimes challenging knowledge and how their disciplines work in profound ways as well...

10. Mathematicians 
African-American mathematicians had long struggled to participate in national mathematical meetings. Even when William S. Claytor gave an address to the American Mathematical Society (AMS), he was not allowed to stay at the hotel. And that was still going on into the ’60s. [PDF] Walter R. Talbot put it this way:
When I entered the college teaching scene, it was 1934… It was 35 years later before I had a chance to start existing in the national activities of the mathematical bodies.

He also said:
Nowadays our promising youth are even more menacingly threatened by exposure to teachers who have not only been vigorously and successfully indoctrinated relative to the difficulty of mathematics, but also have been convinced to their viscera that Blacks, however successful in sports, music, politics, law, medicine, and so on and so on, are abysmally and irrevocably hopeless as far as mathematics is concerned.
Talbot organized and got funding for the meetings to form an African-American mathematical society. [PDF] In 1969, 17 gathered at the annual national mathematical meeting and formed the National Association of Mathematicians (NAM).
Read more... 

Additional resources
 
Robert F. Boyd, from his 1902 paper “”What are the causes of the great mortality among the Negroes in the cities of the South, and how is that mortality to be lessened?”
Photo: via Project Gutenberg

Stories of African-American STEM Societies: Part 1 — The First Wave (1895 to 1947) by Hilda Bastian, Absolutely Maybe - PLoS Blogs.

Source: PLoS Blogs 


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How to Become an Actuary in 9 Steps | Life Insurance - TheStreet.com

Actuaries can make a very high salary, but it takes a ton of work. Here's what you need to know, recommends Steve Fiorillo, writer for TheStreet.



Are you someone with a love of data and statistics? Someone with a keen interest in computer software? If you're a math whiz, or even just someone with a passion for the subject, an awful lot of companies could use you and there are ways to make a career out of it.

One such career is an actuary. It's a career that may be heavily associated with insurance but can be far more wide-reaching than that. If you put in the work needed to become a professional actuary, you could find yourself in a lucrative, stable career. But be warned: it's a lot of work.

If you think this could be a worthwhile line of work that's worth the prep, you'll need to ask: what is an actuary, and how can I become one?

What Does an Actuary Do? 
An actuary is essentially an analyst for risk management, doing the math to figure out how risky something might be and determining how best to minimize it in the future.

Actuaries are most often needed in the insurance industry where there is a lot of financial risk involved in health insurance, life insurance and home insurance. Here, actuaries use data and a number of factors to determine just how risky an insurance policy is to give to someone.

An actuary is expected to determine how likely a risky scenario is to play out - and then determine a way to minimize that damage. If risky events keep happening, an actuary could be asked to use their numbers to figure out how to decrease the times they occur.

Much of this is done through computer software, since the math is particularly advanced - it's why you'll need not just math courses, but computer science ones in your education as well... 

How to Become an Actuary 
Actuaries are expected to be in high demand over the next several years, so it's smart to get prepared for it sooner than later. Becoming an actuary is a multi-step process that is still ongoing even in the beginning of your actual career.

Here's how to get your start as an actuary.
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Source: TheStreet.com


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Never say ‘I am not a maths person’ in front of children: expert | gulfnews.com


Paul Bradwell, Subject Leader Mathematics, Kings School Barsha, Dubai, explains how parents and teachers can make the subject be appreciated for its beauty and application.
 
Photo: Supplied


1. Who is responsible for making maths seem like a chore? Parents? Teachers?
It can be very frustrating for a student to be sat across from a parent with them saying, “I was never very good at maths” or “I’m not a maths person”. This can be damaging as it normalises the idea of being bad at maths for the child and validates any thoughts that being good at maths is a natural ability. There is a responsibility on all of us to ensure that every child believes the truth, which is that anyone can study maths successfully. Any student can succeed at anything if they are willing to put in the effort.
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Source: gulfnews.com


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