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Charles Thacker 1943/02/26 – 2017/06/12

The pioneering personal computer designer Charles Thacker, a co-inventor of Ethernet, has died at the age of 74 in nearby Palo Alto. In 1972, just like personal computers of today, his Xerox Alta did not require a remote serial monitor since its tilt and swivel portrait screen was mapped directly to its hardware internals, it boasted a GUI supported directly by its OS, a three button mouse, and a detachable keyboard.

Charles Thacker based some, but not all, of the features of the Xerox Alta, on a computer system developed by Douglas Engelbart and demonstrated in 1968. These feature can be seen in a video (including interactively) called The Mother of a Demos. See below.


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Charles P. Thacker, an electrical engineer who played an early, central role in some of the most important ideas in personal computing and computer networking, died on Monday at his home in Palo Alto, Calif. He was 74.

His daughter Christine Thacker said the cause was complications of esophageal cancer.

In the 1970s, Mr. Thacker was part of a group that designed the first modern personal computer, the Alto, working out of the Xerox Palo Alto Research Center, known as PARC.

More here (obit.): https://goo.gl/ZZ4TtV


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In this short one-minute commercial, Xerox introduces its vision for the office of the future. Years ahead of its time, the 1972 Xerox Alto featured Ethernet networking, a full page display, a mouse, laser printing, e-mail, and a windows-based user interface. Although it's high price limited sales, the Alto was a groundbreaking invention and the inspiration for the Apple Macintosh and Microsoft Windows operating systems.

Video (YT ~1min): https://goo.gl/AkxJp6


The Xerox Alto and Charles Thacker's engineering were in part inspired by the earlier 1968 demo of the NLS by Douglas Engelbart.

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The Alto was conceived in 1972 in a memo written by Butler Lampson, inspired by the oN-Line System (NLS) developed by Douglas Engelbart, and Dustin Lindberg at SRI International (SRI). It was designed mostly by Charles P. Thacker. Industrial Design and manufacturing was sub-contracted to Xerox, whose Special Programs Group team included Doug Stewart as Program Manager, Abbey Silverstone Operations, Bob Nishimura, Industrial Designer. An initial run of 30 units was produced by Xerox El Segundo (Special Programs Group), working with John Ellenby at PARC and Doug Stewart and Abbey Silverstone at El Segundo, who were responsible for re-designing the Alto's electronics. Due to the success of the pilot run, the team went on to produce approximately 2,000 units over the next ten years.

Xerox Alto (Wikip): https://goo.gl/WKdyPS


Talking of Douglas Engelbart and the inspirational NLS...


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On December 9th, 1968 Doug Engelbart appeared on stage at the Fall Joint Computer Conference in San Francisco to give his slated presentation, titled "A Research Center for Augmenting Human Intellect." He and his team spent the next 90 minutes not only telling about their work, but demonstrating it live to a spellbound audience that filled the hall.

Instead of standing at a podium, Doug was seated at a custom designed console, where he drove the presentation through their NLS computer residing 30 miles away in his research lab at Stanford Research Institute (SRI), onto a large projection screen overhead, flipping seamlessly between his presentation outline and live demo of features, while members of his research lab video teleconferenced in from SRI in shared screen mode to demonstrate more of the system.

More here: https://goo.gl/FNUWxP


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Video: The Mother of All Demos (Internet Archive): https://goo.gl/JWH1Mf


Image: https://goo.gl/2skVz1
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Jean Sammet 1928/03/23 – 2017/05/20

Mathematician and Computer Scientist Jean Sammet who reached the top of her profession despite the resistance of the educational system to the progress of smart women, has died at the age of eighty-nine. Amongst other accomplishments she was part of a small team that provided an initial design for the business-oriented computer programming language COBOL.


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The programming language Ms. Sammet helped bring to life is now more than a half-century old, but billions of lines of COBOL code still run on the mainframe computers that underpin the work of corporations and government agencies around the world.

More here (obit.): https://goo.gl/fD0MwF


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Jean E. Sammet was born on March 23, 1928 in New York City. Jean and her sister Helen were born to Harry and Ruth Sammet who were both lawyers. Jean and Helen attended public elementary schools in Manhattan. Sammet had a strong interest in mathematics but was unable to attend the Bronx High School of Science because it did not accept girls. Instead, Sammet attended Julia Richman High School.

Sammet chose to enroll at Mount Holyoke College based on the strength of its mathematics program. Sammet majored in mathematics and took education courses, which allowed her to be certified to teach high school mathematics in New York. She minored in political science. After graduating from Mount Holyoke, Sammet pursued graduate studies at the University of Illinois, where she received her MA in 1949. While taking courses toward a Ph.D., she was a teaching assistant in the Mathematics department at the University of Illinois from 1948 to 1951.

In 1951 Sammet began looking for a position in education. Sammet was forced to search for positions in New Jersey because New York City was not hiring new teachers. The authorities in New Jersey determined that Sammet was missing two courses from her studies: a course in education and one in the history of New Jersey. Sammet fought this determination, stating that her knowledge of New Jersey history did not strengthen her ability to teach mathematics in high school. This forced Sammet to seek other types of employment.

More here (Wikip): https://goo.gl/qGaUZw


Image: Computer History Museum https://goo.gl/ACYdmA
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Cavendish Science

The wealthy aristocratic Cavendish family over the centuries has had an interest and sometimes competence in Mathematics and Science and as recently as the 19th Century donated the funds needed to create Britain's first University Laboratory; the now famous Cavendish Laboratory at Cambridge.


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From the 1600s to the 1800s, scientific research in Britain was not yet a professional, publicly-funded career. So the wealth, status and freedom enjoyed by British aristocrats gave them the opportunity to play an important role in pushing science forwards - whether as patrons or practitioners. The Cavendish family produced a whole succession of such figures.

In the 1600s, the mathematician Sir Charles Cavendish and his brother William collected telescopes and mathematical treatises, and promoted dialogue between British and Continental thinkers. They brought Margaret Cavendish, William's second wife, into their discussions and researches, and she went on to become a visionary, if eccentric, science writer, unafraid to take on towering figures of the day like Robert Hooke.

In the 1700s, the brothers' cousin's great-grandson, Lord Charles Cavendish, emerged as a leading light of the Royal Society. Underpinned by his rich inheritance, Charles' son Henry became one of the great experimental scientists of the English Enlightenment. And in the 1800s, William Cavendish, Henry's cousin's grandson, personally funded the establishment of Cambridge University's Cavendish Laboratory. In subsequent decades, the Lab become the site of more great breakthroughs.

Listen here: https://goo.gl/5vp66x
Available worldwide online as a stream, MP3 download or Podcast. Also see links for references and more reasding.

There is also a dedicated mobile app.
Post: https://goo.gl/oJBwf0

For those who prefer a read...


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All this created, of course, a great deal of interest in Cambridge, particularly among the group of young mathematicians, mostly recent graduates, who were likely to be the first students at the new lab. It might at first seem surprising that the prospective students should nearly all be mathematicians, and in addition mostly graduates, but maths had, at that time, a very firm hold on Cambridge life. Introduced in 1747, the Mathematical Tripos eventually became the course for all serious students. Indeed, until 1850 no student could obtain an honours degree without first qualifying in the Maths Tripos, and those of a non-mathematical disposition either "ploughed it", like Macaulay, or entirely refused to graduate, like Gray. Mathematics was described as the vampire of the Cambridge schools, and had absorbed not only philosophy, but also the arts and natural sciences. The nineteenth century finally saw the breaking of this monopoly with the establishment of several Triposes for Classics (1822), Moral Sciences (1851), and, as we have seen, Natural Sciences, also in 1851. But the development of these Triposes was relatively slow, and even in 1874 the N.S.T. could boast only 19 students, compared with some 1500 a century later. The Mathematical Tripos itself, with its rigid order of merit, was an extremely competitive one and undergraduates in it could not fairly be expected to do practical work as well. So the first students at the projected Cavendish Laboratory were bound to be Mathematics graduates.

More here (The Foundation of the Cavendish Laboratory): https://goo.gl/ID274A


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An inaugural lecture was then, even more than now, a special occasion to be attended by all the leading personalities of the University. However, Maxwell made only a casual announcement of his inaugural lecture which was not to be in the Senate House, as expected, but in an out-of-the-way lecture room. Consequently only his students got to hear of it and it was to them, rather than a general gathering, that he delivered an exciting and interesting lecture, mapping out his plans for the future of Cambridge physics. "The familiar apparatus of pen, ink and paper will no longer be sufficient for us, and we shall require more room than that afforded by a seat and desk, and a wider area than that of a blackboard", he said, emphasising the revolution in learning that the new laboratory was about to initiate. "We should begin, in the lecture room, with a course of lectures on some branch of physics, aided by experiments of illustration, and conclude, in the laboratory, with a course of experiments of research." This was perhaps the first positive statement that the new laboratory was to be a place of original research as well as of teaching.

When, a few days later, Maxwell began his first course with a lecture on Heat, his students had the delight of seeing the lecture room packed with their tutors, lecturers, professors and all the important personages of the University. Thinking that this was his first public appearance they sat, in their formal academic dress, while Maxwell, "with a perceptible twinkle in his eye", gravely expounded the difference between Fahrenheit and Centigrade, and the principle of the air thermometer.

More here (Maxwell's Cavendish): https://goo.gl/5U2KdF


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In addition to the gift of new equipment, Rayleigh also expanded the workshops, but his most important step was the setting up of an organised practical course. Garnett left after Maxwell's death, and in his place were appointed jointly (Sir) R.T. Glazebrook and W.N. Shaw. Together they perfected the new type of practical teaching that is now standard - a series of set experiments are laid out and allotted in rota to the students. Handouts are available and the demonstrator wanders round solving any problems that arise. Trivial as this step forward may seem, it completely revolutionised practical instruction. Rayleigh himself did a lot of preparatory work, and Glazebrook and Shaw's book on Practical Physics became the standard (and only) practical textbook for many years.

More here (Rayleigh's Time): https://goo.gl/VRvdCx


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Margaret Lucas Cavendish (post): https://goo.gl/9bjTuI


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Duke of Devonshire (Wikip): https://goo.gl/LlHvaL


Image: PD https://goo.gl/o1WFMD
William Cavendish, 7th Duke of Devonshire, by Henry Rose Barraud, c1880_
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Different Fields

Under the auspices of the French National Centre for Scientific Research (CNRS) and their National Institute for Mathematical Sciences (INSMI) in particular, Christoph Sorger its director, interviews two Mathematicians notable for their early promise and French connections: Cédric Villani, Fields Medalist 2010, and Artur Ávila, Fields Medalist 2014.

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Christoph Sorger: Artur, you received the medal more recently, in August 2014 in Seoul. Tell us about your experience.
Artur Ávila: Immediately after the event, there was obviously a bit of pressure to talk about it, especially in the media. There seems to be much greater interest in mathematics in France than in other countries. It’s odd that the French value a prize like this one so much—I don’t know why it’s different elsewhere. I am particularly keen to make the most of this opportunity to promote mathematics in my native country of Brazil: things are on the right track there for the moment, but no one knows what the future holds. The next International Congress of Mathematicians (ICM) will be held in Rio de Janeiro in 2018. I see it as a kind of duty for me to be on hand, doing whatever I can since I’m not especially good at that kind of thing, and to help boost the image of mathematics in the collective imagination.

More here (interview): https://goo.gl/q4h1he


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The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The Fields Medal is sometimes viewed as the highest honour a mathematician can receive. The Fields Medal and the Abel Prize have often been described as the mathematician's "Nobel Prize". The Fields Medal differs from the Abel in view of the age restriction mentioned above.

The prize comes with a monetary award, which since 2006 has been C$15,000 (in Canadian dollars). The colloquial name is in honour of Canadian mathematician John Charles Fields.[5] Fields was instrumental in establishing the award, designing the medal itself, and funding the monetary component.

Fields Medal (Wikip): https://goo.gl/v63st7

CNRS: https://goo.gl/l42Qa3

INSMI: https://goo.gl/wmoVZe

Image from first link.
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Early Islamic Maths

This week's In Our Time featured the subject of Early Islamic Maths and its origins. Expert guests were: Colva Roney-Dougal, Reader in Pure Mathematics, at the University of St Andrews; Peter Pormann, Professor of Classics & Graeco-Arabic Studies at the University of Manchester; and Jim Al-Khalili, Professor of Physics at the University of Surrey.


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Melvyn Bragg and guests discuss the flourishing of maths in the early Islamic world, as thinkers from across the region developed ideas in places such as Baghdad's House of Wisdom. Among them were the Persians Omar Khayyam, who worked on equations, and Al-Khwarizmi, latinised as Algoritmi and pictured above, who is credited as one of the fathers of algebra, and the Jewish scholar Al-Samawal, who converted to Islam and worked on mathematical induction. As well as the new ideas, there were many advances drawing on Indian, Babylonian and Greek work and, thanks to the recording or reworking by mathematicians in the Islamic world, that broad range of earlier maths was passed on to western Europe for further study. You may learn that Omar Khayyam was famous for more than his Rubaiyat.

More here (stream (~45 mins), download MP3, podcast, further reading, links): https://goo.gl/dz88bN

In Our Time Archive: https://goo.gl/gFI4rF

Subscribe: https://goo.gl/mkqPMk

Related post: Golden Age https://goo.gl/qTBpH5


Image: https://goo.gl/gXZN5J
Omar Khayyam Maths Paper
"Cubic equation and intersection of conic sections" the first page of two-chaptered manuscript kept in Tehran University
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Johannes Kepler

In the days before the Internet made knowledge so easy to come by, I stood bewildered in this square in a small village near Leonberg in Germany, astonished to see this monument and to read that Johannes Kepler was born in Weil der Stadt, where his Father was the mayor. The adjacent Kepler museum seemed the only other monument to him there, and was closed all the time, and so the one available reference to Johannes Kepler was a handful of words on the plinth (http://goo.gl/M6eW3a).

Melvyn Bragg and guests discuss the German astronomer Johannes Kepler (1571 - 1630). Although he is overshadowed today by Isaac Newton and Galileo, he is considered by many to be one of the greatest scientists in history. The three laws of planetary motion Kepler developed transformed people's understanding of the Solar System and laid the foundations for the revolutionary ideas Isaac Newton produced later. Kepler is also thought to have written one of the first works of science fiction. However, he faced a number of challenges. He had to defend his mother from charges of witchcraft, he had few financial resources and his career suffered as a result of his Lutheran faith.

The expert guests include Ulinka Rublack, Professor of Early Modern European History at the University of Cambridge and Fellow of St John's College, who was born in Tübingen near Stuttgart and Kepler's birthplace, Weil der Stadt.

Professor Ulinka Rublack wrote a book, The astronomer & the witch : Johannes Kepler's fight for his mother, which tells the story of how Kepler's Mother was accused of witchcraft by Ursula Reingold in the village of Eltingen (https://goo.gl/yQD4vG) near Leonberg, who was, by the way, arguing with his brother Christoph about money.

Kepler's widowed mother Katharina was incarcerated for over a year, sometimes chained-up, verbally tortured with territio verbalis (terrifying descriptions of the physical torture in-store for her) and then tried for six years. Professor Rublack explains how Johannes had to drop what he was doing and return without explanation to save his Mother and his own reputation.

Johannes Kepler (1571-1630) was one of the most admired astronomers who ever lived and a key figure in the scientific revolution. A defender of Copernicus's sun-centered universe, he famously discovered that planets move in ellipses, and defined the three laws of planetary motion. Perhaps less well known is that in 1615, when Kepler was at the height of his career, his widowed mother Katharina was accused of witchcraft. The proceedings led to a criminal trial that lasted six years, with Kepler conducting his mother's defense. In 'The Astronomer and the Witch', Ulinka Rublack pieces together the tale of this extraordinary episode in Kepler's life, one which takes us to the heart of his changing world. First and foremost an intense family drama, the story brings to life the world of a small Lutheran community in the centre of Europe at a time of deep religious and political turmoil-- a century after the Reformation, and on the threshold of the Thirty Years' War. Kepler's defense of his mother also offers us a fascinating glimpse into the great astronomer's world view, on the cusp between Reformation and scientific revolution. While advancing rational explanations for the phenomena which his mother's accusers attributed to witchcraft, Kepler nevertheless did not call into question the existence of magic and witches. On the contrary, he clearly believed in them. And, as the story unfolds, it appears that there were moments when even Katharina's children wondered whether their mother really did have nothing to hide ...

The astronomer & the witch : Johannes Kepler's fight for his mother (local library): https://goo.gl/7pXLP2

Johannes Kepler (Wikip): https://goo.gl/3Cz9mI

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In Our Time: Johannes Kepler (listen here): https://goo.gl/tXRCyy
(Stream, download MP3, podcast, links, reading)

Image: https://goo.gl/MZYcjv
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Margaret Cavendish

Danielle Dutton has written a book about the rather unique and possibly eccentric, flamboyant dresser and extravagant bower, and some say mad, 17th Century English aristocrat, Margaret Cavendish. The Duchess of Newcastle-upon-Tyne was the first female to attend +The Royal Society where she met René Descartes and Robert Boyle and had a row with Robert Hooke over the reliability of scientific data based on the primitive microscopes, and inconsistent lighting, of the time, and their inability to see inside the small organisms at their true mechanisms.

Margaret Cavendish also wrote poetry, plays, romances and essays and was a Philosopher, Scientist and was one of the world's earliest Science Fiction writers.

The problems of lenses and lighting were, if you like, the known unknowns about the reliability of microscopes. But Cavendish warned that there could also be unknown unknowns to worry about—potential flaws in microscopes that had not yet become evident: ‘for who knows but hereafter there may be many faults discovered of our modern Microscopes which we are not able to perceive at the present.’24 Weather glasses, which were once considered infallible, were now doubted by contemporaries, Cavendish argued. Consequently, it would be unsafe to base claims of experimental truth on such ‘brittle, inconstant and uncertain ground’ as the untested microscope.

More here (Royal Society blog post): https://goo.gl/hmr6ae



Margaret the First was not a queen, like Katherine of Aragon or Ann Boleyn. But she could be considered an early queen in the history of women’s literature: Margaret Lucas Cavendish, a 17th century Duchess, the daughter of Royalists, fled to France when Charles I was overthrown. Cavendish was an accomplished writer and thinker who published poems, philosophy, plays and utopian science fiction. Danielle Dutton’s novel, Margaret the First, published by Catapult, is a literary page-turner, which explores Cavendish’s adventurous life, weaving historical details into a spool of crafted, poetic prose.

More here (book review): https://goo.gl/QHyR4j

Margaret The First (local library): https://goo.gl/P0mG5W



Virginia Woolf wasn't terribly impressed with Margaret Cavendish.

[...] When she heard that the Queen, since the outbreak of the Civil War, had fewer maids-of-honour than usual, she had “a great desire” to become one of them. Her mother let her go against the judgement of the rest of the family, who, knowing that she had never left home and had scarcely been beyond their sight, justly thought that she might behave at Court to her disadvantage. “Which indeed I did,” Margaret confessed; “for I was so bashful when I was out of my mother’s, brothers’, and sisters’ sight that . . . I durst neither look up with my eyes, nor speak, nor be any way sociable, insomuch as I was thought a natural fool.” The courtiers laughed at her; and she retaliated in the obvious way. People were censorious; men were jealous of brains in a woman; women suspected intellect in their own sex; and what other lady, she might justly ask, pondered as she walked on the nature of matter and whether snails have teeth? But the laughter galled her, and she begged her mother to let her come home. This being refused, wisely as the event turned out, she stayed on for two years (1643-45), finally going with the Queen to Paris, and there, among the exiles who came to pay their respects to the Court, was the Marquis of Newcastle. To the general amazement, the princely nobleman, who had led the King’s forces to disaster with indomitable courage but little skill, fell in love with the shy, silent, strangely dressed maid-of-honour. [...]

More here: https://goo.gl/IYjbfD



You can judge the philosophy of Margaret Cavendish for yourself.

Margaret Lucas Cavendish was a philosopher, poet, scientist, fiction-writer, and playwright who lived in the seventeenth century. Her work is important for a number of reasons. One is that it lays out an early and very compelling version of the naturalism that is found in current-day philosophy and science. It also offers important insights that bear on recent discussions of the nature and characteristics of intelligence and the question of whether or not the bodies that surround us are intelligent or have an intelligent cause. Another reason that the work of Cavendish is important is that it anticipates some of the central views and arguments that are more commonly associated with figures like Thomas Hobbes and David Hume. She also anticipates discussions in the work of contemporary philosophers, such as David Chalmers and Colin McGinn, about whether or not our ability to understand how matter thinks is relevant to the question of whether it does think.

Margaret Cavendish (Stanford Encyclopedia of Philosophy): https://goo.gl/adCIHu



Margaret Cavendish (Wikip): https://goo.gl/r00ier

The Margaret Cavendish Society: https://goo.gl/Yq8eGR

Image: PD https://goo.gl/keInQJ
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Modern Mathematics

Reddit user/No-Spoilers asked r/AskScience Have any new forms of math been created in recent years? Number Theorist u/functor7 and others replied.

So much.

Alan Turing basically invented the math that is the groundwork for every computer ever. Also played a significant role in WWII as a code-breaker, where he constructed one of the first modern computers.

Alexander Grothendieck, arguably the most important mathematician of the 20th Century. Revolutionized how we think of arithmetic and geometry as the same thing. He died relatively recently, so there are a few good and accessible articles about his life, which was interesting on its own.

John Nash, _another key figure in the 20th Century. Notably, he laid the groundwork for Game Theory, which has applications all over the place.

Emmy Noether was a prominent female mathematician in a time when the profession was all but closed to women, whose contribution cannot be overstated. She helped set the tone of math from the early 20th Century, and contributed a lot to physics as well.

Nicholas Bourbaki isn't one mathematician, but an underground secret society of prominent mathematicians who published under this pseudonym, who had radical views about math and were a major reason why math is a formal/rigorous as it is today.

Paul Erdos is quite a character. He never really stayed put and collaborated with hundreds of mathematicians as a result. If you're familiar with the Bacon Number (the number of films removed an actor is from Kevin Bacon), then the Erdos Number is the same thing but for math (and the Bacon Number was inspired by the Erdos Numbers).

Terry Tao is a contemporary mathematical genius. He's attacking some of the most difficult unsolved problems today, using radical ideas. He already won the Fields Medal, one of the most prestigious awards in math, and at a relatively young age (even for the Fields Medal).

Shinichi Mochizuki, probably one of the most fascinating mathematicians alive today. For 20 years, he worked in relative isolation creating a ridiculously powerful and abstract theory to solve one of the biggest unsolved problems in math, the ABC-Conjecture. His results have been known since 2012, but even the best mathematicians alive can't understand it yet. There was a big conference at the beginning of the year to assess whether or not the ideas seemed legit enough to invest the hundreds/thousands of hours that even the top mathematicians would need to invest to understand Mochizuki's ideas. There are some pretty good layman articles about him out there.

I'll stop here, but the list could go one for a long time.

EDIT:

How could I forget Srinivasa Ramanujan, one of the most unconventional, yet incredibly influential, mathematicians ever. In a time of increasing rigor, Ramanujan didn't care for proofs, yet came up with astounding results and ideas based wholly off of otherworldly intuition and we're still trying to understand some of them even today! According to him, "otherworldly" is quite literal, since they are insights given to him by the Hindu gods. His story is quite tragic though.

More and all the even more links here (AskScience): https://goo.gl/pK7hi5

Image: PD https://goo.gl/mVk1Lh
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David Thouless Nobel Laureate 2016

Here's something a little different about this year's Nobel Prize for Physics. It's a brief profile on the man, David Thouless, and his background, thanks to research by Phoebe Keane of the BBC.  It's a part of a recommended 'get smart' series called Profile that provides 15 minute briefings on prominent figures and features recordings and interviews.

Professor J. Michael Kosterlitz: "I was my first year at Cambridge University, sitting in this lecture hall waiting for a lecture on Mathematics for Physics and then this young kid, looked more like a schoolboy, wandered in and we all thought, he looks a bit out of place, he's a bit young for this. Then suddenly, he ended up on the podium and started talking and everyone looked at each other and thought "Good God, are we being taught by a schoolchild?""

More and listen here: https://goo.gl/vqIj9Z
(Stream, Podcast, MP3)

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Zeno's Paradoxes

Melvyn Bragg, Mathematician +Marcus du Sautoy, and Philosophers Barbara Sattler and James Warren, explore Zeno's Paradoxes and how they may still inform and interact with the modern world, including Quantum Physics.  These discussions reveal interesting differences between the Mathematical and Philosophical understanding of the limits of certain infinite series and infinity itself.

Melvyn Bragg and guests discuss Zeno of Elea, a pre-Socratic philosopher from c490-430 BC whose paradoxes were described by Bertrand Russell as "immeasurably subtle and profound." The best known argue against motion, such as that of an arrow in flight which is at a series of different points but moving at none of them, or that of Achilles who, despite being the faster runner, will never catch up with a tortoise with a head start. Aristotle and Aquinas engaged with these, as did Russell, yet it is still debatable whether Zeno's Paradoxes have been resolved.

Listen, and more (links and further reading) here: https://goo.gl/B5fJSt
(Stream, podcast, download MP3)

A related series of five fifteen minutes episodes is being presented from a largely Philosophical perspective with, at least to me, a mildly annoying didactic style, by Adrian Moore of Oxford University.

Adrian Moore starts his journey through philosophical thought on infinity over the last two and a half thousand years. In the first episode, he finds out why the idea made the Greeks so uncomfortable and introduces us to some of the first great thinkers on infinity.

We meet Pythagoras and his followers who divided the world into two fundamental cosmic principles. On one side was everything they thought of as limited or finite, and therefore good, and on the other everything they considered unlimited or infinite, and therefore bad.

The Pythagoreans thought they could explain the world around them in terms of the numbers - 1, 2, 3, 4, etc. - which we use to count finite collections of things, and they were utterly dismayed when they discovered that not every calculation produced the neat answer they expected. According to legend, one of their number was shipwrecked at sea for revealing this discovery to their enemies!

And we meet Zeno of Elea who, after wrestling with the notion of infinity, came to the conclusion that movement itself was impossible.

Horror of the Infinite (episode 1): https://goo.gl/UQkQHj
(Stream, podcast, download MP3)

Use next/previous episode function to navigate.
A History of the Infinite: (episode guide may be muddled) https://goo.gl/fNMtIL

Image: Martin Grandjean https://goo.gl/cNRGN0
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