Sunday, May 21, 2017

Mancala/Oware, a math game with a 5000-year-old history

Left: an African mancala board

To close out the math posts, here's an ancient board game from Africa. Today, we can learn to play online. It's usually played on a wooden board, but in a pinch, players can use an egg carton and forty-eight small stones, seeds or marbles. Mancala has a long history. Also called oware, it has many variants. Math began with the Ancient Sumerians, and this game is thought by many to have originated with them, five millennia ago.

Was its original function record-keeping, or did it have a ritual purpose? Historians aren't sure, but the presence of the game boards at African temples, laid out in alignment with the rising and setting sun, suggests some sort of symbolic significance.

It is thought that Arab traders brought the game from Sumeria (today Iraq and Kuwait) to ancient Egypt, from whence it spread over Africa and beyond. In its various forms, this mathematical game of skill and strategy is still played widely today.

Saturday, May 20, 2017

Julia Robinson, a rare mathematical woman

Much like Germany's David Hilbert, American mathematician Julia Robinson saw her breed as a single nation, "without distinction of geographical origins, race, creed, sex, age, or even time." (quoted in Marcus du Sautoy)

Born in Missouri, Julia Bowman lost her mother and was raised by her grandmother in the Arizona desert. A childhood illness afforded lots of time to think. After marrying a fellow mathematician, Rafael Robinson, she settled in California. Advised against having children by her physician, she devoted her energy to mathematics, tackling Hilbert's tenth problem of existential definability.

After spending much time on this problem, she collaborated with a twenty-year-old Russian mathematician, Yuri Matiyasevich, and visited him in Leningrad. Together they proved Hilbert's tenth problem unsolvable. Julia was delighted to meet the young man, opining that she must have been waiting for him to be born and grow up so they could work together on their proof.

Robinson was elected to the National Academy of Sciences in 1975, the first woman mathematician to receive this honour. She received a professorship at Berkeley the same year. In 1983, she was elected president of the American Mathematical Society, again the first woman to hold this post. Sadly, she died of leukemia before her term was complete.

Each year, in her honour, The American Institute of Mathematical Sciences holds the Julia Robinson Mathmatics Festival.

Friday, May 19, 2017

Bertrand Russell, mathematician and philosopher

Image from sapiengames

Bertrand Russell (1872-1970) was a well known 20th century mathematician and philosopher. His books include Principles of Mathematics (1903), Why I am not a Christian (1927), The Conquest of Happiness (1930) , and A History of Western Philosophy (1945).

He made new mathematical contributions to formal logic and discovered what came to be called Russell's paradox. He is ranked with Kurt Godel as one of his century's top logicians.

In 1950, he received the Nobel Prize for Literature, and in the 1960s, his anti-nuclear and anti-war protests inspired the youth of the day.

Russell was known for his bons mots, many of which are ironic or paradoxical. He said for instance, "...fools and fanatics are always so certain of themselves, and wiser people so full of doubts." Another of his statements: "It has been said that man is a rational animal. All my life I have been searching for evidence which could support this." He said that humans were born "ignorant, not stupid," and "made stupid by education," and that "To be without some things that you want is an indispensable part of happiness."

His famous personal essay, What I have lived for, is considered a model of its kind of writing.

Thursday, May 18, 2017

Alan Turing, mathematician, marathon runner, and father of computing

Alan Turing was an avid cyclist and marathon runner, and the mathematician who conceived of artificial intelligence. He built the world's first computer at the WWII code-breaking centre of Bletchley Park, enabling the break of the German naval code, Ultra. Many believe this breakthrough shortened the war by a couple of years. Math and computing science were not his only areas of knowledge. For his groundbreaking work on morphogenesis, he was made a Fellow of the Royal Society. 
Sadly, although Turing's nation used his skills in war time, the government treated him shockingly afterwards. In 1948, he'd been named Deputy Director of the computer laboratory at Manchester University, where he became the first person to use a computer for mathematical research. 

The trouble began in Manchester in 1952. While investigating a theft of money from Turing, the police learned of a homosexual affair which he did not attempt to hide, though homosexual activity was illegal. He was tried for gross indecency and found guilty. To avoid a prison sentence, he agreed to take estrogen injections. 

In the post-war period, Alan Turing was still working for GCHQ, with Hugh Alexander, whom he'd known at Bletchley Park. However, under the cold war alliance with the Americans, who considered homosexuals ineligible for security clearance, his own government stripped him of the clearance he'd had since the war. 

In June of 1954, he was found by his housekeeper, dead of cyanide poisoning. The presence of a half-eaten apple and the presence of cyanide on his fingers led to speculation that he'd died accidentally, while carrying out an experiment. However, the coroner found the death to be suicide. Yet it seemed strange; for one thing, he'd just enrolled in an upcoming conference. At the time of his death, this talented thinker was only forty-two years old.

The Turing Award for Computing was established in 1966, and later a Turing monument was put up in Manchester. In 1998, his birthplace in London was marked with a blue plaque, according to the custom. In 2013, Queen Elizabeth granted him a full pardon for his former "crime." 

Tuesday, May 16, 2017

Hardy, Littlewood and Ramanujan, a mathematical trio

After an exchange of letters with Srinivasa Ramanujan revealed his amazing mathematical insights, GH Hardy and John E. Littlewood, two Cambridge dons, encouraged the talented but untrained young mathematical genius to come to Cambridge. There they arranged to get him a position and collaborated with him on mathematical work. 

Sadly, Ramanujan did not adapt well to the climate of England, and found it difficult as a vegetarian to stomach the food in college. When his health began to fail, Hardy encouraged him to return to India for a holiday. He lived to see his home and family, but died in Madras of a parasitic infection. He was only thirty-three years old.
At the request of a friend, Hardy penned a memoir, A Mathematician's Apology, during his final illness. This is a seen by many as a study of the creative mind and process. Published in 1940, a year into the war, the book reveals a somewhat gloomy outlook.

Sunday, May 14, 2017

David Hilbert, German mathematician

Image from britannica

"Mathematics knows no races or geographic boundaries;...the cultural world is one country." So thought David Hilbert. He wrote Mathematics and the Imagination, and Nature and Mathematics, among other books.

Born in 1862 in Konigsberg, where Euler solved the problem of the Seven Bridges of Konigsberg, Hilbert died in 1943 in Gottingen, which had been the European centre of mathematics before the war. He contributed to geometry, invented "Hilbert space" in calculus, established a formalist school of mathematics, and expanded his work into mathematical physics.

At the Paris International Congress of Mathematicians in 1900, he gave a key lecture in which he assigned his fellow mathematicians "homework" for the new century. Among his twenty-three problems, several remain unsolved today. At the top of Hilbert's list is the Riemann Hypothesis, about which he once said, "If I were to awaken after a thousand years, my first question would be, 'Has the Reimann Hypothesis been proven?'"

In a blog post seven years ago, I recorded an anecdote about something strange Hilbert did. It's right here.

Thursday, May 11, 2017

Fiction with Heart: Elinor Florence at Canadian Authors

Bestselling novelist Elinor Florence carries Canadian history in her DNA. Wednesday she talked to Canadian Authors about salting fiction with nuggets from real life. The protagonist of Bird's Eye View is a prairie farm girl who works as a map interpreter at RAF Medmenham.

Born and raised on a former airport in North Battleford, Florence spoke of going to sleep thinking about the ghosts of airmen on her family's farm. One pilot crashed and died across the road on a training flight. Her father bought the farm land from the air force, and until he built the house, the family lived in a former airport building.

This airport, along with many more across the prairies, was built for the Commonwealth Air Training Plan, to ensure that pilots from Britain and the Commonwealth could learn to fly in safety before entering the Battle of Britain.

A journalist who worked on newspapers in BC and across the prairies, Florence talked about how she unearthed the telling details that place readers in the heart of the story.

The book was a long time in the making, and over a period of years, she interviewed people who remembered and served in the war. She read memoirs, including one by Constance Babington-Smith, the map interpreter who discovered the first V1 rocket on a German aerial map. Known today as cruise missiles, these flying bombs were a serious threat to London, and potentially to Halifax and New York as well, before the Normandy invasion.

To ensure she described the setting accurately, Florence visited Danesfield House, now a hotel. At this former site of RAF Medmenham, she met and interviewed a woman who had worked there during the war. By an amazing coincidence, this was the former map reader's first one day visit back to see her old workplace.

Florence also tracked down letters and pictures from obscure corners of museums. Astonishingly, a photo of the pilot who crashed in North Battleford led her, via the internet, to his relatives in Tasmania. She learned that the mother knew the young man and had written to his mother when he died. The Tasmanian cousin was delighted to learn where he was buried, and arranged to have the RCAF lay a wreath in remembrance.

A warm audience of Canadian Authors members and guests enjoyed Elinor Florence's fascinating presentation. Another book, My Favourite Veterans, is based on interviews she posts regularly on her blog, Wartime Wednesdays.