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How do you spark off an interest in maths when the curriculum seems dreary? | Education | The Guardian
ut then my mathematics teacher took me aside after one lesson and recommended a few books that he thought might interest me. He conspiratorially intimated that the maths we were doing in the classroom wasn't really what maths was about. It was something much more exciting, creative, imaginative. Those books provided me with a key to the secret garden of mathematics.\n\nIn that garden I discovered that mathematics also has great stories. Unsolved mysteries like the enigma of prime numbers. Magical mathematical machines that could help you see in four dimensions. Mathematicians who had journeyed to infinity and beyond, discovering that there are many sorts of infinity, some bigger than others. Like my son reading Shakespeare, I certainly didn't understand everything I read, but it inspired me to want to navigate this world, to put in the hard graft to master the language and grammar of maths so that I could read and one day create my own mathematical stories.\n\nOne of the books my teacher recommended was GH Hardy's A Mathematician's Apology. At the time, I was very interested in music, I was learning the trumpet, hanging out with the arty crowd, doing plays and singing in choirs. Science hadn't really captured my imagination. But I also had a desire for things that made logical sense, for solving puzzles, for a rational perspective on the world. A Mathematician's Apology suddenly opened up a bridge between these two competing desires, these two cultures.\n\nAs I read Hardy's book, there were sentences which revealed to me that mathematics shared a lot in common with the creative arts. It seemed to be compatible with things I loved doing: languages, music, literature. Here for example is Hardy writing about being a mathematician: "A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas." Later he writes: "The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colours or t
Hacking Primes in Mathematica - O'Reilly Radar
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This morning, Tim
Bray tweeted about a post on prime numbers and Benford's law. To cut the esoterica short,
one of the big problems in prime numbers is that people don't know how they're
distributed. This post suggests that Benford's Law describes the distribution of
the first digit of prime numbers. One of the comments asked an important
question: is this really just an artifact of base 10? Math really doesn't "know
anything" about bases, so if this idea doesn't generalize to bases other than
10, it doesn't mean much.That challenge was a bit hard to ignore. A bit of futzing with Mathematica
later, I got it. Here's a graph of the distribution of prime numbers in base 36,
for primes less than 36^5 (about 60 million, 3.5 million primes): primes.tiff -
This certainly isn't rigorous math, from the standpoint of proving anything
about the distribution of prime numbers. Just some fun hacking--it's great to
have a mathematical language in which you can say "Give me all the primes less
than 32^5 and sort them by their first digits in base 36"--in about that much
space.
Sexy maths: Formula won ... the key to boosting faster travel - Times Online
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You arrive at an airport for a flight connection but the timing is tight. You
discover that your next plane is leaving from the far end of the airport. There
is a moving walkway for part of the journey. You’ve got enough energy to do a
short burst of running, but otherwise you’ll walk at a constant speed. However,
one of your shoelaces is undone so you’re going to need to stop at some point to
do it up.You want to get to the gate as quickly as possible, so the question is: when
should you use your burst of energy? Should you run on or off the moving
walkway? And that shoelace? Should you tie that on the moving walkway? Or should
you stop on the portion of the journey without a moving walkway? Or does it make
no difference where you run or stop? -
There is an economic maxim that underlies both decisions: a worker should spend
as much time as possible on the most efficient machine. In this case, staying on
the walkway for as long as possible is the best strategy. Stop to tie the
shoelace on the walkway but don’t press the boost button as it will get you off
the walkway quicker. Save that for the bit of the airport without the moving
walkway. - 1 more annotations...
Marcus du Sautoy forecasts the future - 18 November 2006 - New Scientist
athematicians have wrestled for 2000 years to understand how nature chose these enigmatic numbers. As you count higher and higher through the universe of numbers, it seems impossible to predict where you are going to find the next prime. They appear as wild as lottery numbers. Deeply frustrating for the pattern searcher.\n\nIn the past 150 years, though, we have gained new insights into these numbers. Scientists have picked up strange resonances between the primes and energy levels in heavy nuclei of elements such as uranium. These new connections provide the hope that the next generation of mathematicians will finally discover the hidden template to explain the distribution of these numbers.
Proof (play) - Wikipedia, the free encyclopedia
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The play concerns Catherine, the daughter of Robert, a recently deceased
mathematical genius and professor at the University of Chicago, and her struggle
with mathematical genius and mental illness. Catherine had cared for her father
through a lengthy mental illness. Upon Robert's death, his ex-graduate student
Hal discovers a paradigm-shifting proof about prime
numbers in Robert's office. The title refers both to that proof and to the
play's central question: Can Catherine prove the proof's authorship? Along with
demonstrating the proof's authenticity, the daughter also finds herself in a
relationship with 28-year-old Hal. Throughout, the play explores Catherine's
fear of following in her father's footsteps, both mathematically and mentally
Sexy maths: the Fibonacci sequence's prime rate - Times Online
What's the next number in this sequence: 1, 1, 2, 3, 5, 8, 13, 21...? Anyone who has read Dan Brown's The Da Vinci Code will know that the answer is 34. The sequence is one of the first codes that readers are challenged with in the thriller. Even if you haven't read Dan Brown, spotting the underlying pattern is not too difficult. You get the next number in the sequence by adding together the two previous numbers. So 5+8 gives you 13, for example.
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