# AOK math

Is Mathematics Invented or Discovered? Mathematics is the language of science and has enabled mankind to make extraordinary technological advances.

There is no question that the logic and order that underpins mathematics, has served us in describing the patterns and structure we find in nature. The successes that have been achieved, from the mathematics of the cosmos down to electronic devices at the microscale, are significant. Einstein remarked, “How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?” Amongst mathematicians and scientists there is no consensus on this fascinating question. The various types of responses to Einstein’s conundrum include: 1) Math is innate. 2) Math is a human construct. 3) Math is not so successful. Roger Antonsen: Math is the hidden secret to understanding the world.

Mathematics Illuminated. Wallpaper Pattern In mathematics, symmetry has more than just a visual or geometric quality.

Mathematicians comprehend symmetries as motions—motions whose interactions and overall structure give rise to an important mathematical concept called a "group. " This unit explores Group Theory, the mathematical quantification of symmetry, which is key to understanding how to remove structure from (i.e., shuffle) a deck of cards or to fathom structure in a crystal. Pollock's Fractals. In 1949, when Life magazine asked if Jackson Pollock was "the greatest living painter in the United States," the resulting outcry voiced nearly half a century of popular frustration with abstract art.

Some said their splatter boards were better than Pollock's work. Others said that a trained chimpanzee could do just as well. A Pollock painting, one critic complained, is like "a mop of tangled hair I have an irresistible urge to comb out. " Yet Pollock's reputation has outlived his detractors. What are Formal Systems? Introduced here: the MIU puzzle as an example of a formal system.

A formal system is composed of axioms, to which rules of inference are applied to produce theorems to which the rules can be applied again. Confused? Try to MIU puzzle yourself – it’s fun! Why the history of maths is also the history of art. When I was a graduate student in art history, I read many explanations of abstract art, but they were invariably inadequate and misleading.

So after completing my PhD, I went on to learn the history of biology, physics, and astronomy, and to publish a book detailing how modern art is an expression of the scientific worldview. Yet many artworks also express the mathematics and technology of their times. To research Math and Art I had to learn maths concepts like calculus, group theory and predicate logic. As a novice struggling to understand these ideas, I was struck with the poor quality and confusing content of illustrations in most educational books. So I vowed to create for my book a set of cogent math diagrams that are crystal-clear visualizations of the abstract concepts. Here are ten images followed by descriptions: Why Pi Matters. Every March 14th, mathematicians like me are prodded out of our burrows like Punxsutawney Phil on Groundhog Day, blinking and bewildered by all the fuss.

Yes, it’s Pi Day again. And not just any Pi Day. They’re calling this the Pi Day of the century: 3.14.15. Pi to five digits. The great mystery of mathematics is its lack of mystery. In one sense, there’s less mystery in mathematics than there is in any other human endeavour.

In math, we can really understand things, in a deeper way than we ever understand anything else. (When I was younger, I used to reassure myself during suspense movies by silently reciting the proof of some theorem: here, at least, was a certainty that the movie couldn’t touch.) So how is it that many people, notably including mathematicians, feel that there’s something ‘mysterious’ about this least mysterious of subjects? What do they mean? A Cambridge professor on how to stop being so easily manipulated by misleading statistics — Quartz. “There are three kinds of lies: Lies, damned lies, and statistics.”

Few people know the struggle of correcting such lies better than David Spiegelhalter. Since 2007, he has been the Winton professor for the public understanding of risk (though he prefers “statistics” to “risk”) at the University of Cambridge. In a sunlit hotel room in Washington DC, Quartz caught up with Spiegelhalter recently to talk about his unique job. The conversation sprawled from the wisdom of eating bacon (would you swallow any other known carcinogen?) , to the serious crime of manipulating charts, to the right way to talk about rare but scary diseases. When he isn’t fixing people’s misunderstandings of numbers, he works to communicate numbers better so that misunderstandings can be avoided from the beginning. Did Nate Silver actually get anything wrong about Donald Trump? Photo illustration by Sofya Levina.

Images by Dimitrios Kambouris/Getty Images and Slaven Vlasic/Getty Images. Ever since Donald Trump locked up the Republican nomination, there has been no shortage of recrimination and mockery directed at political analysts who failed to take his candidacy seriously. No one has taken a bigger beating than FiveThirtyEight editor-in-chief Nate Silver, the famed data journalist whose careful reading of poll numbers in the runup to the previous two presidential elections established him as a lonely voice of rationality and wisdom in a sea of dumb, emotional pundits. Leon Neyfakh is a Slate staff writer. Silver did not perform as well during the 2016 GOP primary. At the end of January, I examined Silver’s thought process in an attempt to figure out what he missed.

Is it possible that Silver was correct that Trump’s nomination was extremely unlikely? Our conversation originally aired as an episode of the Slate Trumpcast. 6 Math Concepts Explained by Knitting and Crochet. This crocheted Lorenz manifold gives insight "into how chaos arises.

" Image credit: © Hinke Osinga and Bernd Krauskopf, 2004 Using yarn and two pointy needles (knitting) or one narrow hook (crochet), pretty much anyone can stitch up a piece of fabric. Or, you can take the whole yarncraft thing light-years further to illustrate a slew of mathematical principles. How the Königsberg bridge problem changed mathematics - Dan Van der Vieren. IB Maths Resources from British International School Phuket. Is Mathematics invented or discovered? – this is one of the classic ToK maths questions. Read this essay and decided for yourself! Examples - Proofs without words. This should really be a comment on Marco Radeschi's answer from Feb 22 involving the area formula for spherical triangles, but since I'm new here I don't have the reputation to leave comments yet.

In reply to Igor's comment (on Marco's answer) wondering about an analogous proof for the area formula of hyperbolic triangles: there is one along similar lines, and you're rescued from non-compactness by the fact that asymptotic triangles have finite area. Quick Study: Edward Frenkel on math: It's a lot like borscht. EDWARD FRENKEL is a Russian mathematician working in representation theory, algebraic geometry and mathematical physics. He is professor of mathematics at the University of California, Berkeley, and the author of “Love and Math”, recently published by Basic Books. You describe math as "beautiful". What do you mean?

Imagine you had an art class in which they taught you how to paint a fence, but never showed you the great masters. Of course, you would say; ‘I hate art.' How did you discover it? When I was growing up near Moscow I thought mathematics was the most boring and irrelevant subject, but I was fascinated with quantum physics and elementary particles. Can complex mathematical ideas be explained to someone who is not a mathematician? Mathematicians dispute claims that the 'golden ratio' is a natural blueprint for beauty - Science - News.

But the widespread belief that the golden ratio is the natural blueprint for beauty is pseudo-scientific “hocus-pocus” and a “myth that refuses to go away”, according to leading mathematicians. The issue has flared up again, after one of the United States’s leading scientific organisations, the Smithsonian, promoted highly contentious claims about the ratio at the National Math Festival in Washington DC earlier this month. Theories that the Parthenon in Athens, pictured, and Great Pyramid in Egypt were built according to the golden ratio have also been disproved (EPA) Eve Torrence, a professor at Randolph–Macon College in Virginia, said she was appalled to find a Smithsonian-branded stall which claimed the golden ratio is found in the human body. It offered visitors the chance to put their head through an oval, allegedly to demonstrate whether their face was in accordance with what is also known as the “divine proportion”.

Loading gallery. Is math discovered or invented? - Jeff Dekofsky. Homer Simpson's scary maths problems. For a character living in two dimensions, grasping the idea of life in 3D can be tough - especially if the character in question is Homer Simpson. But one Halloween episode of The Simpsons forces him to confront the concept, and gives viewers a mathematical workout too. Eighteen years ago, the writers of The Simpsons celebrated Halloween with one of their traditional Treehouse of Horror episodes, which included three short stories.

After Attack of the 50-Foot Eyesores and Nightmare on Evergreen Terrace, viewers were treated to Homer³, which contains the most intense five minutes of mathematics ever to appear on prime time television. For many people, mathematics is more terrifying than being attacked by an army of zombies, werewolves and vampires, but in this case the various equations were included because the writer of Homer³, David S Cohen, is a fan of numbers. The storyline involves Homer diving through a portal and entering a peculiar three-dimensional universe. The numbers that keep our world afloat. Here is a quick quiz of three questions that you will get wrong. Do Your Patriotic Duty: Learn Math. Mathematics: Why the brain sees maths as beauty. Brain scans show a complex string of numbers and letters in mathematical formulae can evoke the same sense of beauty as artistic masterpieces and music from the greatest composers.

Mathematicians were shown "ugly" and "beautiful" equations while in a brain scanner at University College London. The same emotional brain centres used to appreciate art were being activated by "beautiful" maths. The researchers suggest there may be a neurobiological basis to beauty. Is the nature of mathematical proof changing? « Math Drudge.

Prime numbers In the field of mathematics, prime numbers are whole numbers that cannot be evenly divided by any integer other than itself and one. The surprising beauty of mathematics: Jonathan Matte at TEDxGreensFarmsAcademy. Is Math a Feature of the Universe or a Feature of Human Creation? Mathematical equations that changed the world. Ethiopian mathematics. I’ve got a word for Scrabble champions: mathematicians. The world of Scrabble is AGOG (score 24 if you managed to got one of the Gs on a double-letter score and the whole word on a triple-word score; give up if you’ve used it without the multipliers). The golden ratio has spawned a beautiful new curve: the Harriss spiral. Mathematicians like to come up with new stuff. Al-Khwarizmi: The father of algebra. Quick Study: Edward Frenkel on math: It's a lot like borscht. Intuition and math: A powerful correlation. Poincaré on intuition in mathematics.

Intuition and Logic in Mathematics byHenri Poincaré. Origami Jumping Frog Instructions. The most random correlations to ever occur. The mathematical secrets of Pascal’s triangle - Wajdi Mohamed Ratemi. Math is really fun! Visit this site and find out more about Pascal’s Triangle! TEDxKC - Francis Cholle - The Intuitive Intelligence Movement.

Learned Intuition: Patrick Schwerdtfeger at TEDxSacramentoSalon. When intuition and math probably look wrong. Intuition and Mathematics. There’s more to mathematics than rigour and proofs. Mathematical Intuition—What Is It? 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35... Nested fish and golden triangles: adult colouring and the beauty of maths.