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85

A tragic example of this is the case People v. Collins, in which a prosecutor asked a mathematician (as an expert witness) a question of the form, "assuming these events are independent, what is the probability that...". The events were obviously not independent, things like "drives a convertible", "has a caucasian girlfriend", "girlfriend has blond hair", ...


82

"The best card trick", an article by Michael Kleber. Here is the opening paragraph: "You, my friend, are about to witness the best card trick there is. Here, take this ordinary deck of cards, and draw a hand of five cards from it. Choose them deliberately or randomly, whichever you prefer--but do not show them to me! Show them instead to my lovely ...


64

Here are some examples, ranging from the comical to the debatable. Comical: Pretty much any mention of mathematics in Jacques Lacan. To give you an idea, here is a typical passage: This diagram [the Möbius strip] can be considered the basis of a sort of essential inscription at the origin, in the knot which constitutes the subject. This goes much ...


60

Actually even schoolchildren calculate group co-cycle. (Without knowing that it is called like this). Cohomology occurs in everyday life as soon as one learns to count. 5+7 = 1 2 4 + 5 = 0 9 2 + 8 = 1 0 What is the function on which sends a pair (a,b) to the $0$ or $1$ depending result is greater than 9 or not ? ( e.g. f(5,7)= 1, f(4,5) = 0, ...


51

Title: Logicomix: An epic search for truth Authors: Apostolos Doxiadis, Christos Papadimitriou Artists: Alecos Papadatos, Annie Di Donna Short description: A comic book biography of Bertrand Russell, focusing on his work on the foundation of mathematics. (About 345 pages. I just started reading it, so I haven't formed a firm opinion on it yet, but I like ...


51

My favourite in this direction is an application of Noether's theorem to public relations: Sha, "Noether's Theorem: The Science of Symmetry and the Law of Conservation", J. Public Relations Research, 16 (2004) 391-416. I quote from the abstract: Noether's Theorem shows that symmetry-or change-can only exist simultaneously with conservation or ...


50

Title: Flatland Author: A. Square / Edwin A. Abbot Short Description: Imagine how life would be in less than three dimensions.


50

Title: Godel, Escher, Bach: an Eternal Golden Braid Author: Douglas Hofstadter Short Description: It's mildly debatable whether this is in fact a book about mathematics, but any mathematician who has read this book will understand why I recommend it and any who has not should. Probably best for those with either a philosophical or musical bent.


45

This was fascinating for me. Somehow the man takes a bagel and with one cut arrives with two pieces that are interlocked. Whether this qualifies as "magic" I dunno (it's hard to say once the trick's been explained), but it sure seems like it to me. It doesn't hurt that I love bagels, and have the opportunity to perform this with friends/family/non-math ...


43

Title: Mathematics: A very short introduction Author: Timothy Gowers Short description: As the title says, very short. Gives the non-mathematical reader a good idea what mathematics is all about in just about 100 small pages.


42

I get asked this question a lot, so I'll give my pat (but serious) answer: Find yourself an editor. That is, find someone who'll take what you think is crystal clear, engaging prose, and turn it into something that actually is crystal clear and engaging. I couldn't do my job without my editors. (For those who don't know me, I work as a freelance ...


36

Five unrelated items: Mobius strip One of the best mathematical tricks is what happens when you cut a Mobius strip in the middle. (Look here) (And what happens when you cut it again, and when you cut it not in the middle.) This is truly mind boggling and magicians use it in their acts. And it reflects deep mathematics. Diaconis mind reading trick I also ...


35

math.AC Commutative algebra Reed-Solomon codes (a type of error correction codes based on polynomials over finite fields - this is why CDs and DVDs still work even after being scratched!)


32

I feel I should have a good answer to this question, since I've been writing about mathematics for the general public for many years -- but after some thought, I'm not coming up with any specific advice. But I can say this. To write about popular mathematics well, you must write well. Your explication of the main idea can be as clear and correct as you ...


32

Title: The Man Who Loved Only Numbers Author: Paul Hoffman Short Description: A biography of Paul Erdős. No previous knowledge of math.


32

"classic" Title: Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem (US) Fermat's Last Theorem: The story of a riddle that confounded the world's greatest minds for 358 years (UK) Author: Simon Singh Short Description: The history of Fermat's Theorem, from the famous note "It is impossible to separate a cube into two cubes, ...


31

Robert Ghrist is all about applied topology: Sensor Network, Signal Processing, and Fluid Dynamics. (homepage: http://www.math.upenn.edu/~ghrist/index.html ). For instance, we want to use the least number of sensors to cover a certain area, such that when we remove one sensor, a part of that area is undetectable. We can form a complex of these sensors ...


30

Title: A Mathematician's Apology Author: G. H. Hardy Short Description: In the style of Plato and Xenophon, G. H. Hardy offers a justification for pure mathematics.


29

This is not an answer. Just a very long comment. Mostly I am stunned by the answers given. (1) I'm surprised to see Lacan featured as the main example. What I see in these quotes is an attempt to formalise human condition. Is it laughable? Yes! But no more that 16th century physics and widely taken as such. I'm pretty sure 99,9% of the human population ...


29

A couple of misapplications of physics come to mind: Conservation of angular momentum does not mean what people think it means. If you have an object spinning on a flat surface, it can't turn around without outside forces, right? Wrong, the rattleback toy does this (video). The Coriolis effect is real, but the idea that this has something to do with the ...


28

There are very many examples of the misuse of probability arguments in legal cases. See e.g. the Prosecutor's fallacy.


28

I saw this trick demonstrated at a math camp once. When it works, it is extremely impressive to non-mathematicians and mathematicians alike. Have a volunteer shuffle a deck of cards, select a card, show it to the audience, and shuffle it back into the deck. Take the deck from him, and fling all of the cards into the air. Grab one as it falls, and ask the ...


27

math.AT Algebraic Topology Algebraic Topology finds applications in sensor network design, coverage analysis for sensor networks, and in expanding data analysis techniques to give better visualizations for large data sets. It has also been applied to computer vision and pattern recognition algorithms, for instance here. Algebraic Topology can be used in ...


26

math.GR Group Theory Group theory provides methods for understanding the Rubik's cube, and for generating algorithms for solving the cube remarkably quickly from any state the cube may be in. Groups find various applications in chemistry, eg. in the study of crystal structures and spectroscopy. Cryptography - various hard algorithmic problems about groups ...


26

math.DG Differential geometry Lie groups are used in robotics (to find the most efficient way to maneuver a robotic arm, for instance). Spherical trigonometry is essential for navigation (a few centuries ago, this was THE application of mathematics to the real world - naval empires were built upon this!) Finsler geometry can be used in planning shipping ...


26

Title: Journey Through Genius Author: William Dunham Short Description: A fencepost history of mathematics. For each highpoint it describes some fun history and then the actual math. Examples of topics covered are Heron's formula for triangular area, Euler's evaluation of $\zeta(2)$ and Cantor's set theory.


26

Title: The Book of Numbers. Author: John Conway and Richard Guy. Short Description: A beautifully illustrated book with all sorts of facts about all sorts of numbers. The difficulty is variable throughout the book: parts are written at a + level, while other parts are closer to +++.


24

Title: Innumeracy: Mathematical Illiteracy and its Consequences Author: John Allen Paulos, mathematician and well-known skeptic (in the good, modern sense of the word). Short description: Paulos explains for the general public (and he does it fairly well) why it should understand a little more mathematics and know how to do Fermi calculations and educated ...


23

As you mentioned, an often misapplied mathematical statement is Heisenberg's uncertainty principle, which for me, as a reader of Chriss-Ginzburg, is the purely mathematical statement that any subvariety of classical phase space ($\mathrm{Specm}(\mathrm{gr}A)$) that arises from a noncommutative system of equations (an ideal in A) is coisotropic. The ...



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