수학은 어디에 활용되는가?

icm2006

BUT WHAT’S THE USE OF MATHEMATICS? An overwhelming majority of mathematicians would say that mathematics are beautiful in themselves and that they are their own justification. But mathematics are also important, not to say necessary. They could be called the invisible science; part of their importance arises from the fact that they are behind many aspects of daily life, at once hidden and essential. They are also the engine of change; there is no aircraft, no robot, no computer … no future technology without mathematics. Here are just a few examples:

수학은 대체 어디에 유용한가? 거의 대다수의 수학자는 수학은 그 자체로 아름답고 그 자체로 정당화된다고 말할 것이다. 그러나 수학은 유용한 것일뿐 아니라 중요하기도 하다. 수학이 중요한 이유중의 일부는 수학이 많은 일상 생활의 뒤에서 숨어 있는 동시에, 본질적인 역할을 하고 있기 때문인데, 그렇기에 수학을 보이지 않는 과학이라 부를 수 있을 것이다. 수학은 또한 변화의 원동력이기도 하다. 비행기, 로봇, 컴퓨터와 같은 미래 기술들은 수학없이 있을 수 없다. 이것은 몇몇 예일 뿐이다.

Should I take the umbrella today? Mathematics play a vital role in weather forecasting. For this purpose the atmosphere surrounding the planet is divided into imaginary boxes with sides 50 kilometres long and dozens or hundreds of metres high. Data on the climate in these boxes is taken by means of satellites and meteorological stations and the variables entered into powerful computers where they are combined with the laws of dynamics and physics in a process of complicated calculations in order to forecast the behaviour of the weather over the next few days. For predictions in the long term, the interaction of the atmosphere with the oceans, and the ice caps with the biosphere, are incorporated into mathematical models similar to those used in this process in order to study the possible effects of climate change.

오늘 우산을 가지고 나가야 할까? 수학은 일기예보에 필수적인 역할을 한다. 이를 위해 지구를 둘러싼 대기는 옆으로 50 킬로미터, 높이는 수십 수백 미터 정도인 가상의 상자들로 나누어 진다. 단시일 내의 날씨를 예보를 위해 위성과 기상 관측소에서 이 상자들 속의 기후에 대한 자료가 얻어지고, 성능이 좋은 컴퓨터에 입력된 변수들이 동역학과 물리학의 법칙을 따르는 복잡한 계산 과정을 거치게 된다. 장기간에 대한 예보를 위해서는 이 과정에 사용되는 것과 유사한 수리 모형에 기후변화의 가능한 영향을 연구하기 위해 대기와 해양, 만년설과 생물권의 상호작용이 추가되어야 한다.

I’m sorry, I don’t speak Spanish. Sometimes considered a universal language, mathematics are also vital for the automatic translation of all languages, from French to Zulu. This is possible because computer programmes for translation are based on statistics and probabilities as well as on enormous data bases of words in order to come up with the correct translation of every term.

Picking up the telephone. Dialling a number and speaking with someone on a cell phone is much more complicated than it seems. The GSM (Global System for Mobile Communications) standard alone, which enables one receiver to connect with another, consists of more than 5,000 pages of technical specifications. Mathematics and algorithms not only simplify this process, they are also fundamental to each of the steps comprising every call; the transformation of the voice into numerical series, its transmission by Hertzian waves, the encryption of the call, and the different radio frequencies of each operator…

Protected Comunication How can a telephone conversation be encrypted to prevent it from being overheard by other people? Or how can a credit card be made secure? Since the Second World War, in which mathematics played a decisive role in the decryption of secret messages, this science has been a key factor in many security systems used today on a daily basis. Many of these systems are based on the RSA protocol, which is founded on the idea that although extremely long figures can be constructed from prime numbers (N = p x q), it is very difficult to find the factors p y q if only N is known.

• http://www.icm2006.org/press/dossier/#11

• Bid and win.  What do you have to do to make the most of bidding at an auction?  Game Theory, created by the Hungarian mathematician John von Neumann between 1920 and 1940, analyses the different players and the different strategies for anticipating their preferences.  For example, in a symmetrical situation in which the different players are all following the same train of thought, a bidder must seek maximum benefit while knowing that the others are following the same strategy as he or she. 
• Is this skyscraper going to fall?  Numbers have also enabled complex mathematical models to be developed for the computer representation of practically any solid or fluid with the aim of simulating the way it behaves in reality.  In other words, these models are a way of predicting the future, and have already been used for analysing the stability of skyscrapers and bridges in earthquake conditions, or for simulating the landing of space probe on a distant planet.  Attempts are currently being made to reproduced organs of the human body by computer in order to be able to predict how a patient will respond to surgery in an operating theatre. 

• The chances of developing cancer.   Many diseases are determined by hereditary factors, which means that a person carrying a particular gene may be predisposed to suffering from a certain illness.  This is the case with the BRCA1 gene, whose mutation was discovered in 1990 and is involved in a high percentage of cases of women suffering from breast cancer.  In order to isolate this gene, researchers were obliged to carry out many statistical analyses on people from the same family groups.    
• From Jurassic Park to Star Wars.  Creating toy models that come to life on the cinema screen or making an audience grip their seats under imminent attack by a Tyrannosaurus Rex is in large part possible thanks to mathematics.  Many of the most amazing special effects in feature or animated films are a combination of pixels and geometrical shapes created mathematically by means of computer programmes. 
• Reliving the past.  Reconstructing a broken vase is never an easy task.  But what happens if the vase is hundreds of years old and must be put together again from hundreds or thousands of small, incomplete and jumbled fragments, without an overall notion of what the vase was like originally?  Mathematics are also an indispensable tool in archaeology, since they enable surfaces of all kinds to be reconstructed, even including parts of the human body using a few ancient remains.  The available parts are digitalized and included in computer programmes that recompose the object virtually by means of geometry, combinations and statistics. 
• Protecting the environment.  The combination of mathematics and ecology enables us to understand the complex interactions of nature.  With the help of algebra, numerical simulations, stochastic processes, differential equations and statistics, many models can be created for determining for example the extent of territory required for conserving a particular animal population, or at what rate an invading species of plant is propagated.   
• Music and literature.  Whether it be an opera by Mozart or a guitar riff by Keith Richards, all the music stored on a CD is made up of long series of zeros and ones.  But this is far from being the only relation of mathematics with music and with art.  Musical composition is closely linked with mathematics, the same as many paintings and works of art.  Mathematics is also present in many classical works of literature, such as “Alice in Wonderland” or “Gulliver’s Travels”.  And in the case of Borges, who studied mathematics for several years, the traces of this science can be found in all his work, especially in his story “The Aleph”, which refers to a mathematical theory stating that the sum is not necessarily greater than the parts.   

애니메이션

• Moving Remy in Harmony: Pixar's Use of Harmonic Functions
• “Pixar: The Math behind the Movies - Tony DeRose.” YouTube. Accessed April 3, 2014. http://www.youtube.com/watch?v=_IZMVMf4NQ0.

 

메모

• Stockie, John M. “Mathematics For Industry: A Personal Perspective.” arXiv:1509.03272 [math], September 4, 2015. http://arxiv.org/abs/1509.03272.
• 국가 정책으로서의 산업응용수학 활성화 전략수립, 대한수학회, 2015-2
• PUMAS Example, Practical Uses of Math And Science
• WeUseMath.org
• Real world applications of representation theory of non-abelian groups
• 게임 프로그래머는 수학을 배워야 할까?
• 샤이아에 적용된 망토 시뮬레이션은 어떻게 구현했을까?
• The Mathematical Sciences' Role in Homeland Security:Proceedings of a Workshop
• Fueling Innovation and Discovery: The Mathematical Sciences in the 21st Century
• Applied Mathematics: Body and Soul http://www.bodysoulmath.org/books/
• Crashing waves, awesome explosions, turbulent smoke and beyond
• Math at Google 구글을 만드는데 사용된 수학 요소들을 정리한 슬라이드 http://j.mp/PNcV1K
  • PageRank
  • 스팸검출
  • 시계열(구글트렌즈)
  • 음성검색
  • OCR(구글북스).
• http://commons.bcit.ca/math/examples/

 

L'explosion des mathématiques

• http://smf4.emath.fr/en/Publications/ExplosionDesMathematiques/index_en.html