Emmanuel Morand. One Hundred Interesting Mathematical Calculations, Number 9: Archive Entry From Brad DeLong's Webjournal. One Hundred Interesting Mathematical Calculations, Number 9 One Hundred Interesting Mathematical Calculations, Number 9: False Positives Suppose that we have a test for a disease that is 98% accurate: if one has the disease, the test comes back "yes" 98% of the time (and "no" 2% of the time), and if one does not have the disease, the test comes back "no" 98% of the time (and "yes" 2% of the time).
Suppose further that 0.5% of people--one out of every two hundred--actually has the disease. Your test comes back "yes. " How worried should you be? How likely is it that you have the disease? Suppose just for ease of calculation that we have a population of 10000, of whom 50--one in every two hundred--have the disease. If you test "no" you can be very happy indeed: there is only one chance in 9752 that you are the unlucky guy who had the disease and yet tested negative.
If you test "yes" you are less happy. From John Allen Paulos's Innumeracy . Kurt Gödel. Kurt Friedrich Gödel (/ˈkɜrt ɡɜrdəl/; German: [ˈkʊʁt ˈɡøːdəl] ( ); April 28, 1906 – January 14, 1978) was an Austrian, and later American, logician, mathematician, and philosopher. Considered with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell,[1] A.
N. Whitehead,[1] and David Hilbert were pioneering the use of logic and set theory to understand the foundations of mathematics. Gödel published his two incompleteness theorems in 1931 when he was 25 years old, one year after finishing his doctorate at the University of Vienna. The first incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (for example Peano arithmetic), there are true propositions about the naturals that cannot be proved from the axioms. Life[edit] Les mathématiques avec Pascal. FIBONACCI. "...considering both the originality and power of his methods, and the importance of his results, we are abundantly justified in ranking Leonardo of Pisa as the greatest genius in the field of number theory who appeared between the time of Diophantus [4th century A.D.] and that of Fermat" [17th century] R.B.
McClenon [13]. [Numbers in square brackets refer to REFERENCES at the end of this article.] 1. The world of Fibonacci. During the twelfth and thirteenth centuries, many far-reaching changes in the social, political and intellectual lives of people and nations were taking place. Europe had emerged from the period of barbarian invasions and disruption known as the Dark Ages. By the end of the twelfth century, the struggle between the Papacy and the Holy Roman Empire had left many Italian cities independent republics. Into this world of change and cross-fertilisation of Christian and Moslem cultures, Fibonacci, a man for all seasons, was born in Pisa. 2. No portraits of Fibonacci exist.