Then we ask the probability that a parent contributes an A gene to its child. Slide: What is the probability that a parent contributes an A gene to its child? I shall now calculate the probability that a parent contributes an uppercase A gene to its child. These three probabilities add up to 1.Īlso assume, as did Hardy that these probabilities are the same among males and females and also that mating is random. Suppose the probability of having an AA pair is, an Aa pair, and an aa pair. Now each parent contributes one gene so the child's genetic make-up must be one of the three types: AA or Aa or aa. I will first set up some notation to describe the situation. In a word, there is not the slightest foundation for the idea that a dominant character should show a tendency to spread over a whole population, or that a recessive should tend to die out. Hardy showed in this article in Science that: Before Hardy's work it was thought that a dominant characteristic would over generations become so widespread as to eliminate its recessive counterpart. So if an offspring receives an A gene from either parent then the offspring will have the characteristic, say brown eyes, but if the offspring receives an a from both parents then the child will have the opposite characteristic, say blue eyes. in genes of type uppercase A or lowercase a, where A is dominant and a is recessive. In 1908, of course, the mathematical and biological principles of genetics were in their infancy. The title of the article is Mendelian Proportions in a Mixed Population. The complete article is on the left and is, as you can see, short. It is now known as the Hardy-Weinberg Law. I need hardly say that I find such criticisms very gratifying, as the best evidence that the book has to some extent fulfilled the purpose with which it was written.Īlso in that year, 1908, and in spite of his lifelong distaste for applied mathematics, he made a significant contribution to a problem in genetics, using only simple algebra and probability, and sent it to the journal Science. I was too meticulous and pedantic for my pupils of fifteen years ago: I am altogether too popular for the Trinity scholar of to-day. It is curious to note how the character of the criticisms I have had to meet has changed. In the preface to the third edition Hardy wrote: This is the title page of the third edition published in 1921 and available online at: Littlewood later described the book's author as a missionary talking to cannibals. Previously analysis had been a neglected area of mathematics even in Cambridge. It was a model of clarity and presented elementary analysis to students in a rigorous yet accessible way. This book had a tremendous influence on generations of mathematicians in the British Isles. His textbook, A Course of Pure Mathematics, was published in 1908. Slide: Title page of A Course of Pure Mathematics Hardy's first research paper in 1900 was on integration he later wrote another sixty-eight papers on the same subject. He attended Winchester College before proceeding to Trinity College, Cambridge in 1896. His parents were schoolteachers and he had an enlightened upbringing in a typical religious Victorian household, although in adult life he was a militant atheist. Into their world came Ramanujan, one of the most brilliant and intuitive mathematicians of all time, who left India to work with them in Cambridge until his untimely death at the age of 32. Dominating the English mathematical scene for the first half of the 20th century, they produced a hundred joint papers of great influence, most notably in analysis and number theory. Littlewood was the most productive in mathematical history. The lengthy and fruitful collaboration of G. You will see that I have amended the title to include Mary Cartwright, because this talk is about the value of collaboration between mathematicians and I wanted to include the work between Littlewood and Cartwright during the Second World War. Thank you for coming to my lecture today. Hardy, Littlewood, Ramanujan and Cartwright
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |