The London Mathematical Society has a webpage in which they “take a look at some of the people who’ve made major contributions in the world of mathematics”. Indeed, it is always nice to put a face to the names we read about. My only comment about the page is that I do not think all the information is up to date, but never mind.
Link
Faces of Mathematics, London Mathematical Society
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This month marks the 60th anniversary of the discovery of deoxyribonucleic acid, or DNA to most of us. In the USA, there is DNA Day, which is a holiday celebrated on the 25th of April. The holiday commemorates the day in 1953 when James Watson and Francis Crick published their paper in Nature on the structure of DNA. It is also the 10th anniversary of the first sequencing of the human genome. |
Knot theory
One area of mathematics that has been rather useful in the study of DNA, and in particular how it tangles is knot theory. DNA is tightly packed into genes and chromosomes. This packing can be thought of as two very long strands that have been intertwined many times and tied into knots. Before the DNA can replicate it needs to be arranged much neater than that and so needs to be unpacked. Thus knot theory is important in understanding this “unknotting” of DNA.
The way the knots were classified had nothing to do with biology, but now you can calculate the things important to you.
Nicholas Cozzarelli, in [1].
A knot is just a embedding of a circle in 3d.
The knot diagram of the Trefoil knot
The classification of knots has been a harder problem that one might expect. The general idea is to construct ways to see if two knots are equivalent, meaning they are the same knot. More mathematically two knots are equivalent if they can be transformed into each other via a special kind of transformation known as an ambient isotopy. Such transformations are really just “distortions” of the knot without any cutting.
A powerful way of deciding of knots are the same or not, is to calculate their Jones polynomial [2]. Interestingly, there is a relation between the Jones Polynomial and Chern-Simons gauge theory, which was first discovered by Witten [3].
References
[1] David Austin, That Knotty DNA, Feature Column of the AMS.
[2] Jones, V.F.R. (1985),A polynomial invariant for knots via von Neumann algebra, Bull. Amer. Math. Soc.(N.S.) 12: 103–111
[3]Edward Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. Volume 121, Number 3 (1989), 351-399
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Professor Piotr Pragacz, a mathematician working in the area of algebraic geometry here at IMPAN, has collected a few quotes on mathematics and science a little more generally. |
Some of my favorites listed include
Nicolaus Copernicus: “Mathematics is written for mathematicians.”
Godfrey H. Hardy: “Young men should prove theorems, old men should write books.”
Albert Einstein: “The important thing is not to stop questioning; curiosity has its own reason for existing.”
David Hibert: “One can measure the importance of a scientific work by the number of earlier publications rendered superfluous by it.”
Henri Poincaré: “The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it, and he takes pleasure in it because it is beautiful.”
And my personal favorite
Winston Churchill: “Success consists of going from failure
to failure without loss of enthusiasm. ”
Follow the link below for many more quotes.
14th March has been officially designated Pi Day, a day for which we can celebrate the glorious number that starts with 3.14. Coincidentally, the 14th of March is also Albert Einstein’s birthday.
\(\pi\) -the ratio of the circumference of a circle to its diameter- has been calculated to over one trillion decimal places. The record as far as I know belongs to Alexander J. Yee & Shigeru Kondo, who have calculated \(\pi\) to 10 trillion digits [1]. As an irrational and transcendental number, \(\pi\) will continue infinitely without any repetition or patterns emerging.
 The “pi man” Larry Shaw |
The first Pi Day was organized by Larry Shaw and held in San Francisco in 1988. In 2009, the US House of Representatives backed its official designation. |
What to do for Pi Day?
Suggestions include bake a pie for Pi Day, or be artistic and write a piece of music, a poem or make a painting. You can find lots more suggestions by following this link.
The Welsh connection
The earliest known use of the symbol \(\pi\) to represent the ratio of the circumference of a circle to its diameter is by Welsh mathematician William Jones FRS (1675 – 3 July 1749) in 1706 [2].
Portrait of William Jones by William Hogarth, 1740 (National Portrait Gallery)
Jones was a close friend of Sir Isaac Newton and Sir Edmund Halley. In November 1711 he became a Fellow of the Royal Society, and was later its Vice-President.
References
[1] Alexander J. Yee & Shigeru Kondo, Round 2… 10 Trillion Digits of Pi 2013.
[2] William Jones, Synopsis Palmariorum Matheseos, 1706.
Links
Pi Day
National Science and Engineering Week 2013 in the UK is running from the 15th to the 24th March. The events are coordinated by the British Science Association, though it is other organisations and community groups that actualy run the events and activities. The theme this year is invention and discovery.
For those of you in the UK, follow the link below and get involved in something near you.
National Science & Engineering Week shines the spotlight each March on how the sciences, technology, engineering and maths relate to our everyday lives, and helps to inspire the next generation of scientists and engineers with fun and participative events and activities.
Last year’s National Science and Engineering Week consisted of something like 500 events and activities from thousands of different organisers. More than 2 million people at schools, museums, universities, shopping centres, cafes etc. attended the various events.
Engineering Education Scheme Wales Awards & Presentation Day 2013
Wednesday, March 20, 2013 – 10:00 to 16:00
Celtic Manor Resort, Newport
Follow the link below for more details.
The British Science Association
The British Science Association is a registered charity that exists works to advance public understanding, accessibility and the accountability of the sciences and engineering in the UK.
Link
National Science and Engineering Week 2013
Engineering Education Scheme Wales Awards & Presentation Day 2013
The above cartoon from Abstruse Goose demonstrates the not always linear path of new discoveries in mathematics. How mathematics is discovered is not the same as how mathematics is presented.
This also reminds me of a very famous humorous quote:
mathematicians can prove only trivial theorems, because every theorem that is proved is trivial!
Richard Feynman in “Surely You’re Joking, Mr. Feynman!”: Adventures of a Curious Character, Richard Feynman, Ralph Leighton (contributor), Edward Hutchings (editor), 1985, W W Norton, ISBN 0-393-01921-7
The London Mathematical Societry launched its report Advancing women in mathematics: good practice in UK university departments at the House of Commons on 27th February.
The LMS is concerned about the loss of women from mathematics, particularly at the higher levels of research and teaching, and at the missed opportunities that this represents. Through its Women in Mathematics Committee it established a Good Practice Scheme and supporting departments participated in a benchmarking survey which led to this report.
http://lms.ac.uk/news-entry/26022013-1401/house-commons-launch-good-practice-report
The report is avaliable here (opend PDF)
Ricardo Cortez of Tulane University, and Dagan Karp of Harvey Mudd College have set up a blog that address questions that students, postdoctoral researchers and junior faculty may have regarding their advancement in mathematics. The blog is part of the American Mathematical Society blogs and I am sure will become a very useful resource.
 Ricardo Cortez |
 Dagan Karp |
An extract from the first post
Two years ago, at the 2011 Joint Mathematics Meetings in New Orleans, I attended a panel discussion sponsored by the MAA. The session title was “Good intentions are necessary but not sufficient: Steps toward best practices in mentoring underrepresented students” and one of the goals of the session was to propose specific ideas that could be implemented as a result of the comments made by panelists and participants. In other words, there was a desire to go beyond offering opinions and advice. There was a desire to come up with concrete actions. I really liked the idea.
Ricardo Cortez, Building a community of mentors
The House of Lords Science and Technology Select Committee has published a report focusing on the implementation of the Government Open Access policy.
The debating chamber of the House of Lords in the Palace of Westminster
Things the report covers includes arrangements for article processing charge funds, international issues and risks for learned societies, such as the Institute of Physics and the London Mathematical Society.
Link
The implementation of open access (Opens PDF)
