Archive for the ‘Mathematics’ Category

WhyTo: Foster anarchy in research and teaching

April 6, 2010

A piece in EPW Vela Velupillai writes (Unfortunately, EPW does not allow one to give the exact URL to the piece):

In this paper I attempt to make a case for anarchy in research against the current practice of picking winners in universities at advanced levels of education and research. By considering a paradigmatic example of freedom in speculative intellectual activities leading to unintended consequences of enormous benefit to mankind, I try to substantiate a case for this. The example I consider is the way issues in the foundations of mathematics paved the way for what came to be known as the it revolution. It is a counter-factual narrative and may – hopefully, will – provide an antidote to the current orthodoxy’s regimented non-vision of “picking winners”, ex ante, without any historical substantiation.

While you are at it, a piece on Periyar’s views on science from the same issue might also be of interest.

Update: These lines from Velupillai’s piece are too tempting to be not quoted:

…I continued to learn from [Goodwin], both in the substance of economic theory …. and in a more subtle way that I do not know how to describe except as a matter of intellectual style. The unspoken language was that if a thing is worth doing it is worth doing playfully. Do not misunderstand me: ‘playful’ does not mean ‘frivolous’ or ‘unserious’. It means, rather, that one should follow a trail the way a puppy does, sniffing the ground, wagging one’s tail, and barking a lot, because it smells interesting and it would be fun to see where it goes.

Have fun!

Mathematisation of …

March 30, 2010

Sexual attraction; here is the abstract:

Pollen tubes follow attractants secreted by the ovules. In a recent paper in BMC Plant Biology, Stewman and colleagues have quantified the parameters of this attraction and used them to calibrate a mathematical model that reproduces the process and enables predictions on the nature of the female attractant and the mechanisms of the male response.

Here is the last paragraph of the piece:

As with many other mathematical approaches to complex biological behavior, this new model from Stewman et al. [3] raises more questions than answers. But the fact that new approaches are contributing to a precise experimental description of the system [2,11,12] may make mathematical modeling an important tool for testing and selecting candidate molecules that may fit the in vivo biological profile of the final step of plant sexual attraction.

Here are the references in question:

[2] Dresselhaus T, Márton ML: Micropylar pollen tube guidance and burst: adapted from defense mechanisms? Curr Opin Plant Biol 2009, 12:773-780.

[3] Stewman SF, Jones-Rhoades M, Bhimalapuram P, Tchernookov M, Preuss D, Dinner AR: Mechanistic insights from a quantitative analysis of pollen tube guidance.

BMC Plant Biol 2010, 10:32.

[11] Márton M, Dresselhaus T: A comparison of early molecular fertilization mechanisms in animals and flowering plants. Sex Plant Reprod 2008, 21:37-52.

[12] Okuda S, Tsutsui H, Shiina K, Sprunck S, Takeuchi H, Yui R, Kasahara RD, Hamamura Y, Mizukami A, Susaki D, Kawano N, Sakakibara T, Namiki S, Itoh K, Otsuka K, Matsuzaki M, Nozaki H, Kuroiwa T, Nakano A, Kanaoka MM, Dresselhaus T, Sasaki N, Higashiyama T: Defensin-like polypeptide LUREs are pollen tube attractants secreted from synergid cells.

Nature 2009, 458:357-361.

Here is Reference 3. Have fun!

The balancing act for Universities

March 17, 2010

Michael Atiyah, in an interview in Mathematical Intelligencer (published long ago, in 1984):

Universities are institutions that are educational and involved in research. I think that is very important–there should be unity in the university and unity in the whole social structure that attempts to keep a broad balance between mathematical research and mathematical education. And when universities give courses for educational purposes, they should be sure that they are performing the right task for the students, not just giving courses in (say) advanced topology because they are interested in turning out research students. That’s a disastrous mistake.

Universities must try to balance two activities. They ought to know what’s useful for students to learn, bearing in mind what they are going to be doing later on. At the same time, they ought to foster research. Some people will be doing all research and some people will be mostly teaching, and mainly people will be in between. Although I am only involved with the research end of it, I live in the university, I have colleagues in the university, I know what they are involved with, so I am concerned to see that a proper balance is struck between the different functions of the university.

A good one!

A must-see video

March 14, 2010

The half-an-hour of video that this blogpost points to is a must watch; I liked the two definitions of teacher given by J C Bose that Prof. Vaidya refers to towards the end of the movie. Link via Anant Observations.

Two positives do make a negative

February 15, 2010

I just lo……ved this bit:

The eminent linguistic philosopher J. L. Austin of Oxford once gave a lecture in which he asserted that there are many languages in which a double negative makes a positive, but none in which a double positive makes a negative — to which the Columbia philosopher Sidney Morgenbesser, sitting in the audience, sarcastically replied, “Yeah, yeah.”

From here. By the way, in case I forgot to mention, the entire piece is a great one and a must-read.

Capitalism and mathematics

February 7, 2010

Capitalism and mathematics are intimately related; mathematics functions as the grammar of techno-scientific discourse which every form of capitalism has relied upon and initiated. … feasible, in other words, to see in the realist account of mathematics an ideological formation serving certain (techno-scientific) ends within twentieth-century capitalism.

Brian Rotman, in Towards a semiotics of mathematics (of course, from 18 unconventional essays on the nature of mathematics).

What makes mathematics hard

January 17, 2010

What makes mathematics hard is both how easy it is to make mistakes and how difficult it is to hide them. Contrast this with poetry. It’s as easy to make mistakes in poetry — write stunningly bad poetry — as it is to blunder in mathematics. But it is much easier to cover up poetic blunders. Why that is is extremely interesting …

This is a quote (in a footnote) from Judy Azzouni’s How and why mathematics is unique as a social practice — which is one of the 18 unconventional essays on the nature of mathematics.

This is the third essay that I am reading from the book — that of Azzouni. The other two I have read so far are Leslie A White’s The locus of mathematical reality: an anthropological footnote and William Timothy Gowers’ Does mathematics need a philosophy?

All the pieces I have read so far, as with the above quote, are quite provocative and are interesting even if one disagrees with some of what it said in the piece. The remaining essays look pretty promising too!

Strongly recommended!

Two things about Euler that I learnt today

November 23, 2009

From Rolf Jeltsch’s colloquium in the Mathematics Department are the following:

[1] Euler was probably one of the earliest mathematical modellers: for example, he turned the Koenigsburg bridge problem into one of graph theory; and, apparently, he is also the first one to consider control volumes in fluid dynamics while the other hydrodynamicists were looking at the entire fluid under different circumstances and tried to describe its behaviour.

[2] Euler was pretty open by the then scientific standards; while his contemporaries were trying to keep their discoveries secret, apparently, he wrote expository pieces and circulated them, and, never indulged in priority disputes.

I have read great things about Euler through his great admirer (probably the greatest) Clifford Truesdell. After learning about his open science approach, I am more impressed.

Rejecta Mathematica

July 16, 2009

Rejecta Mathematica is a real open access online journal publishing only papers that have been rejected from peer-reviewed journals in the mathematical sciences.

From here, where the inaugural edition is available; link via MR.

Don’t miss to read the manuscript submission guidelines; a great journal, as far as I can see!

Some math-y links

July 7, 2009

All the following are from Notices of AMS (and, pdf):

  1. Solving Sudoku puzzles — paper and pencil algorithm
  2. TeX family in 2009
  3. LaTeX — breaking free!
  4. Mathematical models in science and engineering
  5. A special issue on formal proof
  6. Last poem of James Clark Maxwell (This one is a real gem!)

Have fun!