A Differential Equation

Thursday 21 September 2006 at 11:46 am | In Articles | 1 Comment

It’s nice to see mathematics in a newspaper, but in this case it’s just there to baffle. In the printed version of today’s Guardian financial viewpoint Nils Prately wrote (the online version doesn’t include the equation):

    At last, proof that PartyGaming, king of online poker, will soon find its flush busted. Here is the first line of the mathematical equation, fresh from UBS, the investment bank:

      \displaystyle \frac{\delta\! f}{\delta t}=\left(\phi (t) - 2s \right) - \frac{1}{10}\left(\phi (t) - 2s \right)

    Wha’d’y’a mean you don’t get it? It’s a variation of a Lotka-Volterra differential equation for the modelling of eco-systems. Surely you’re familiar …

Lotka-Volterra consists of a pair of differential equations so how can you print just the first line 😕 it’s like printing half a word. Then again, the printed equation isn’t a differential equation – I thought perhaps \displaystyle \frac{\delta\! f}{\delta t} was a misreading of \displaystyle \frac{\partial\! f}{\partial t} but t seems to be the only independent variable so it’s probably \displaystyle \frac{df}{dt}. I presume there’s also another error since the equation, as printed, obviously simplifies to \displaystyle \frac{\delta\! f}{\delta t} = \frac{9}{10}\left(\phi (t) - 2s \right)

The good news though is that they printed the equation using proper fonts and symbols so it did really look like mathematics 🙂

Notes & Queries

Wednesday 20 September 2006 at 9:11 pm | In Articles | 3 Comments

Each week the Guardian newspaper runs a Notes & Queries column where readers answer other readers’ questions. It’s been going for 15 years and often has fascinating questions and answers. I had one of my replies printed (about the VideoPlus system for numbering television programmes). It was born long before online forums became popular and spawned a number of books.

Today a question has been asked which totally astonishes me. I can’t think what the questioner thinks about mathematics.

    Gravity existed before Newton discovered it. Did mathematics exist before the first mathematician evolved?

I don’t believe it is a sophisticated question about whether mathematics is invented or discovered.

If you want to answer the question, and maybe see it published, then email your (short) answer to the column at nq@guardian.co.uk

Added 27th September: In the answers given to this question (not as far as I know available online) one contributor recommends reading Conversations on Mind, Matter and Mathematics where J.-P. Changeux and Alain Connes debate questions like

    Do numbers and the other objects of mathematics enjoy a timeless existence independent of human minds, or are they the products of cerebral invention? Do we discover them, as Plato supposed and many others have believed since, or do we construct them?

Mathematical Intrigue 2

Tuesday 19 September 2006 at 11:54 am | In Articles | Post Comment

Following on from Mathematical Intrigue below, a lawyer acting for Shing-Tung Yau, a mathematician mentioned in the New Yorker article, has written to the New Yorker disputing a number of points in the article and an ‘insulting’ illustration (which is not shown in the online version). You can see the Press Release with links to the letter. The letter is well worth reading. It makes many allegations of errors in the article; I found the following sentence in the letter the most interesting:

    The truth is that there was no “battle” over who should receive credit for solving the Poincaré Conjecture*

This is highly unusual in mathematics – yes, people have occasionally argued about who proved what but I can’t think of a case where lawyers got involved. There’s even a webcast tomorrow Wednesday 20th September at noon, New York time.

Ars Mathematica’s article on this is worth reading. This one could run and run and is bound to be picked up by newspapers.

*The pdf’s document properties says that content copying or extraction is allowed

Web Page Puzzle

Friday 15 September 2006 at 4:54 pm | In Articles | Post Comment

There’s a popular puzzle going round that seems to have been spread by viral marketing which gives you a web page and asks you to solve a puzzle in order to find the next page.

If you are bored then visit Hacker Puzzle and see if you can get to the final page (page 23, in case you’re wondering). Despite what it says, there’s no hacking or dodgy pages but there is some elementary mathematics.

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