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What I'm reading, and more

July 13th, 2003

Riemann’s zeta function by HM Edwards (includes translation of Riemann’s original paper as an Appendix) . What with A Beautiful Mind and the proof of Fermat’s Last Theorem a few years back, the Riemann hypothesis is the last big maths question accessible to amateurs like myself. It’s hard going though – heaps of complex analysis applied to concepts as simple as those of prime numbers and factorials. In fact, the zeta function is a relatively simple modification of the factorial n!, extended from positive integers to complex numbers in general, and the Riemann hypothesis says that all zeros of this function lie on a given line. With a bit more work I hope to understand this better, and will try to post or link to a good explanation.

Meanwhile, Sunday being the day of religious observance in Australia, I finally did something about the change of religion I announced last year, taking the family out to the Gabba. I’m pleased to report an exciting victory by the Brisbane Lions over the Hawthorn Hawks, 14.9 (93) to 11.15 (81). As a neophyte, I was happy,if surprised, to learn that my new club song is to the stirring tune of La Marseillaise.This set me thinking about other possibilities -perhaps the Horst Wessel Lieder would fit Carlton and Rupert Murdoch’s rugby league teams could use The Star-Spangled Banner.

This was the first AFL game I’ve ever been to, and the first top-grade Aussie rules game I’ve been to since I followed West Torrens in the SANFL 40 or so years ago (In the intervening years, I’ve lived in rugby league territory almost continuously). Things have changed in all sorts of ways, but the change in relative prices is the most obvious. Back then (B&W) TV was a luxury while going to the footy was taken for granted. Today I could get a brand-new colour TV for the price I paid for tickets for the family (not the cheapest on offer, but nothing special). It’s not hard to explain given technology, wages and so on, but it’s striking nonetheless. And despite the prices, the ground was packed.

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  1. July 14th, 2003 at 10:01 | #1

    The twin primes conjecture doesn’t count as a big maths question? Or has it been solved? I don’t think it’s a particularly important question – esp compared to the Riemann hypothesis which I’m told does matter for lots of other things – but then again Fermat’s theorem wasn’t that relevant to many other questions.

    If you do find a simple way of presenting the Riemann hypothesis so it’s understandable to amateurs it’d be fun to see a post on this. Of course, if I really wanted to find out about it I suppose I should read the book myself.

  2. John Quiggin
    July 14th, 2003 at 11:10 | #2

    The Riemann hypothesis is closely related to the Prime Number Theorem, which gives the intuitive basis for the best generalization of the twin primes conjecture, due to Hardy and Littlewood. So I think RH is in a class above the twin primes conjecture. Similar points apply to Goldbach’s conjecture (every even number >4 is the sum of two primes).

  3. July 15th, 2003 at 01:00 | #3

    The Horst Weseel Lied for Carlton? OUCH damn that’s a slap and a half!

    The reason why your ticket prices are a tad higher is they pay the players properly these days. All things are relative. British blogger Stephen Pollard said he pays £750 for a season ticket to English Premier League club Spurs.

    That works out to over $100 a game, per seat.

  4. Jack
    July 16th, 2003 at 17:34 | #4

    As an example of the importance of the Riemann Hypothesis it has been known for a long time that the truth of the RH would imply Fermat’s Last Theorem.

    Once you have mastered the RH, Edwards earlier book about Galois Theory is also a great read with historical context.

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