Musical Interlude: Robert Webb’s Disconnectica

Robert Webb is an amazing guy. Burkard and I first met Robert years ago, when he began attending our public talks. Robert is quiet and un-self-promoting, but we slowly realised how creative he is. Robert has written Stella, really cool software for visualising and creating nets for polyhedra; Burkard and I wrote about Robert and Stella in our Age column, which we included in Dingo, our first book of columns. It turns out that Robert, under the name Disconnectica, also composes and performs very good music, complete with videos. Very strange videos. Continue reading “Musical Interlude: Robert Webb’s Disconnectica”

Erdős’s (not Thue’s) Proof of the Infinity of Primes

(19/10/22 In a comment below,  Bernard has noted the proof should be properly attributed to Paul Erdős, not Thue. Thue’s counting argument is similar in spirit, but not as quick.)

This post has no deeper meaning.1 Its purpose is just to present a very nice argument, which we gave in our talk last week, and which we feel should be better known.

One of the beautiful theorems that every school student should see is the infinity of primes.2 The standard Euclid proof tends to be difficult for students to appreciate, however, since, although the arithmetic is trivial, the argument is typically clouded with the unsettling concepts of infinity and contradiction.3

The following proof by Norwegian mathematician Axel Thue involves counting and a little more arithmetic, but avoids a head-on confrontation with infinity. Instead, Thue provides a direct guarantee of the number of primes up to a certain point. Versions of Thue’s argument can also be found at cut-the-knot and in Hardy and Wright,4 but the following seems cleaner to us. Continue reading “Erdős’s (not Thue’s) Proof of the Infinity of Primes”

OUP’s Missed Chance on Knowledge and Skills

A bit over a week ago, the Australian arm of Oxford University Press, in collaboration with the Australian Maths Trust, released a White Paper: The knowledge and skills gap in Australian primary mathematics classrooms. Yeah, it’s in the “well, duh” category of reports, on the massive range of student mathematics levels, which primary school teachers must then manage. But, still, the report can’t be a bad thing, can it? Well, …

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The Stupidest Idea Ever Productivitied

We probably should have known that the Productivity Commission was no more than a safe place for pompous, pseudo-rational windbags. But, we didn’t. And so earlier this year, by request, we made a submission to the PC’s review of the National School Reform Agreement. The PC’s Interim Report appeared in due course, and it provided sufficient reason to never again bother with these clowns. Until now.

Last week, the Productivity Commission released its Interim Report on, um, Productivity. Which makes one wonder what all their other reports are about. No matter. We have a report. It is special.

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Marty Talk – Not Quite The Prime Number Theorem

Having foolishly ventured out to Monash Uni last Tuesday to see the Evil Mathologre give a Lunchmaths talk, I found myself roped in to giving the next one. So, anyone who is around Monash next Tuesday and has nothing better to do is welcome to attend. Details below, and here. Continue reading “Marty Talk – Not Quite The Prime Number Theorem”

The Awfullest Australian Curriculum Algebra Lines

We’ve now gone through all the algebra – more accurately, “algebra” – sections of ACARA’s new mathematics curriculum. Parallel to our Worst Number Lines post, the following is our list of the worst algebra lines. Once again, it is important to note that these few lines do not begin to convey the unrelenting stupidity and triviality of the curriculum, but the real question is who invented letters in math?

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Can Smart Victorian Students Avoid Mathematical Methods?

Note that our question is not whether smart Victorian students should avoid Methods. Given that Methods is the ugliest, stupidest, most aimless, digitally perverted, anally retentive, error-strewn, little Hitler managed, God forsaken heap of anti-mathematical garbage ever conceived, or even conceivable, of course all students should avoid Methods if they possibly can. The question is, can they?

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