Archimedes and Pythagoras Vavasor

Archimedes and Pythagoras Vavasor are probably the most famous set of twins in the history of mathematics. However, as far as the general public is concerned, they are primarily well-known for the manner of their deaths. Pythagoras (known to everyone as Pye) was found stabbed through the heart with a metal set square, while Archimedes (known as Archie) was found hanged in a wood several days later in an apparent suicide. Despite much speculation, no credible motive for the murder has ever been established.

In fact, Archie murdered Pye in a fit of anger on finding out that the latter had been having a secret affair with his lover Cressida Fox, whom both brothers had met while working for her husband Rufus Fairbanks, laundering money for the Belarusian mafia.

Early Life

Archie and Pye's parents were Arthur and Elsie Vavasor. Arthur was an actuary, although it turned out much later that he was completely hopeless with figures. This led to him leading a curious double life, whereby he would spend the day sitting at his desk in the offices of Penge Life, pretending to work but actually writing very bad poetry. At the end of the day, he would smuggle the papers home in his briefcase, handing them over to Elsie, who would spend the evening doing his work for him. When it later emerged that she had been one of the leading lights at Bletchley Park during the second world war, no-one in the family was the least bit surprised.

They had another son, Isaac, although Arthur left not long after he was born, intending to seek his fortune as a travelling bard. Nothing was ever heard from him again, but after due reflection, no-one in the family really missed him that much either. Meanwhile, Elsie, having failed to convince Penge Life that she had been doing Arthur's work for him and that they should take her on in his stead, set up her own insurance operation and very soon put them out of business.

Archie and Pye both took after their mother and demonstrated an early aptitude for mathematics, and it wasn't long before they were helping her to keep up with her increasing workload. By this time, they had also left conventional education far behind, partly through sheer ability but also because they increasingly communicated with each other via their own secret language, which the teachers at their school just found annoying. Elsie took them out of school altogether at this point and they took their A levels early, following which they both gained scholarships to read mathematics at Clare College, Cambridge University at the age of 15.

University

The Vavasors quickly established themselves as the leaders of their peer group at Cambridge, despite their tender age. They completed their set work with ease, before moving on to finding novel solutions to a series of hitherto unsolved problems, such as:

• The Fenwick-Kawasaki paradox
• Diquad's theorem
• Farrago's third postulate
• The 'evil hamster' dilemma
• Erdős's disrupted connection
• 0/00
• Maxwell's Viennese inversion
• The full solution to the soft cheese equation

More recent analysis of their work as undergraduates has led some researchers to conclude that most of these supposed problems and their solutions are in fact completely bogus, although given that they were formulated in the twins' own increasingly hermetic language, there also remains the possibility that they are entirely genuine. This is a recurring theme in the world of Vavasorology.

At the end of their undergraduate careers, Archie and Pye went on to complete the Part III tripos before being accepted into the PhD programme, eventually becoming - after a brief, failed attempt to disentangle the contents into two separate entities - the first-ever twins to defend a joint thesis. This was, appropriately, in the burgeoning field of chaos theory. Once again, the academic world is split as to whether the Vavasors' thesis was a work of such brilliance that no-one else in the field was truly capable of understanding it or what Professor David Crowdsense of Godsown University, York describes as

A bloody load of old bollocks.

Post-Doctoral Work

After completing their PhDs, the twins continued their studies, supplementing whatever meagre grants they could get by taking in their own PhD students. On the death of their mother, their share of her considerable estate enabled them to purchase a cottage in Little Wilbraham and employ a live-in housekeeper, Mrs Standage, to look after their everyday needs.

One of these students during their later years was Patrice Ambrose, whose work on the Konyagi fractal pattern ended up causing so many problems.

However, things took a difficult turn when they came across an aspect of chaos theory that seemed to offer a surefire way of making money at gambling, whether in the casino or on the turf. Unfortunately, the algorithm took some time to perfect and very soon they were massively in debt, so much so that there was nothing left of their inheritance and they were in danger of losing the lifestyle that they had so carefully built up.

At this point, their younger brother Isaac, by now an expert himself on the work of Saint Hildegard of Bingen, received an approach from a monk from the Order of the Romanesco who were interested in Archie and Pye's work on fractals. The brothers were happy to work with the monks, but in the course of their work for them, they came across some algorithms that seemed to offer a way to make considerable amounts of money in the financial markets, thus getting them out of the financial hole that they had found themselves in. This precipitated an acrimonious split with the monks, who felt that the beautiful work that they had done together would be debased by contact with the world of mammon. In this, they were almost certainly correct.

The twins' subsequent success in the City attracted the attention of Rufus Fairbanks, and thence the Belarusian mafia, and one thing led to another, resulting in Isaac's lament that if he hadn't introduced them to the monks, they might still be alive today.

Legacy

There is still much debate as to the value of the work that the Vavasor twins have left behind. The continuing absence of their papers has done nothing to dispel the suspicion that what they were working on for all those years in Little Wilbraham has little value beyond the accidental discovery of some nifty financial trading algorithms. However, the world community of Vavasorologists continues to grow and theorise and perhaps one day we will come to understand the whole truth about what the Vavasors have done for us.