The Math Maniacs

Murderous Maths: Catriona Shearer's Puzzles Catriona is a maths teacher in Cambridge and she loves mixing up numbers with music because her favourite hobby is bellringing!

Lisbon, 1871.
Maria de Sá was born in a brothel but dreamed in numbers. By candlelight, she copied ledgers and merchant logs while her mother entertained clients behind a curtain. At 14, she ran away and took a job at a fish market, tallying crates faster than the men could shout them. A retired sailor noticed her skill and gave her a battered math textbook. She devoured it, line by line. Soon, she was tracking tides, calculating profits, correcting captains. She never went to university—women weren’t allowed. So she started teaching poor girls in a wine cellar. Arithmetic. Accounts. Navigation. In 1884, she published a book under a male pseudonym: Numbers for the Daughters of Lisbon. It was banned for “encouraging female arrogance.” Maria laughed, then printed more copies in secret. She died penniless but left behind a generation of shopkeepers, sea traders, and scholars who never forgot the woman who taught them to count their worth.

The new Pope was as undergraduate mathematics major.

And more!

2025 = the sum of the cubes of the first nine positive integers.

An Australian mathematician cracked the code of a famous 3,700 year old Babylonian clay tablet revealing that they were doing more accurate trigonometry nearly 1,500 years before the Greeks.

In 2017, Australian mathematician Dr. Daniel Mansfield from the University of New South Wales decoded a 3,700-year-old Babylonian clay tablet known as Plimpton 322. The tablet, which was originally discovered in the early 20th century in southern Iraq, contains a series of numbers arranged in four columns and 15 rows. For a long time, the purpose of these numbers remained a mystery.

Dr. Mansfield and his team discovered that Plimpton 322 is a trigonometric table. Unlike Greek trigonometry, which is based on angles and circles, Babylonian trigonometry used ratios of sides of right-angled triangles and a base 60 (sexagesimal) number system. This system, the researchers found, enabled the Babylonians to create a trigonometric table that is more accurate than the Greek method, as it avoids irrational numbers and provides exact ratios.

Key points about this discovery include:

1. Plimpton 322 predates Greek mathematicians such as Hipparchus, who is often credited with founding trigonometry, by more than a millennium.

2. The Babylonians' use of a base 60 number system allowed them to make complex calculations with great precision. Their method is particularly advantageous for some practical applications, such as surveying and architecture.

3. The tablet shows that the Babylonians had a sophisticated understanding of right-angled triangles and could solve problems related to their sides with exceptional accuracy.

4. This finding suggests that the history of mathematics is richer and more complex than previously thought, with advanced mathematical practices emerging in different cultures independently.

The discovery of the true purpose of Plimpton 322 has reshaped our understanding of ancient mathematical knowledge and highlights the advanced capabilities of Babylonian scholars long before similar concepts were documented in Greek mathematics.

a0=7; a_n = a_(n-1) + 2n + 7. Determine sum(n=0..infty, 1/a_n).