Mathistory

Chapter VIII

Visual maps

How mathematics learned to draw

MDCXXXV

In textbooks, formulas look as if someone thought them up alone at a desk. In reality they travelled in letters, along roads and across the sea, from one person to the next. In this chapter we draw them on a map.

Question

How did a mathematician in Toulouse find out what a colleague in Amsterdam was working on?

Picture Europe around 1635. There are no scientific journals, universities are mostly busy with theology, law and medicine, and new mathematics often happens outside them: in the studies of lawyers, officials and priests. Pierre de Fermat is a judge in Toulouse. René Descartes lives in the Netherlands and keeps changing his address. Galileo Galilei is under house arrest near Florence.

When one of them discovers something, how do the others hear about it? And when one of them is stuck, whom does he ask?

The answer: he writes to Paris, to a monk.

Person

The secretary of learned Europe

Marin Mersenne

8 September 1588 – 1 September 1648 · Minim friar

  1. 1588born in Oizé in the French province of Maine
  2. 1604studies with the Jesuits at La Flèche, the same school as the slightly younger Descartes
  3. 1611joins the Minims; later lives in their Paris convent near the Place Royale
  4. 1635founds the Academia Parisiensis
  5. 1636Harmonie universelle, a book on music and acoustics
  6. 1648dies in Paris; his cell holds letters from dozens of scholars

Marin Mersenne was a Minim friar, but above all he was the hub through which the correspondence of scientific Europe flowed. He was interested in mathematics, music, acoustics and physics. He translated, published and, above all, asked questions.

Every week, mathematicians and natural philosophers met in his cell in the Paris convent. The circle is called the Academia Parisiensis, or simply Mersenne’s academy. Those who could not come to Paris wrote instead. Mersenne read the letters, copied them and sent them on, often with a question of his own added. When Descartes moved to the Netherlands, Mersenne became his main link with the world.

He was a one-man scientific journal at a time when journals did not yet exist.

Mersenne primes – why you know his name from mathematics

Numbers of the form 2n − 1 are now called Mersenne numbers. In 1644 Mersenne claimed to know for which n up to 257 they are prime. His list contained mistakes, but it made the question famous. The largest known primes are still Mersenne primes today.

Map

Mersenne’s correspondence network

Click a place on the map

The lines show correspondence with Paris. Click a dot to see who worked there. Click a name to learn more.

Paris, Mersenne’s cell correspondents elsewhere · number = people in that place

Places show where each person mainly worked while in contact with Mersenne (approximately). The notes are brief; full biographies are on MacTutor History of Mathematics. Map: Marie Vestenická.

§What the map shows

At first glance the network is shaped like a star. Almost every line leads to Paris, and the correspondents wrote to each other far less. Anyone who wanted Europe to hear about a result sent it to Mersenne.

This shape had advantages and drawbacks. News spread fast, but everything depended on one man. Mersenne also liked to add fuel to the fire: a problem he received from one scholar he would send to another as a challenge. This led to a number of famous quarrels, for example between Descartes and Fermat over tangents, or between Descartes and Roberval over the cycloid.

Notice also who did not travel to Paris. Fermat never attended the Paris meetings, and after 1628 Paris saw Descartes only on short visits. Without Mersenne, their work would have stayed in a drawer much longer.

One of the questions that travelled through this network is an ordinary curve drawn by a nail on a wheel. You will find its story in Chapter IX: The cycloid.

Legacy

From one cell to the whole world

Mersenne died on 1 September 1648. After his death the network broke up into smaller groups, which showed how fragile it had been. Seventeen years later, in 1665, the first two scientific journals appeared: the Paris Journal des sçavans in January and the London Philosophical Transactions in March. Their editor in London, Henry Oldenburg, secretary of the Royal Society, did essentially what Mersenne had done: he read letters from all over Europe and passed them on, only now in print.

Mersenne’s letters were published in full in the twentieth century in seventeen volumes (Correspondance du P. Marin Mersenne, 1932–1988). Thanks to them we know today who wrote to whom and about what, and we can draw it on a map.

MERSENNE’S NETWORK

28 scholars · 12 places

1 cell in Paris

Every formula was once a letter.

Sources. TANNERY, Paul; DE WAARD, Cornelis (eds.). Correspondance du P. Marin Mersenne. Paris: CNRS, 1932–1988. · O'CONNOR, J. J.; ROBERTSON, E. F. Marin Mersenne. MacTutor History of Mathematics. · Map data: world-atlas (Natural Earth).

END OF CHAPTER EIGHT

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