The so-called Stampioen Affair publicly involves only two mathematicians: Jacob Waessenaer, a Utrecht surveyor and cartographer, and owner of a school in applied mathematics, who died in 1688 (date of birth unknown), and Jan Stampioen, born in 1610 (he probably died in 1653 in a gunpowder explosion at Arras), who had a somewhat similar position at Rotterdam before being appointed in 1638 or 1639 as teacher of mathematics to Prince William of Orange (1626–50), the son of the stadholder – something which Descartes initially does not seem to have realized (see AT III 736–42). Waessenaer was an able mathematician (according to John Pell [1611–85] one of the best in the United Provinces), who perfectly understood Descartes’ Geometry (see AT III 735–36). Stampioen seems to have been an excellent teacher and made innovative proposals in the field of mathematical notation (Cajori 1974). In 1633 Stampioen proposed a mathematical problem to Descartes, probably at the instigation of Isaac Beeckman. In his answer, Descartes feigns to be an amateur in mathematics but meanwhile solves Stampioen's problem and challenges him to solve the problem of Pappus (AT I 275–79). But although Descartes clearly is pulling Stampioen's leg, there is no animosity. It is not clear why Descartes became involved in what seems to have started as a quarrel between two rival mathematicians. The only intellectual motive one can think of is that in 1639 Stampioen published what he self-importantly called a “new algebra” (Stampioen 1639), which Descartes clearly found bogus. Nor do we know who took the initiative: Waessenaer who sought support against Stampioen, or Descartes himself who either wanted to expose Stampioen as a charlatan or tried to promote the cause of someone interested in his Geometry. Descartes’ first letter to Waessenaer (and the only one known) dates from February 1640 (AT III 21–28), but he must have been involved earlier (see AT III 6). Waessenaer may even be the Utrecht mathematician referred to in a letter to Mersenne of March 31, 1638 (AT II 99).

In 1638 Stampioen published two problems under the assumed name of Joannes Baptista Antwerpiensis (cf. AT II 601–2). The first concerns the attack on a horn-work (hoornwerk–a double bastion vaguely resembling a bull's head). Waessenaer published his solution in a lost pamphlet of 1638, using Descartes’ “notes” (AT II 605).