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Descartes: The Brilliant Mathematician

René Descartes, a French philosopher, mathematician, physicist, and lay Catholic, invented analytic geometry, bringing areas of geometry and algebra together.

Descartes was regarded as a leading mathematician, the creator of a novel and complete physics or natural-sciences theory, and the proponent of a new philosophy by his contemporaries. His philosophy became well-known and debated after his death. Components of his research, particularly his physiology and his project in the eighteenth century, were popularised. He was remembered for his failed metaphysics and his use of sceptical reasons for thinking. 

René Descartes, a French philosopher and mathematician, stated the rule of signs in La Géométrie without providing any justification (1637). Sir Isaac Newton, an English scientist and mathematician, reformulated the formula in 1707, though no proof has been found. Some mathematicians assume that he thought the evidence was too simple to write. 

The rule for determining the maximum number of positive real number solutions (roots) of a polynomial equation in one variable based on the number of times the signs of its real number coefficients change when the terms are arranged in canonical order (from highest power to lowest power) is known as Descartes’ rule of signs.

The Life and Works of Descartes

Descartes is regarded as the founder of modern philosophy. He is well-known for establishing a crucial link between geometry and algebra, allowing algebraic equations to solve geometrical problems. He promoted a new philosophy of matter that allowed mechanical explanations to be used to account for physical occurrences.

The Formative Years

On March 31, 1596, Descartes was born in La Haye, France, to Jeanne Brochard and Joachim Descartes. He was just one of many children that made it out alive. His father practised law and worked as a magistrate. Therefore, he did not have much time for his family. In May, Descartes’ mother passed away after he was born, leaving him, his brother, Pierre, and his sister, Jeanne, to be cared for by their grandmother in La Haye. In 1606, he was sent to the Jesuit institution at the age of ten. He studied there until 1614, then transferred to the University of Poitiers in 1615, where he earned his Baccalaureate and Licence in Canon and Civil Law a year later.

Discourse and the World

Descartes’ movements for the few years after he left the army in 1619 are unknown. There is the suggestion that he spent time around Ulm based on what he states in the Discours de la Methode (Discourse on the Method), published in 1637 (Descartes attended the coronation of Ferdinand II in Frankfurt in 1619). There is proof that he was in France in 1622 because the property he had inherited was sold at that time, and the earnings would provide him with a simple income for many years.

René Descartes’ Family Life

His grandmother raised him and his brothers because their father was preoccupied with business and serving as a council member in the provincial legislature. Descartes never married, although he and Helena Jans van der Strom had a child in 1635. Francine was the name given to the child. Sadly, he died of scarlet fever when he was five years old.

The Fundamentals

Descartes’ public life was further complicated by the Dutch theologian Gisbert Voetius (1588–1676) shortly after his confrontation with the Sorbonne. Regius, a Dutch physician who taught medicine at the University of Utrecht, had been assailed by Voetius for teaching certain ‘Cartesian’ notions that ran counter to conventional religious orthodoxy. Regius was a close friend of Reneri and Descartes and a firm believer in Descartes’ philosophy. Regius’ status as a professor was threatened by Voetius, who criticised Descartes’ work and his character.

René Descartes’ Notable Works

Descartes’ philosophical writings affected Western philosophy and created the groundwork for the Cartesian method, a philosophy, mathematics, and scientific approach. Cartesianism is founded on several significant publications.

Discourse on the Method of Correctly Conducting One’s Reason and Seeking Truth in the Sciences (1637): Descartes’ most famous remark, ‘Je pense, donc Je Suis’ (‘I think; therefore I am’), is introduced in this work. It also serves as a foundation for his methodological scepticism, one he would return to in later works.

Meditationes de Prima Philosophia (First Philosophical Meditations, 1641): This brief publication introduced Descartes’ philosophy and returned to his methodological scepticism (also referred to as ‘Cartesian doubt’). He gives a series of proofs for the existence of God, humanity, and the self, using both ontological and metaphysical arguments.

Philosophical Principles (1644): The Latin phrase ‘Cogito ergo sum’ is a translation of the French phrase ‘Je pense, donc Je Suis’ and the English phrase ‘I think; therefore I am’. It builds on the ideas of epistemology found in Descartes’ Meditations, but its reputation was tainted by a few physics claims that were later discredited.

The Passions of the Soul (Les Passions de l’âme, 1649): Descartes’ final philosophical essay was published in this work. The link between science and moral philosophy is explored in this text.

Awards and Honours

The Descartes Prize was an annual award awarded by the European Union in the field of science. René Descartes, a French mathematician and philosopher, was honoured with the name.

A research prize was given to groups of academics that ‘achieved remarkable scientific or technological discoveries through collaborative study in any discipline of science, including economics, social science, and the humanities.’ Nominations for this award were made by either the research teams or appropriate national bodies.


This brings us to the conclusion of this article. René Descartes was a philosopher, a mathematician, and a rationalist who believed in the power of reason.

Descartes’ conclusion that mind and body are truly distinct gave rise to the famous mind-body dilemma. The essence of the problem is the assertion that the natures of mind and body are completely distinct and, in some ways, opposed.


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