**Thomas Hobbes** was an English scholar and amateur mathematician who wrote on optics and on geometry. He attacked the 'new' methods of mathematical analysis.

- Thomas began his schooling in Westport Church when he was four years old.
- From age eight Hobbes, who was by this time proficient at reading and arithmetic, attended Mr Evan's school in Malmesbury, then later Robert Latimer's private school in Westport.
- Hobbes showed his brilliance at this school and was an outstanding Greek and Latin scholar by the time he left this school at age fourteen, having already translated Euripides' Medea from Greek into Latin iambics.
- For around two years Hobbes did little in the way of academic studies, being more of a companion to Cavendish who was only a little younger that he was.
- In 1610 Hobbes went with Cavendish on a European tour and they visited France, Germany, and Italy.
- On his return Hobbes took up studying Greek and Latin again.
- So far we have not mentioned any interest by Hobbes in mathematics, and perhaps even more surprisingly no particular interest in philosophy.
- Hobbes was about forty years old before he became fascinated by mathematics.
- Back in England in 1637 Hobbes worked on The Elements of Law, Natural and Politic which was not published at the time.
- When the Civil War began in 1640 Hobbes feared for his life, especially as he was a well known Royalist, and he fled to save his life.
- Hobbes's theory of vision and images serves him to ground his philosophy of man on his philosophy of body.
- Furthermore, since this part of Hobbes's work on optics is the most thoroughly geometrical, it reveals a good deal about the role of mathematics in Hobbes's philosophy.
- Hobbes published a new expanded edition of De Cive in 1647, then three years later, in 1650, his earlier work The Elements of Law, Natural and Politic was published without his permission.
- Hobbes was the mathematics tutor of the Prince of Wales between 1646 and 1648.
- Passages near the end of the Leviathan appeared to indicate that Hobbes was trying to make his peace with the English government, which angered the Royalists.
- In these passages Hobbes was remaining consistent with his view that one showed allegiance to a ruler only so long as that ruler could provide protection.
- Hobbes had also attacked the Roman Catholic Church which made his position in Paris pretty untenable.
- Hobbes' masterpiece Leviathan set out his ideas with great clarity.
- It is, Hobbes argues, the rational way for people to behave so moral behaviour is rational.
- Although Hobbes was himself a Christian, these arguments were seen as many as removing the need for God as the giver of moral code, for Hobbes argues that it follows by reason alone.
- Another aspect of the work which caused many to attack it was Hobbes' vitriolic arguments against the university system.
- Before this Hobbes had been seen by many as promoting a mechanistic scientific approach which was much in tune with those who would form the Royal Society.
- At this stage, however, although Hobbes had published little in the way of mathematics, he certainly was considered by some as a leading mathematician on a par with Roberval and Fermat.
- In 1655 Hobbes published De Corpore Ⓣ(On the Body) which, was one part of his trilogy of philosophy.
- Hobbes saw mathematics as an essential part of knowledge, but he also saw his own materialistic approach as revolutionising the subject and he set out to reform mathematics in this work.
- His approach is certainly consistently materialistic, denying abstract ideas; for Hobbes mathematics is the study of quantity, and quantities are the measures of 3-dimensional bodies.
- It is fair to say that much of Hobbes' mathematical ideas are generalised from Galileo's study of mechanics and of motion.
- The new method of indivisibles, as put forward by Cavalieri, was accepted by Hobbes but he rejected Wallis's version as given in Arithmetica infinitorum Ⓣ(Infinitesmal arithmetic).
- Hobbes had originally planned De Corpore Ⓣ(On the Body) without this result and, having added it late on, it did not really fit with the material surrounding it.
- Before De Corpore Ⓣ(On the Body) reached completion, however, Hobbes' friends pointed out an error in his squaring the circle argument.
- Hobbes did not remove the "proof" but renamed it "From a false hypothesis, a false quadrature".
- This was a phrase that Wallis would pour scorn on when he attacked Hobbes' ideas.
- Although Hobbes did not believe that the "proofs" in De Corpore Ⓣ(On the Body) proved the result, he would go on to publish several "proofs" of squaring the circle over the next 25 years which he did believe to be correct.
- Wallis attacked the whole of Hobbes' mathematical work of De Corpore Ⓣ(On the Body) and a vigorous argument between the two arose which lasted for 25 years.
- Hobbes claimed that the algebraic symbols could denote different things such as lines, surfaces or volumes, and therefore were unreliable in mathematical proofs.
- Hobbes responded to the attack by Wallis and others of De Corpore Ⓣ(On the Body) by publishing Six Lessons to the Professors of Mathematics in the University of Oxford in 1656.
- In 1660 Hobbes attacked the 'new' methods of mathematical analysis.
- In Dialogus Physicus, sive de Natura Aeris Ⓣ(Dialogue on physics or the nature of air) (1661) he attacked Boyle and those setting up the Royal Society which, as a matter of interest, never elected Hobbes as a Fellow (it is probably that since he was perceived as an atheist entry would have been impossible).
- Hobbes ended the argument about disloyalty with Mr. Hobbes Considered in His Loyalty, Religion, Reputation, and Manners (1662).
- Hobbes could win arguments when his morality was attacked, but when it came to mathematics Wallis had a clear upper hand understanding mathematics far more deeply than Hobbes.
- Over the years Hobbes attempted to solve a number of outstanding mathematical problems.
- Hobbes's attempts to resolve three important mathematical controversies of the seventeenth century: the debates over the status of analytic geometry, disputes over the nature of ratios, and the problem of the 'angle of contact' between a curve and tangent.
- Although Hobbes is highly regarded as a philosopher, his mathematics has been essentially laughed at.
- Hobbes defended his mathematical works to the end of his life.
- Let us end with the summary of what Hobbes believed that he had achieved in mathematics, written near the end of his life.
- If Hobbes' mathematics was worthless why has so much effort been expounded on it even in the last few years (as the references show).

Born 5 April 1588, Westport, Malmesbury, Wiltshire, England. Died 4 December 1679, Hardwick Hall, Derbyshire, England.

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Astronomy, Origin England

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive