ISAAC BARROW: BIOGRAPHY AND CONTRIBUTIONS - MATHS - 2025

Isaac Barrow was a mathematician, professor, and theologian born in England in 1630. Although less known than Isaac Newton, who was his disciple, Barrow's contributions to the field of mathematics were very important and laid the foundation for further research.

Specifically, his most important work for mathematics was the union of the differential calculus and the integral calculus. In fact, one of the laws that govern this type of calculation is called Barrow's Law, named after his pioneering work in the field of mathematics.

As a teacher he spent his career at the University of Cambridge, with a short interlude that he devoted to traveling forced by problems with the university leaders in a period of religious confrontation in the country. In his last years he abandoned both teaching and scientific research.

He gave his chair to Newton and devoted himself to theology, his other passion. In fact, in his day he excelled as a sermon writer. A man with a somewhat eccentric temperament, he died very young, leaving the memory among his contemporaries of having always had an impeccable conduct.

Isaac Barrow biography

Isaac Barrow was born in London in October 1630. His first years of study were spent at Carterhouse, where he stood out more for his bad behavior than for being brilliant.

His aggressiveness and provocative character made his father despair, to the point of wishing God would shorten the boy's existence.

In any case, that way of being did not prevent him from taking advantage of the teachings he received. Before entering the University, he spent time at Felstes, taking a preparation course.

He learned Greek, Hebrew, Latin and logic, and was ready to enter Trinity College, Cambridge. According to some biographers, he received the help of his uncle, who was part of the Governing Board of the center.

From there he did begin to show signs of his intelligence. He is described as a very diligent student, who excelled especially in mathematics.

First jobs

With great academic results, Barrow graduated in 1648. He immediately began working at the same institution, doing research work and, shortly after, as a teacher. Thus, the mathematician established his permanent residence in Cambridge.

The first subject he taught was the Greek language. However, political and religious problems affected his work. In 1655 the university authorities dismissed him, since he had refused to swear the commitment to the Commonwealth.

However, Barrow took advantage of the time when he had to leave Cambridge. For a few years he devoted himself to traveling through Europe, visiting France, Italy and Constantinople, among other places. He lived numerous adventures, including an interesting encounter with pirates in the Mediterranean.

Return to england

Upon returning to England, Barrow is ordained. Similarly, he regained his post at Cambridge, this time as regius professor of Greek.

The next position he held was that of Professor of Geometry, in 1662. The following year he managed to be elected as the first Lucasian professor at Cambridge, quite an achievement at the time.

Apart from his teaching work, he continued researching and publishing works. The most important in the field of mathematics were Geometry and Optics. At the end of that decade, specifically in 1669, Barrow left the chair, replaced by Isaac Newton.

Last years

After leaving teaching, Barrow turned to theology. He published several works on that discipline and became a renowned sermon writer.

His treatise called Supremacy of the Pope is one of the most recognized examples of controversial treatises ever published.

He still had time to return to Cambridge. In 1672 he became part of the management of Trinity College. From that position, he was one of the founders of the institution's library. Isaac Barrow died in London on May 4, 1677, at just 47 years old.

Contributions

Fundamental theorem of calculus

Isaac Barrow's best known theoretical work was the creation of a methodology for calculating tangents. His method had an approach that approximated the forms of calculation. In this way, he was a pioneer in describing derivation and integration processes as inverse operations.

Another of its merits was the construction of the so-called “characteristic triangle”. In this, the hypotenuse is established as an infinitesimal arc of curve. For their part, the legs are infinitesimal increments, with differing and ordered abscissa at the ends of the arc.

Geometric lessons

It was in 1669 when the theorist published his masterpiece: Geometric Lessons. That was where he developed his method for creating tangents to curves.

It was Isaac Newton himself who wrote the preface. Some say that he contributed some of his ideas, but in general it is considered that he only made some contribution of his own in the field of optics.

In summary, in this work Barrow established that to mark a tangent line to a curve, the relation with the quadrature of the other curve must always be taken into account. This has been considered as a first version of the Fundamental Theorem of Calculus

In short, the mathematician was a pioneer in formulating a geometric version of the aforementioned Fundamental Theorem of current calculus. As a tribute to his work, the second fundamental theorem of integral calculus (or Newton-Leibniz rule) is called Barrow's rule.

Other works

Another outstanding work of Barrow was the simplified version of the work Elements of Euclides, which he published in 1655. In 1683 a compilation of several of his readings was published, under the name of Mathematical Lessons, with a content in which he relates metaphysics with the maths.

He was also the author of an analysis on the work of Archimedes, as well as another analysis on Theodosius.

As noted above, he also had experience as a writer. In that regard, he gained much fame as an author of sermons and for some controversial treatise centered on religion, the other passion of his life. As a curiosity, it can be noted that there is a lunar crater that bears his name in his honor.

References

1. Easy math. Isaac Barrow. Recovered from matesfacil.com
2. EcuRed. Isaac Barrow. Obtained from ecured.cu
3. Ponce Campuzano, Juan Carlos. Isaac Barrow and his geometric version of the Fundamental Theorem of Calculus. Obtained from oei.es
4. JJ O'Connor, EF Robertson. Isaac Barrow. Retrieved from groups.dcs.st-and.ac.uk
5. Charles Scribner's Sons. Barrow, Isaac. Retrieved from encyclopedia.com
6. National Council of Teachers of Mathematics. Isaac Barrow 1630–1677. Recovered from jstor.org
7. Ron Larson, Bruce Edwards. Isaac Barrow. Retrieved from larsoncalculus.com