Maria Gaetana Agnesi
Maria Gaetana Agnesi was the first woman to write a mathematics textbook and the second woman to be appointed as a professor at a university. But, that’s not the end of her extraordinary achievements and qualities. Maria took care of her 20 younger siblings selflessly after the death of her mother, setting aside her own aspirations to join a convent and become a nun.
Maria Gaetana Agnesi was a great mathematician, philosopher, and theologian. She transcended all the boundaries of being a woman in 18th-century Italy to make an impact not only in the world of mathematics, but also in the life of regular people living in her hometown of Milan.1
Maria Gaetana Agnesi (1718 – 1799) was an Italian mathematician, philosopher, theologian, and humanitarian. Agnesi was the first western woman to write a mathematics textbook. She was also the first woman to be appointed professor at a university.
Her textbook, the Analytical Institutions for the use of Italian youth combined differential and integral calculus, and was an international success.
Agnesi also studied a bell-shaped curve described by the equation . This function is now called the Witch of Agnesi. The strange name might come from a pun in the Italian language, were the word “versiera” for “witch” sounds similar to the ropes used when sailing.2
1 “Maria Gaetana Agnesi: A Life Of Devotion To Mathematics And Charity”. 2022. Medium. https://anagrath.medium.com/maria-gaetana-agnesi-a-life-of-devotion-to-mathematics-and-charity-66eb04b04f5b.
2 “Maria Gaetana Agnesi – Timeline Of Mathematics – Mathigon”. 2022. Mathigon. https://mathigon.org/timeline/agnesi.
“Maria Gaetana Agnesi”. 2022. mathwomen.agnesscott.org. https://mathwomen.agnesscott.org/women/agnesi.htm.
“Maria Gaetana Agnesi – Wikipedia”. 2022. en.wikipedia.org. https://en.wikipedia.org/wiki/Maria_Gaetana_Agnesi.
“The 18Th-Century Lady Mathematician Who Loved Calculus And God”. 2018. Smithsonian Magazine. https://www.smithsonianmag.com/science-nature/18th-century-lady-mathematician-who-changed-how-calculus-was-taught-180969078/.
Philosopher and mathematician René Descartes is regarded as the father of modern philosophy for defining a starting point for existence, “I think; therefore I am.”1
René Descartes invented analytical geometry and introduced skepticism as an essential part of the scientific method. He is regarded as one of the greatest philosophers in history. His analytical geometry was a tremendous conceptual breakthrough, linking the previously separate fields of geometry and algebra. Descartes showed that he could solve previously unsolvable problems in geometry by converting them into simpler problems in algebra. He represented the horizontal direction as x and the vertical direction as y. This concept is now indispensable in mathematics and other sciences.2
René Descartes has been dubbed the “Father of Modern Philosophy“, but he was also one of the key figures in the Scientific Revolution of the 17th Century, and is sometimes considered the first of the modern school of mathematics.3
One of Descartes’s most enduring legacies was his development of Cartesian or analytic geometry, which uses algebra to describe geometry. Descartes “invented the convention of representing unknowns in equations by x, y, and z, and knowns by a, b, and c”. He also “pioneered the standard notation” that uses superscripts to show the powers or exponents; for example, the 2 used in x2 to indicate x squared. He was first to assign a fundamental place for algebra in the system of knowledge, using it as a method to automate or mechanize reasoning, particularly about abstract, unknown quantities.4
1 “René Descartes”. 2021. Biography. https://www.biography.com/scholar/rene-descartes.
2 “René Descartes – Biography, Facts And Pictures”. 2021. famousscientists.org. https://www.famousscientists.org/rene-descartes/.
3 “René Descartes: Father of Modern Philosophy”. 2021. storyofmathematics.com. https://www.storyofmathematics.com/17th_descartes.html.
4 “René Descartes – Wikipedia”. 2021. en.wikipedia.org. https://en.wikipedia.org/wiki/Ren%C3%A9_Descartes#Mathematical_legacy.
“Why Do We Generally Use The Letter ‘X’ In An Equation Instead Of Another Letter?” 2022. Quora. https://qr.ae/prhOxy.
Leonhard Euler; 15 April 1707 – 18 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of mathematics such as analytic number theory, complex analysis, and infinitesimal calculus. He introduced much of modern mathematical terminology and notation, including the notion of a mathematical function. He is also known for his work in mechanics, fluid dynamics, optics, astronomy and music theory.
Euler is held to be one of the greatest mathematicians in history and the greatest of the 18th century. A statement attributed to Pierre-Simon Laplace expresses Euler’s influence on mathematics: “Read Euler, read Euler, he is the master of us all.” Carl Friedrich Gauss remarked: “The study of Euler’s works will remain the best school for the different fields of mathematics, and nothing else can replace it.” Euler is also widely considered to be the most prolific; his more than 850 publications are collected in 92 quarto volumes, (including his Opera Omnia) more than anyone else in the field. He spent most of his adult life in Saint Petersburg, Russia, and in Berlin, then the capital of Prussia.1
1 “Leonhard Euler – Wikipedia”. 2021. en.wikipedia.org. https://en.wikipedia.org/wiki/Leonhard_Euler.
Marcus du Sautoy argues that mathematics is the driving force behind modern science: Leonard Euler and an 18th-century puzzle.
Hoare, Graham. “Leonhard Euler (1707-1783).” The Mathematical Gazette 91, no. 522 (2007): 406–14. http://www.jstor.org/stable/40378414.
“How Leonhard Euler Produced The Most Beautiful Equation In Mathematics”. 2021. ThoughtCo. https://www.thoughtco.com/leonhard-euler-biography-4174374.
“Infinity In Numbers — Leonhard Euler”. 2020. Medium. https://www.cantorsparadise.com/the-pursuit-of-truth-and-beauty-in-a-timeless-universe-part-1-baca94d9e587.
“Leonhard Euler – Biography”. 2021. Maths History. https://mathshistory.st-andrews.ac.uk/Biographies/Euler/.
“Leonhard Euler – Biography, Facts And Pictures”. 2021. famousscientists.org. https://www.famousscientists.org/leonhard-euler/.
“Leonhard Euler | Brilliant Math & Science Wiki”. 2021. brilliant.org. https://brilliant.org/wiki/leonhard-euler/.
“Leonhard Euler: Lifelong Curiosity”. 2022. Medium. https://anagrath.medium.com/leonhard-euler-lifelong-curiosity-913d0a5d786c.
The French mathematician Évariste Galois (1811 – 1832) had a short and tragic life, yet he invented two entirely new fields of mathematics: Group theory and Galois theory.
While still in his teens, Galois proved that there is no general solution for polynomial equations of degree five or higher – simultaneously with Niels Abel.
Unfortunately, other mathematicians who he shared these discoveries with repeatedly misplaced or simply returned his work, and he failed his school and university exams while concentrating on much more complex work.
At the age of 20, Galois was shot in a duel (some say a feud over a woman), and later died of his wounds. During the night before his death, he summarised his mathematical discoveries in a letter to a friend. It would take other mathematicians many years to fully understand these letters, and realise the impact of his work.1
This is a story of love and mathematics. A story of a young man so brilliant that his scribblings started one of the most beautiful and interesting fields of mathematics, a revolution in how we think of equations and not only did he solve a 350-year-old problem in the process, his theory also showed a solution to a couple of questions that were about 2000 years old and unsolved at the time.2
1 “Évariste Galois – Timeline Of Mathematics – Mathigon”. 2022. Mathigon. https://mathigon.org/timeline/galois.
2 Müller, Kasper. “For The Love Of Mathematics”. 2022. Medium. https://www.cantorsparadise.com/for-the-love-of-mathematics-84bf86a8ae09.
Marcus du Sautoy argues that mathematics is the driving force behind modern science: mathematics during the French Revolution.
“Évariste Galois – Wikipedia”. 2022. en.wikipedia.org. https://en.wikipedia.org/wiki/%C3%89variste_Galois.
“Évariste Galois, The Teenager Who Revolutionized Mathematics | OpenMind”. 2016. OpenMind. https://www.bbvaopenmind.com/en/science/mathematics/evariste-galois-the-adolescent-who-revolutionized-mathematics/.
Whenever we talk about an essential contribution in any field, we always describe it as “revolutionary”. Perhaps we abuse this term so much that it ends up losing some of its meaning. But in France in the early nineteenth century, being a revolutionary had a more literal character, and therefore a riskier one. Évariste Galois (25 October 1811 – 31 May 1832) was revolutionary in two fields, politics and mathematics, and from a very young age; perhaps too young to enjoy a long life. He died tragically at age 20, though not over politics or mathematics, but for a reason that forged the legend of a romantic genius.
Nagrath, Aditya. “Évariste Galois, The Rebel Rousing Mathematician”. 2022. Medium. https://anagrath.medium.com/%C3%A9variste-galois-the-rebel-rousing-mathematician-35fa11e63da.
Évariste Galois, a French mathematician, lived a very short life of twenty years; but was still able to solve a 350 year old mathematical problem. While in his teens, he determined a condition for polynomials to be solved by radicals. By twenty, he developed Galois theory, as it was named after him. His theory began a whole new part of abstract algebra that drew connections between group theory and field theory.
Though he developed a passion for mathematics at a young age; he spent a lot of his youth “fighting the system”. He was a staunch republican and supporter of the overthrow of King Charles X. In fact, he spent most of his young adulthood in and out of jail where he spent a lot of his time focused on his mathematical concepts; and it was in jail he developed Galois theory. Read on to learn more about his work and life!
Carl Friedrich Gauss
Carl Friedrich Gauss (1777 – 1855) was arguably the greatest mathematician in history. He made groundbreaking discoveries in just about every field of mathematics, from algebra and number theory to statistics, calculus, geometry, geology and astronomy.
According to legend, he corrected a mistake in his father‘s accounting at the age of 3, and found a way to quickly add up all integers from 1 to 100 at the age of 8. He made his first important discoveries while still a teenager, and later tutored many other famous mathematicians as Professor.1
Gauss was born an only child. His parents and his teachers noticed his calculating genius and his knack for picking up languages. At age eight, he was tasked by his elementary school teacher to do a clerical assignment. His class had to add up the numbers between 1 to 100. Gauss saw an ongoing pattern from the sum of the numbers within that range. They all added up to 101. There happened to be fifty pairs of numbers that all added up to 101. So, instead of wasting time adding up each individual number in the range one by one, he multiplied 101 x 50 and got a sum of 5,050. He was the only one in his class that got the right answer.2
1 “Carl Friedrich Gauss – Timeline Of Mathematics – Mathigon”. 2022. Mathigon. https://mathigon.org/timeline/gauss.
2 Nagrath, Aditya. “Carl Friedrich Gauss, The Most Brilliant Mathematician Of His Time”. 2022. Medium. https://anagrath.medium.com/carl-friedrich-gauss-the-most-brilliant-mathematician-of-his-time-419b11033992.
Marcus du Sautoy argues that mathematics is the driving force behind modern science: German mathematician, Carl Friedrich Gauss.
Marie-Sophie Germain (1776 – 1831) decided that she wanted to be a mathematician at the age of 13, after reading about Archimedes. Unfortunately, as a woman, she was faced with significant opposition. Her parents tried to prevent her from studying when she was young, and she never received a post at a university.
Germain was a pioneer in understanding the mathematics of elastic surfaces, for which she won the grand prize from the Paris Academy of Sciences. She also made considerable progress in solving Fermat’s Last Theorem, and regularly corresponded with Carl Friedrich Gauss.1
Sophie Germain is one of the earliest and most influential women mathematicians. She overcame societal pressures to abandon her work during her life and persevered, becoming a pioneering thinker in the fields of number theory and elasticity.
Her story is inspiring for anyone, but especially any girls out there who sometimes feel alone in their love of math. Sophie’s life and work proves that anyone can become a mathematician, as long as they have a passion for math and a love of learning!2
Marie-Sophie Germain (1 April 1776 – 27 June 1831) was a French mathematician, physicist, and philosopher. Despite initial opposition from her parents and difficulties presented by society, she gained education from books in her father’s library, including ones by Leonhard Euler, and from correspondence with famous mathematicians such as Lagrange, Legendre, and Gauss (under the pseudonym of «Monsieur LeBlanc»). One of the pioneers of elasticity theory, she won the grand prize from the Paris Academy of Sciences for her essay on the subject. Her work on Fermat’s Last Theorem provided a foundation for mathematicians exploring the subject for hundreds of years after. Because of prejudice against her sex, she was unable to make a career out of mathematics, but she worked independently throughout her life. Before her death, Gauss had recommended that she be awarded an honorary degree, but that never occurred. On 27 June 1831, she died from breast cancer. At the centenary of her life, a street and a girls’ school were named after her. The Academy of Sciences established the Sophie Germain Prize in her honor.3
1 “Marie-Sophie Germain – Timeline Of Mathematics – Mathigon”. 2022. Mathigon. https://mathigon.org/timeline/germain.
2 “Sophie Germain’s Secret Love Of Mathematics In 18Th Century France”. 2021. Medium. https://anagrath.medium.com/sophie-germains-secret-love-of-mathematics-in-18th-century-france-19be00cf2434.
3 “Sophie Germain – Wikipedia”. 2022. en.wikipedia.org. https://en.wikipedia.org/wiki/Sophie_Germain.
“Sophie Germain – Mathematician Biography, Contributions And Facts”. 2022. Famous Mathematicians. https://www.famousmathematicians.net/sophie-germain/.
Marie-Sophie Germain was a nineteenth-century French mathematician. Along with that she had also explored other field of studies, for instance, philosophy and physics. Being a woman it was not easy for Germain to not only acquire education but then to further expand her horizon, in the society possessing a medieval mindset regarding women’s education. Germain braved on the odds and eventually proved herself to that conservative society. She received grand prize from the Paris Academy of Sciences on her essay on elasticity theory. She is credited for laying foundation for future mathematician to further explore her Fermat’s Last Theorem. Despite being a genius and a gifted mathematician, she could not succeed to make a career out of it owing to the despicable prejudice against her gender.
“Sophie Germain Biography – French Mathematician, Physicist, And Philosopher”. 2022. pantheon.world. https://pantheon.world/profile/person/Sophie_Germain/.
Joseph-Louis Lagrange (1736 – 1813) was an Italian mathematician who succeeded Leonard Euler as the director of the Academy of Sciences in Berlin.
He worked on analysis and the calculus of variations, invented new methods for solving differential equations, proved theorems in number theory, and laid the foundations of group theory.
Lagrange also wrote about classical and celestial mechanics, and helped establish the metric system in Europe.1
Joseph-Louis Lagrange was once considered “the greatest mathematician in Europe” by Frederick II, King of Prussia. Throughout his mathematical career, he was courted to take a number of prestigious positions in his hometown of Turin, Italy; in Berlin, Germany, and Paris, France. He was a self-taught mathematician, who ironically first found the subject of mathematics to be quite boring. But, he had a change of heart after being influenced by Edmond Halley’s, an English astronomer and mathematician, paper on the use of algebra in optics.2
Joseph-Louis Lagrange is usually considered to be a French mathematician, but the Enciclopedia Italiana refers to him as an Italian mathematician. They certainly have some justification in this claim since Lagrange was born in Turin and baptised in the name of Giuseppe Lodovico Lagrangia. Lagrange’s father was Giuseppe Francesco Lodovico Lagrangia who was Treasurer of the Office of Public Works and Fortifications in Turin, while his mother Teresa Grosso was the only daughter of a medical doctor from Cambiano near Turin. Lagrange was the eldest of their 11 children but one of only two to live to adulthood.3
1 “Joseph-Louis Lagrange – Timeline Of Mathematics – Mathigon”. 2022. Mathigon. https://mathigon.org/timeline/lagrange.
2 Nagrath, Aditya. “Joseph-Louis Lagrange, The Metric System Mathematician”. 2022. Medium. https://anagrath.medium.com/joseph-louis-lagrange-the-metric-system-mathematician-ad1a4492cbcf.
3 “Joseph-Louis Lagrange – Biography”. 2022. Maths History. https://mathshistory.st-andrews.ac.uk/Biographies/Lagrange/.
Gottfried Wilhelm Leibniz
Gottfried Wilhelm Leibniz (1646 – 1716) was a German mathematician and philosopher. Among many other achievements, he was one of the inventors of calculus, and created some of the first mechanical calculators.
Leibniz believed that our universe is the “best possible universe” that God could have created, while allowing us to have a free will. He was a great advocate of rationalism, and also made contributions to physics, medicine, linguistics, law, history, and many other subjects.1
1 “Gottfried Wilhelm Leibniz – Timeline Of Mathematics – Mathigon”. 2022. Mathigon. https://mathigon.org/timeline/leibniz.
Marcus du Sautoy argues that mathematics is the driving force behind modern science: Newton, Leibniz and calculus.
Nikolai I. Lobachevsky
Nikolai Lobachevsky (Никола́й Лобаче́вский, 1792 – 1856) was a Russian mathematician, and one of the founders of non-Euclidean geometry. He managed to show that you can build up a consistent type of geometry in which Euclid’s fifth axiom (about parallel lines) does not hold. 1
Schoolchildren now study Euclidean geometry, all thanks to Greek mathematician Euclid who was born in approx. 300 BC. His main work is “The Elements,” in which he described the five main postulates of geometry, including this: “There is at most one line that can be drawn parallel to another given one through an external point.” This postulate was doubted by many mathematicians, who mused over it obsessively for more than 2,000 years until three mathematicians (Carl Gauss, Janos Bolyai and Nikolai Lobachevsky proved – Bernhard Riemann summarized their research) proved that Euclidean geometry wasn’t the gospel. 2
1 “Nikolai Lobachevsky – Timeline Of Mathematics – Mathigon”. 2022. Mathigon. https://mathigon.org/timeline/lobachevsky.
2 “His hyperbolic geometry disproved the theory about the three-dimensional space.” 2022. rbth.com. https://www.rbth.com/history/326895-mathematician-nikolai–obachevsky.
“Nikolai Lobachevsky Biography – Russian Mathematician”. 2022. pantheon.world. https://pantheon.world/profile/person/Nikolai_Lobachevsky/.
Among mathematicians, Nikolai Lobachevsky ranks 56 out of 828. Before him are Sophie Germain, Brahmagupta, Niccolò Fontana Tartaglia, Simon Stevin, Philolaus, and Ludolph van Ceulen. After him are Marin Mersenne, Karl Weierstrass, Al-Battani, Abu al-Wafa’ Buzjani, Willebrord Snellius, and Zhang Heng.
“Nikolai Lobachevsky”. 2019. Interesting Stories About Famous People, Biographies, Humorous Stories, Photos And Videos.. https://fampeople.com/cat-nikolai-lobachevsky.
“Nikolai Lobachevsky – The Copernicus Of Geometry”. 2021. scihi blog. http://scihi.org/nikolai-lobachevsky-geometry/.
“Nikolai Lobachevsky – Russiapedia Science And Technology Prominent Russians”. 2022. russiapedia.rt.com. https://russiapedia.rt.com/prominent-russians/science-and-technology/nikolai-lobachevsky/.
John Napier was a 16th-century Scottish mathematician who made several important discoveries that facilitated easier and faster computations. He discovered logarithms, popularized the use of the decimal point, and invented his own mechanical system of calculation, called Napier’s bones.1
Napier realized that all numbers can be expressed in what is now called exponential form, meaning 8 can be written as 23, 16 as 24 and so on. What makes logarithms so useful is the fact that the operations of multiplication and division are reduced to simple addition and subtraction. When very large numbers are expressed as a logarithm, multiplication becomes the addition of exponents.2
…there is nothing … so troublesome to mathematical practice … than the multiplications, divisions, square and cubical extractions of great numbers, which besides the tedious expense of time are for the most part subject to many slippery errors, I began therefore to consider … by what certain and ready art I might remove those hindrances.John Napier
1 “John Napier: Champion Of The Decimal Point And An Early Calculator”. 2022. Medium. https://anagrath.medium.com/john-napier-champion-of-the-decimal-point-and-an-early-calculator-a2ec9d72f16f.
2 “The Biography Of John Napier, Famous Scottish Mathematician”. 2022. thoughtco. https://www.thoughtco.com/john-napier-biography-4077399.
“John Napier – Wikipedia”. 2022. en.wikipedia.org. https://en.wikipedia.org/wiki/John_Napier.
“Logarithms: The Early History Of A Familiar Function – John Napier Introduces Logarithms | Mathematical Association Of America”. 2022. maa.org. https://www.maa.org/press/periodicals/convergence/logarithms-the-early-history-of-a-familiar-function-john-napier-introduces-logarithms.
“Napier’s Bones”. 2022. National Museums Scotland. https://www.nms.ac.uk/explore-our-collections/stories/science-and-technology/napiers-bones/.
“Napier’s Bones — From Wolfram Mathworld”. 2022. mathworld.wolfram.com. https://mathworld.wolfram.com/NapiersBones.html.
“Napier Maths”. 2022. napiermaths.com. http://www.napiermaths.com/.
Tabea, Tietz. “John Napier And The Discovery Of Logarithms”. 2021. Scihi Blog. http://scihi.org/john-napier-logarithm/.
Sir Isaac Newton
Sir Isaac Newton (1642 – 1726) was an English physicist, mathematician, and astronomer, and one of the most influential scientists of all time. He was a professor at Cambridge University, and president of the Royal Society in London.
In his book Principia Mathematica, Newton formulated the laws of motion and gravity, which laid the foundations for classical physics and dominated our view of the universe for the next three centuries.
Among many other things, Newton was one of the inventors of calculus, built the first reflecting telescope, calculated the speed of sound, studied the motion of fluids, and developed a theory of colour based on how prisms split sunlight into a rainbow-coloured spectrum.1
Isaac Newton is generally regarded as one of the most famous mathematicians in history. He is credited with the discovery of gravity, the Universal Laws of Motion, calculus, the theory of color as an intrinsic quality of light, and reflecting telescopes.
He was also a notoriously difficult character with many ongoing feuds with fellow mathematicians and scientists. He was superstitious and obsessed with alchemy, and often infuriated the Church with his scientific discoveries. Despite it all, he was already very well-known upon his death and was the first scientist to be buried in Westminster Abbey. Dive deeply into the life of this very famous and unique man! 2
1 “Isaac Newton – Timeline Of Mathematics – Mathigon”. 2022. Mathigon. https://mathigon.org/timeline/newton.
2 Therieau, Lillie. “Isaac Newton: The Most Famous Mathematician Of All Time?” 2022. Medium. https://anagrath.medium.com/isaac-newton-the-most-famous-mathematician-of-all-time-fa6c6bf36a82.
Marcus du Sautoy argues that mathematics is the driving force behind modern science: Newton, Leibniz and calculus.
Budin, Jeremiah. “An Oral History Of Isaac Newton “Discovering” Gravity, As Told By His Contemporaries”. 2018. The New Yorker. https://www.newyorker.com/humor/daily-shouts/an-oral-history-of-isaac-newton-discovering-gravity-as-told-by-his-contemporaries.
“Isaac Newton – Wikipedia”. 2022. en.wikipedia.org. https://en.m.wikipedia.org/wiki/Isaac_Newton.
Sir Isaac Newton PRS (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a “natural philosopher“) widely recognised as one of the greatest mathematicians and physicists of all time and among the most influential scientists. He was a key figure in the philosophical revolution known as the Enlightenment. His book Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687, established classical mechanics. Newton also made seminal contributions to optics, and shares credit with German mathematician Gottfried Wilhelm Leibniz for developing infinitesimal calculus.
Jenkins, Alejandro. “Does Isaac Newton Deserve The Praise And Respect He’s Been Given Throughout History?”. 2022. Quora. https://qr.ae/pvqOhl.
I think that, if anything, Newton’s enormous personal contribution to the establishment of modern science is under-appreciated.
It is now extremely difficult for a casual reader, even one with advanced training in mathematics and physics, to understand Newton’s great work, the Philosophiæ Naturalis Principia Mathematica (“Mathematical Principles of Natural Philosophy”), first published in 1687. The great astrophysicist and Nobel laureate Subrahmanyan Chandrasekhar (1910-1995) dedicated the last five years of his life to reading the Principia and making it understandable to a modern professional physicist. He only managed to get through what he thought were the key bits before he died.
There are three main reasons why the Principia is so difficult to read (aside from the fact that it was written in Latin, which few people learn now). The first is that Newton presented his proofs in a geometrical (“synthetic”) form, in the manner of the ancient Greeks, rather than using the algebraic (“analytic”) language that is favored by modern scientists and which is much easier to systematize and to teach (especially to people who, as the Soviet mathematician V. I. Arnold complained, “don’t really understand it”).
Labh, Sunny. “10 Facts You Probably Didn’t Know About Sir Isaac Newton”. 2022. Medium. https://piggsboson.medium.com/10-facts-you-probably-didnt-know-about-sir-isaac-newton-dacea7ce7d09.
How to use Napier’s 400 year old bones to do long multiplication. Full details including PDF’s to download to make Napier’s Bones are available on www.napiermaths.com.
How to use Napier’s 400 year old Local Arithmetic to do long multiplication. Full details including PDF’s to download to make Napier’s Local Arithmetic are available on www.napiermaths.com.