A History of Mathematics| January

January has been a strange month for us. We have started some interesting projects and we are also going over some old projects of ours that need to be updated. What I am mostly happy about is that we managed to stay on top of the History of Mathematics facts. I cannot believe this is our 6th month we are doing this!!! So excited and thankfull for your support (AugustSeptemberOctober, November and December). Hope you will like these posts!

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In 1872, while on holiday in Interlaken, Dedekind met Georg Cantor. Thus began an enduring relationship of mutual respect, and Dedekind became one of the very first mathematicians to admire Cantor’s work concerning infinite sets, proving a valued ally in Cantor’s disputes with Leopold Kronecker, who was philosophically opposed to Cantor’s transfinite numbers.

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Georg Friedrich Bernhard Riemann (17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rigorous formulation of the integral, the Riemann integral, and his work on Fourier series. His contributions to complex analysis include most notably the introduction of Riemann surfaces, breaking new ground in a natural, geometric treatment of complex analysis. He is considered by many to be one of the greatest mathematicians of all time.

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Newton’s studies had impressed the Lucasian professor Isaac Barrow, who was more anxious to develop his own religious and administrative potential (he became master of Trinity two years later); in 1669 Newton succeeded him, only one year after receiving his MA. He was elected a Fellow of the Royal Society (FRS) in 1672.

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Paul J. Nahin (born November 26, 1940 in Orange County, California) is an American engineer and author who has written 20 books on topics in physics and mathematics, including biographies of Oliver Heaviside, George Boole, and Claude Shannon, books on mathematical concepts such as Euler’s formula and the imaginary unit, and a number of books on the physics and philosophical puzzles of time travel.

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Nicolas Bourbaki is the collective pseudonym of a group of mathematicians, predominantly French alumni of the École normale supérieure (ENS). Founded in 1934–1935, the Bourbaki group originally intended to prepare a new textbook in analysis. Over time the project became much more ambitious, growing into a large series of textbooks published under the Bourbaki name, meant to treat modern pure mathematics. The series is known collectively as the Éléments de mathématique (Elements of Mathematics), the group’s central work. Topics treated in the series include set theory, abstract algebra, topology, analysis, Lie groups and Lie algebras.

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Gauss also claimed to have discovered the possibility of non-Euclidean geometries but never published it. This discovery was a major paradigm shift in mathematics, as it freed mathematicians from the mistaken belief that Euclid’s axioms were the only way to make geometry consistent and non-contradictory.

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In 1815, Niels Abel entered the Cathedral School at the age of 13. His elder brother Hans joined him there a year later. They shared rooms and had classes together. Hans got better grades than Niels; however, a new mathematics teacher, Bernt Michael Holmboe, was appointed in 1818. He gave the students mathematical tasks to do at home. He saw Niels Henrik’s talent in mathematics, and encouraged him to study the subject to an advanced level. He even gave Niels private lessons after school.

Bernt Michael Holmboe supported Niels Henrik Abel with a scholarship to remain at the school and raised money from his friends to enable him to study at the Royal Frederick University.

When Abel entered the university in 1821, he was already the most knowledgeable mathematician in Norway. Holmboe had nothing more he could teach him and Abel had studied all the latest mathematical literature in the university library.

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Évariste Galois (25 October 1811 – 31 May 1832) was a French mathematician and political activist. While still in his teens, he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, thereby solving a problem standing for 350 years. His work laid the foundations for Galois theory and group theory, two major branches of abstract algebra, and the subfield of Galois connections.

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The Indiana Pi Bill is the popular name for bill #246 of the 1897 sitting of the Indiana General Assembly, one of the most notorious attempts to establish mathematical truth by legislative fiat. Despite its name, the main result claimed by the bill is a method to square the circle, rather than to establish a certain value for the mathematical constant π, the ratio of the circumference of a circle to its diameter. The bill, written by the crank Edward J. Goodwin, does imply various incorrect values of π, such as 3.2. The bill never became law, due to the intervention of Professor C. A. Waldo of Purdue University, who happened to be present in the legislature on the day it went up for a vote.

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Numbers (stylized as NUMB3RS) is an American crime drama television series that ran on CBS from January 23, 2005, to March 12, 2010.

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Curtis Niles Cooper is an American mathematician. He currently is a professor at the University of Central Missouri, in the Department of Mathematics and Computer Science.

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In 1675 Leibniz tried to get admitted to the French Academy of Sciences as a foreign honorary member, but it was considered that there were already enough foreigners there and so no invitation came. He left Paris in October 1676.  He was admitted later, in 1699.

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In June 1696, Johann Bernoulli had used the pages of the Acta Eruditorum Lipsidae to pose a challenge to the international mathematical community: to find the form of the curve joining two fixed points so that a mass will slide down along it, under the influence of gravity alone, in the minimum amount of time. The solution was originally to be submitted within six months. At the suggestion of Leibniz, Bernoulli extended the challenge until Easter 1697, by means of a printed text called “Programma”, published in Groningen, in the Netherlands.

The Programma is dated 1 January 1697, in the Gregorian Calendar. This was 22 December 1696 in the Julian Calendar, in use in Britain. According to Newton’s niece, Catherine Conduitt, Newton learned of the challenge at 4 pm on 29 January and had solved it by 4 am the following morning. His solution, communicated to the Royal Society, is dated 30 January. This solution, later published anonymously in the Philosophical Transactions, is correct but does not indicate the method by which Newton arrived at his conclusion. Bernoulli, writing to Henri Basnage in March 1697, indicated that even though its author, “by an excess of modesty”, had not revealed his name, yet even from the scant details supplied it could recognised as Newton’s work, “as the lion by its claw” (in Latin, tanquam ex ungue leonem).

Hope you are enjoying this new series. We are having a lot of time searching and writing about these aspects. Enjoy the day! You can find us on Facebook, Tumblr, Twitter and  Instagram. We will try to post there as often as possible.

Lots of love and don’t forget that maths is everywhere! Enjoy!

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