The Only Thing Worse Than Being Blind Is Having Sight but No Vision. -Helen

BIBHUPRASAD MOHAPATRA RTICLE A

The only thing worse than being blind is having sight but no vision. EATURE

F -Helen Keller, American author, political activist, and lecturer.

Nicholas Saunderson in the chancel of the parish church at Boxworth near Cambridge. Renowned English Scientist, Saunderson possessed the friendship Mathematician and sensible Newtonian of many eminent mathematicians of the was born in the small village of time, such as Sir Isaac Newton, Edmund Thurlstone, Yorkshire, in January 1682 Halley, Abraham De Moivre and Roger ESPITE the fact that they were blind to an exciseman who was a government Cotes. He devised a calculating machine Dphysically, they acquired qualities officer and collected taxes imposed on or abacus, by which he could perform to look at the beauty of the “Queen of goods. He may have been the earliest arithmetical and algebraic operations all Sciences”. Although blind musicians, discoverer of Bayes theorem which was by the sense of touch; this method writers, politicians, and philanthropists named after Thomas Bayes (1701-April 7, is sometimes termed his palpable are most well known, there were some 1761). renowned blind Mathematicians who arithmetic, an account of which is given Unfortunately, when about a year had great vision and also made great in his elaborate Elements of Algebra. old he lost his sight as well as eyes to contributions to Mathematics. Let’s smallpox; but this tragedy did not prevent take a look at some of these great him from acquiring a remarkably good Leonhard Euler mathematicians. education and studying mathematics. He Euler was born on 15 April 1707, in Basel learnt to read by tracing the engravings to Paul Euler and Marguerite Brucker. on tombstones around St. John the Baptist His left eye became blind from cataract Church in Penistone with his fingers. and suffered from eyestrain caused by a His early education was at Penistone near-fatal fever in 1735. Grammar School. In 1707, he arrived Leonhard Euler was a pioneering in Cambridge, staying with his friend Swiss mathematician and physicist of Joshua Dunn. With the permission of the the 18th century who spent most of 3rd Lucasian professor of Mathematics his life in Russia and Germany and who succeeded Isaac Newton, William made discoveries in fields as diverse as Whiston, Saunderson was allowed infinitesimal calculus and graph theory. Nicholas to teach, lecturing on mathematics, He also introduced much of the modern Saunderson astronomy and optics. Whiston was mathematical terminology and notation expelled from his chair on 30 October for mathematical analysis, such as the 1710. Queen Anne awarded Saunderson notion of a mathematical function f(x). a Master of Arts degree on 19 November He is also renowned for his work in 1711 so that he would be eligible to mechanics, fluid dynamics, optics, and succeed Whiston as Lucasian professor. astronomy. A statement attributed to He was chosen as the 4th Lucasian Pierre-Simon Laplace expresses Euler’s professor (1711-1739) the next day. influence on mathematics: “Read Euler, Saunderson was elected a Fellow of read Euler, he is the master of us all.” the Royal Society (FRS) on 6 November His early education started in 1718. He was awarded doctor of laws in Basel, where he was sent to live with his 1728 by the command of George II (King maternal grandmother. At the age of 13 of Great Britain and Ireland). He died of he enrolled at the University of Basel, and scurvy on 19 April 1739 and was buried in 1723, received his Master of Philosophy SCIENCE REPORTER, SEPTEMBER 2014 28 FEATURE ARTICLE Leonhard Euler (left). Lev Pontryagin (right)

Leonhard Euler also renowned for his work in mechanics, fl uid dynamics, optics, and astronomy. A statement attributed to Pierre-Simon Laplace expresses Euler’s infl uence on mathematics. with a dissertation that compared the The city of Königsberg, Prussia was exceptional student. He made major philosophies of Descartes and Newton. set on the Pregel River and included two discoveries in algebraic topology and At this time, he was receiving Saturday large islands which were connected to differential topology. Pontryagin worked afternoon lessons from Johann Bernoulli, each other and the mainland by seven on duality theory for homology while who quickly discovered his new pupil’s bridges. The problem was to decide still a student. He went on to lay the incredible talent for mathematics. In whether it is possible to follow a path foundations for the abstract theory of the 1727, he entered the Paris Academy Prize that crosses each bridge exactly once and Fourier transform, now called Pontryagin Problem competition, where the problem returns to the starting point. In 1736, Euler duality. In topology, he posed the basic that year was to find the best way to solved the problem known as the Seven problem of cobordism theory. This led to place the masts on a ship. He won second Bridges of Königsberg. It is not possible: the introduction around 1940 of a theory place, losing only to Pierre Bouguer there is no Eulerian circuit. This solution of certain characteristic classes, now who was known as “the father of naval is considered to be the first theorem of called Pontryagin classes, designed to architecture”. Euler subsequently won graph theory. He also discovered the vanish on a manifold that is a boundary. this coveted annual prize twelve times in formula V-E + F = 2 In 1942, he introduced the his career. cohomology operations now called Euler worked in almost all areas of Lev Pontryagin Pontryagin squares. Moreover, in operator mathematics: geometry, infinitesimal A Soviet mathematician who was born theory there are specific instances of calculus, trigonometry, algebra, and on 3 September 1908 in Moscow and Krein spaces called Pontryagin spaces. number theory, as well as continuum suffered an accident at the age of 14 – an Later in his career he worked in optimal physics, lunar theory and other areas of explosion that left him blind. His father, control theory. His maximum principle physics. Euler is the only mathematician Semen Akimovich Pontryagin was a civil is fundamental to the modern theory to have two numbers named after him: servant. Despite his pitiable condition, of optimization. He also introduced the immensely important Euler’s Number Pontryagin was able to become a titan there the idea of a bang-bang principle, in calculus, ‘e’ approximately equal of mathematics of the 20th century and to describe situations where either the to 2.71828, and the Euler-Mascheroni that was possible with the help of his maximum ‘steer’ should be applied to a Constant γ (gamma) sometimes referred mother Tatyana Andreevna who read system, or none. just as “Euler’s constant”, approximately mathematical books and papers (notably Pontryagin authored several equal to 0.57721. It is not known whether those of Heinz Hopf, J.H.C. Whitehead influential monographs as well as γ is rational or irrational. and Hassler Whitney) to him. popular textbooks in mathematics. He He also introduced ‘e’ for the base Pontryagin entered the University was accused of anti-Semitism on several of the natural logarithm, the Greek letter of Moscow in 1925 and it quickly became occasions. Antisemitism is prejudice, ∑γ for summations and the letter i (iota) apparent to his lecturers that he was an hatred of, or discrimination against Jews to denote the imaginary unit. The use of for reasons connected to their Jewish the Greek letter γ to denote the ratio of a Lev Pontryagin went on heritage. For example, he attacked Nathan circle’s circumference to its diameter was to lay the foundations for Jacobson for being a “mediocre scientist” also popularized by Euler. In 1772, Euler the abstract theory of the representing the “Zionism movement”, had proved that 2^31 − 1 = 2,147,483,647 is while both men were vice-presidents of a Mersenne prime. It may have remained Fourier transform, now called the International Mathematical Union the largest known prime until 1867. Pontryagin duality. (IMU). 29 SCIENCE REPORTER, SEPTEMBER 2014 FEATURE ARTICLE Abraham Nemeth (extreme left) Bernard Morin (left) Bernard also discovered the Morin surface, a half-way model for the sphere eversion, and used it to prove a lower bound on the number of steps needed to turn a sphere inside out. Majored in psychology at Brooklyn College, Abraham earned MA in Psychology from the Columbia University and studied mathematics and physics at Brooklyn College.

Abraham Nemeth died. Nemeth was a member of the of Strasbourg and retired in 1999. Morin American mathematician and inventor, United States Democratic Party but was also worked at the Institute for Advanced Abraham was born congenitally blind on appointed by a Republican governor Study in Princeton. 16 October 1918 in New York City on the of Michigan as chairman of the state Morin was a part of a group that Lower East Side of Manhattan into a large commission for the blind, a position he first demonstrated an eversion of the family of Hungarian Jewish immigrants served for two years (1991-1993). sphere, i.e. a homotopy (topological who spoke Yiddish (High German metamorphosis) which starts with a language of Ashkenazi Jewish origin). He Bernard Morin sphere and ends with the same sphere attended regular public schools at first but Pioneering mathematician, specifically but turned inside-out. He also discovered did most of his primary and secondary a topologist, born in Shanghai, China the Morin surface, a half-way model for education at the Jewish Guild for the Blind in 1931. His father was a French citizen the sphere eversion, and used it to prove school in Yonkers. Majored in psychology who worked for a bank in Shanghai. He a lower bound on the number of steps at Brooklyn College, he earned MA in was blind since age six due to glaucoma needed to turn a sphere inside out. Psychology from the Columbia University and was taken to France for medical He discovered the first and studied mathematics and physics at treatment. He returned to Shanghai, but parametrization of Boy’s surface (named Brooklyn College. suffered detached retinas and became after German Mathematician Werner Boy Abraham needed a Braille code totally blind. in 1978). His graduate student François that would more effectively handle Morin returned to France and Apéry later discovered (in 1986) another the kinds of math and science material educated in schools for the blind until parametrization of Boy’s surface, which and so developed the Nemeth Code for age fifteen, when he went into the regular conforms to the general method for Mathematics and Science Notation in education system. He studied philosophy parametrizing non-orientable surfaces. 1952. Nemeth Code has gone through four for a few years before switching to “Our spatial imagination is formed revisions since its initial development and Mathematics. His blindness did not by manipulating objects, you act on continues in wide use today. He is also prevent him from having a successful objects with your hands not your eyes,” responsible for the rules of MathSpeak, career in mathematics. said Morin while discussing his work. a system for orally communicating In 1957, he began his career as a mathematical text. researcher at the Centre National de la Amazingly, his obituary was Recherche Scientifique (The National prematurely published twice in Jewish Centre for Scientific Research). He Mr Bibhuprasad Mohapatra is a Postal Assistant, and blindness-related magazines, when earned his PhD in 1972 and spent most Rayagada Head Post Offi ce, Rayagada-765001, in fact his brother and wife had actually of his career teaching at the University Odisha; Email: [email protected] SCIENCE REPORTER, SEPTEMBER 2014 30