Bernard Morin (; 3 March 1931 in

Shanghai Shanghai (; , , Standard Mandarin pronunciation: ) is one of the four direct-administered municipalities of the People's Republic of China (PRC). The city is located on the southern estuary of the Yangtze River, with the Huangpu River flow ...

China China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's most populous country, with a population exceeding 1.4 billion, slightly ahead of India. China spans the equivalent of five time zones and ...

– 12 March 2018) was a French

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, specifically a

topologist In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ho ...

Early life and education

Morin lost his sight at the age of six due to

glaucoma Glaucoma is a group of eye diseases that result in damage to the optic nerve (or retina) and cause vision loss. The most common type is open-angle (wide angle, chronic simple) glaucoma, in which the drainage angle for fluid within the eye rem ...

, but his

blindness Visual impairment, also known as vision impairment, is a medical definition primarily measured based on an individual's better eye visual acuity; in the absence of treatment such as correctable eyewear, assistive devices, and medical treatment� ...

did not prevent him from having a successful career in mathematics. He received his Ph.D. in 1972 from the

Centre National de la Recherche Scientifique The French National Centre for Scientific Research (french: link=no, Centre national de la recherche scientifique, CNRS) is the French state research organisation and is the largest fundamental science Basic research, also called pure research o ...

Career

Morin was a member of the group that first exhibited an eversion of the sphere, i.e., a

homotopy In topology, a branch of mathematics, two continuous functions from one topological space to another are called homotopic (from grc, ὁμός "same, similar" and "place") if one can be "continuously deformed" into the other, such a deforma ...

which starts with a sphere and ends with the same sphere but turned inside-out. He also discovered the

Morin surface The Morin surface is the half-way model of the sphere eversion discovered by Bernard Morin. It features fourfold rotational symmetry. If the original sphere to be everted has its outer surface colored green and its inner surface colored red ...

, which is a

half-way model In geometry, minimax eversions are a class of sphere eversions, constructed by using half-way models. It is a variational method, and consists of special homotopies (they are shortest paths with respect to Willmore energy); contrast with Thurston ...

for the sphere eversion, and used it to prove a lower bound on the number of steps needed to turn a sphere inside out. Morin discovered the first parametrization of

Boy's surface In geometry, Boy's surface is an immersion of the real projective plane in 3-dimensional space found by Werner Boy in 1901. He discovered it on assignment from David Hilbert to prove that the projective plane ''could not'' be immersed in 3-space ...

(earlier used as a half-way model), in 1978. His graduate student François Apéry, in 1986, discovered another parametrization of Boy's surface, which conforms to the general method for parametrizing

non-orientable In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "counterclockwise". A space is ...

surfaces. Morin worked at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

Princeton, New Jersey Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of whi ...

. Most of his career, though, he spent at the

University of Strasbourg The University of Strasbourg (french: Université de Strasbourg, Unistra) is a public research university located in Strasbourg, Alsace, France, with over 52,000 students and 3,300 researchers. The French university traces its history to the ea ...

.
::::''Morin's surface.''

References

George K. Francis & Bernard Morin (1980) "Arnold Shapiro's Eversion of the Sphere",

Mathematical Intelligencer ''The Mathematical Intelligencer'' is a mathematical journal published by Springer Verlag that aims at a conversational and scholarly tone, rather than the technical and specialist tone more common among academic journals. Volumes are released quar ...

2(4):200–3.

External links

Photos of Morin
with

stereolithography Stereolithography (SLA or SL; also known as vat photopolymerisation, optical fabrication, photo-solidification, or resin printing) is a form of 3D printing technology used for creating models, prototypes, patterns, and production parts in a lay ...

models of sphere eversion.
The World of Blind Mathematicians

PDF Portable Document Format (PDF), standardized as ISO 32000, is a file format developed by Adobe in 1992 to present documents, including text formatting and images, in a manner independent of application software, hardware, and operating systems. ...

file at the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

's website. {{DEFAULTSORT:Morin, Bernard 1931 births 2018 deaths French mathematicians French blind people Blind academics Institute for Advanced Study visiting scholars Topologists Academic staff of the University of Strasbourg Scientists from Shanghai Educators from Shanghai Scientists with disabilities

Early life and education

Career

See also

References

External links