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Two prominent mathematicians who were disabled in ways which would have made it difficult to work were Lev Pontryagin and Solomon Lefschetz.

Pontryagin was blind as a result of a stove explosion at the age of $14$, though he learned mathematics because his mother read him math papers and books, and he went on to contribute to algebraic topology, differential topology, and optimal control in significant ways. Several results now bear his name, including Pontryagin's Maximum Principle in optimal control which was a landmark theoretical development in the field.

Solomon Lefschetz lost both of his hands in an electrical transformer fire in his twenties. This accident pushed him towards mathematics and he went on make contributions to algebraic geometry, topology, and nonlinear differential equations. The Picard-Lefschetz formula and the Lefschetz fixed-point theorem are named after him, and his work in nonlinear differential equations helped interest in the field to grow, particularly in the United States.

There are surely other similar examples in the history of mathematics that I don't know about. Accordingly, my question is:

Who are some mathematicians that have made important contributions to mathematics despite their ability to work being hampered by a disability?

An answer to this question should, naturally, contain the name of the mathematician and the way in which their ability to work was impaired. It should also contain a (possibly brief) description of their contributions, with mention of specific results where relevant.

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    $\begingroup$ One that leaps to mind is Bernard Morin en.wikipedia.org/wiki/Bernard_Morin He was blind from a young age, but had a successful career in topology. Why he springs to mind is that he was one of the first to exhibit a way to turn the sphere inside out, a supposedly paradoxical things going against our spatial reasoning. $\endgroup$ – JHance Aug 7 '14 at 1:41
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    $\begingroup$ This may be of interest -ams.org/notices/200210/comm-morin.pdf. If you count theoretical physicists then Stephen Hawking is the most famous example. $\endgroup$ – Mathmo123 Aug 7 '14 at 1:49
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    $\begingroup$ Euler became blind later in life and his Wikipedia article suggests he may have sped up his productivity after that with the help of scribes. $\endgroup$ – Graphth Aug 7 '14 at 1:59
  • $\begingroup$ « Born in Figueras with an almost fully incapacitating physical disability, Fernando Sunyer i Balaguer was confined for all his life to a wheelchair he could not move himself, and was thus constantly dependent on the care of others. […] In 1938, he communicated his first results to Prof. J. Hadamard of the Academy of Sciences in Paris, who published one of his papers in the Academy's "Comptes Rendus" and encouraged him to proceed in his selected course of investigation. From this moment, Fernando Sunyer i Balaguer maintained a constant interchange with the French analytical school […] » $\endgroup$ – Watson Dec 28 '16 at 21:14
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Joseph Plateau should be mentioned. While Wikipedia classifies him as a physicist, this was back when there was much less distinction between physicist and mathematician. He more or less invented the "moving image", and was obsessed with light and the eye. He used to stare at the sun or other bright lights to try to understand the retinal fatigue experienced afterwards. Perhaps because of this, he went blind later in life.

With worsening vision, he went to other aspects of physics. The most interesting in my opinion is the semi-understood phenomenon now called "Plateau's Rotating Drop." If you suspend a viscous liquid in another liquid of the same density, and rotate the suspended drop at the right acceleration, then it will deform from a sphere to an ellipsoid to a torus. Here are some pictures from my old lab (my first research experience!) on this experiment.

It's said that he would rotate drops for hours, making his son describe exactly what was happening.

Plateau also worked a lot with capillary action and soap bubbles - a differential geometer before his time.

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    $\begingroup$ Those pictures and video are awesome! I never thought such a thing could happen. Did you expect that the torus would rejoin the original point? $\endgroup$ – marty cohen Nov 5 '14 at 22:27
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    $\begingroup$ Really cool pictures. Am I seeing a Klein bottle in the vegetable oil experiment? $\endgroup$ – Chris Cave Nov 5 '14 at 22:53
  • $\begingroup$ @mixedmath: do you have an example of an amnesic mathematician? $\endgroup$ – Watson Oct 31 '16 at 19:17
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Louis Antoine was blind from age $29$ after being injured in World War I. After becoming blind, Lebesgue suggested that Antoine work on topology in two and three dimensions, partly because there hadn't been much research on such matters at that point and partly because, in Lebesgue's own words, "in such a study the eyes of the spirit and the habit of concentration will replace the lost vision."

Antoine did indeed pursue two- and three-dimensional topology and came up with what we now call Antoine's Necklace, which is an embedding of the Cantor set in $\mathbb{R}^3$ whose complement is not a simply connected set. This idea was later the inspiration for Alexander's Horned Sphere. Antoine was also an important influence upon Bernard Morin, another blind mathematician.

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A. G. Vitushkin was also blind. Complex analyst at the Steklov institute. Best known for his work on analytic capacity.

For several others, see this paper from the Notices of the AMS.

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  • $\begingroup$ Yes, I knew him in person. Aside of fundamental contributions, many his students work in mathematics. $\endgroup$ – Incnis Mrsi Dec 9 '14 at 17:49
  • $\begingroup$ @mrf: would you have an example of an amnesic mathematician? $\endgroup$ – Watson Oct 31 '16 at 19:17
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Burkhard Heim He was a german theoretical physicist, although his contibutions are quite controversial. He tried to develop his own unified field theory, with limited success. At the age of 19 an accident left him deaf and blind and without hands.

Also worth noting is Abraham Nemeth who was Professor of Mathematics at the University of Detroit Mercy. He developed a system to help blind people to read and write mathematics.

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Caryn Navy. I had posted an answer to the virtually same question on MathOverflow Meta a few months ago but apparently that question and the answers are not available anymore, perhaps deleted.

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