# Can blind individuals excel in mathematics?

• MathJakob
In summary, blind mathematicians can indeed excel in mathematics, as long as they have an intuition that is based on visual thinking. Some of the key players in solving topological problems go blind at a young age, and this may be one of the advantages that they have. Blind mathematicians must use other senses to complement their mathematical intuition, and it is unknown if they have the same intuition as sighted mathematicians. This article provides an overview of some of the world's best blind mathematicians, and it discusses their success in the field.

#### MathJakob

Is it possible to be blind and still be a mathematician? I can't see how anyone can study calculus and other type of math in your head without ever being able to see what you're doing. I think most people have to see their work to understand what to do next, notice patterns ect.

I heard that stephen hawking does all his physics equations in his head... I don't see how this is possible.

When I was an undergrad at Oxford there was a blind student majoring in math in my year, so it must be possible.

It would seem that imagining turning a sphere inside-out requires a lot of visual thinking. That may be how the sighted attack the problem, but one of the key players in solving this topological problem went blind at the age of 6.

Here are some articles on Bernard Marin.
http://www.ams.org/notices/200210/comm-morin.pdf
http://en.wikipedia.org/wiki/Bernard_Morin
http://torus.math.uiuc.edu/jms/Papers/isama/color/opt2.htm

Another famous blind mathematician is Larry Wos.
http://en.wikipedia.org/wiki/Larry_Wos
http://www.mcs.anl.gov/~wos/uofc-bio.html

Here's a profile of four STEM professionals who are blind.
https://nfb.org/images/nfb/publications/fr/fr23/fr06fal02.htm

And some more:
http://www.blindscience.org/blind-stem-professionals

To sum things up, "Blind mathematicians? Certainly!"
https://nfb.org/images/nfb/publications/bm/bm12/bm1207/bm120702.htm

FWIW, one of our engineers at work has a PhD in topology, and he usually shuts his eyes when thinking about hard problems, whether or not they involve topology.

Maybe the OP never heard the saying "listening to the radio always beats watching TV, because the pictures are better."

I believe it can even be an advantage. Once you go to higher dimensional objects it's impossible (for me at least) to visualize them. Yet I still try to do so and most of the time it's taking me more time to try that and fail than to write down rigorously what I know and work from there. *
On the other hand, some of the intuition in maths comes from being able to sketch functions and schematics of spaces, so I don't know whether blind mathematicians can form such an intuition.

When doing trigonometry it's different I believe because you need a very thorough description of the entire situation. And a sketch always makes things a lot easier.

* I had the same problem with tensors, I looked at them as vectors, dual vectors and matrices. Yet this captures very little of the beauty of applying tensors in physics. Just yesterday it occurred to me that I should consider them tensors, nothing more nothing less.

MathJakob said:
Is it possible to be blind and still be a mathematician? I can't see how anyone can study calculus and other type of math in your head without ever being able to see what you're doing. I think most people have to see their work to understand what to do next, notice patterns ect.

There are visual thinkers, there are non visual thinkers. You are probably doing a classical error of generalizing your own experience to everyone else. That's not how the psychology (when it does its best to be a serious science) works.

Those blind mathematicians who excel would have excelled even more if they had been seeing.

arildno said:
Those blind mathematicians who excel would have excelled even more if they had been seeing.

Speculation/personal opinion.

Borek said:
Speculation/personal opinion.
Not really.
Why do you think, for example, that LOGICAL intuition, as a feature of the brain is something independent of the sensory functionality of the same brain?
That is the underlying premise of the idea that one could do away with all the senses and retain the same sense of logical intuition.

THAT is speculative to a fault; regarding the "higher mental faculties" as surprising by-products of the "lower sensory capacities" is not.

One of my instructors in college was blind. He wrote equations on the board, kept track of everything that he wrote and answered questions on various parts. We all kept expecting him to make mistakes but he never did. It was fascinating to watch.

Borg said:
One of my instructors in college was blind. He wrote equations on the board, kept track of everything that he wrote and answered questions on various parts. We all kept expecting him to make mistakes but he never did. It was fascinating to watch.

Exceptional!
But it does not follow from this that it is equally exceptional to be a highly gifted mathematician when one compares the set of the seeing vs. the set of the blind.

A interesting article which provides some insight on the topic.
The World of Blind Mathematicians
-American mathematical society(1246. NOTICES OF THE AMS. VOLUME 49, NUMBER 10)

I would quote some excerpts but I just can't decide what to quote and what to leave out...just read the whole thing- its worth it.

I referenced that article in post #3, but I did so poorly.

Last edited:
D H said:
I referenced that article in post #3.

Ooops
(post deleted)

Enigman said:
Ooops
(post deleted)
No reason to be embarrassed. I'm the one who should be embarrassed as I should have given a better preface to that link.

I restored your post because it gives a better description of the article.

Euler went blind in one eye, then the other, but his mathematical output continued more or less unabated.

Of course, that was long after Euler had already become very well established in his field (and he'd completed all the basic "studies").

It's akin to Hawking being almost completely paralysed and still being able to do advanced physics and mathematics pretty much in his head.

Curious3141 said:
Euler went blind in one eye, then the other, but his mathematical output continued more or less unabated.

he said he'd have less distraction

Curious3141 said:
It's akin to Hawking being almost completely paralysed and still being able to do advanced physics and mathematics pretty much in his head.

I may be wrong, but I recall a documentary from a few years back that Hawking was in. It stated that his grad students helped him out a fair bit (using the computers, doing math etc.).

I think Norbert Wiener went blind and did some work after that, had to have some help, it is in his autobiog.

The unbelievable but true examples of chess masters beating everybody in simultaneous matches suggest everything could be achieved but not necessarily by many people.

Last edited:
One of my professors told me that some of the best geometers in the world are blind. He theorized that it is because they aren't "biased" towards seeing 3d, euclidean shapes, etc

1MileCrash said:
One of my professors told me that some of the best geometers in the world are blind. He theorized that it is because they aren't "biased" towards seeing 3d, euclidean shapes, etc

I think this may be true because you're working with a totally blank canvas, nothing to distract you.

epenguin said:
The unbelievable but true examples of chess masters beating everybody in simultaneous matches suggest everything could be achieved but not necessarily by many people.

Like Magnus Carlsen was the worlds youngest grandmaster at age 13 and he was on 60 minutes tv show where he played 10 games of chess simultaneously and was facing away from the boards from start to finnish. He won all 10.

He said that is the great thing about chess, that you can create the board in your head and play from that. Then the interviewer said well keeping track of all the peices in your head from just 1 game is hard enough, and you can do 10?

That is crazy insane memory.

Leonhard Euler suffered an fever which caused the loss of sight in his right eye when he was a young man. Later, as he aged, a cataract robbed him of sight in his left eye, leaving him blind. Euler had a tremendous memory, though, and, with the help of scribes, was able to dictate his mathematical and scientific papers. Euler is famously known for the volume of his scientific and mathematical writings, the amount of which was not diminished following the onset of total blindness.

http://en.wikipedia.org/wiki/Leonhard_Euler

Also to note I'm not only talking about people who learned math and then went blind, how about someone who is born blind?

Maybe they wonder how we can concentrate with so many distractions.

## 1) Can blind individuals learn and understand mathematical concepts?

Yes, blind individuals can learn and understand mathematical concepts just like sighted individuals. They may use alternative methods such as tactile diagrams, verbal descriptions, and assistive technology to access and process information.

## 2) Are there any successful blind mathematicians?

Yes, there are many successful blind mathematicians, such as Bernhard Auinger, Ron Graham, and James Holzmann. These individuals have made significant contributions to the field of mathematics despite their visual impairment.

## 3) How do blind individuals solve math problems without being able to see?

Blind individuals may use a variety of techniques to solve math problems, including mental math, tactile diagrams, braille, and screen-reading software. They may also use assistive technology such as talking calculators or abacus.

## 4) Are there any accommodations for blind students in math classes?

Yes, there are accommodations available for blind students in math classes, such as providing materials in a format they can access (such as braille or audio), allowing extra time for assignments and exams, and providing access to assistive technology.

## 5) Can blind individuals pursue a career in mathematics?

Yes, blind individuals can pursue a career in mathematics. Many universities and companies have accommodations in place to support blind individuals in their academic and professional pursuits. With determination and access to necessary resources, blind individuals can excel in the field of mathematics.