The Eccentric Lives of Steinhaus, Banach and Ulam (2014)

I wonder sometimes if our modern structured and red taped upper education model could ever cope with such exceptional individuals at all. I cannot stop thinking they will never get the unbridled space they need to express their ideas and concot together without an heavy amount of supervision and channeling toward 'agreed' topics and behaviours, I think education and the application of the law should be very flexible when exceptional individuals are at stake...

Steinhaus, Ulam and many other mathematicians in the Lviv school were Jewish, and had to flee or go into hiding to survive the German occupation. Interesting that there is no mention of this in the article.

Notice Ulam, Feynman, and von Neumann at Los Alamos in<p><a href="http:&#x2F;&#x2F;www-history.mcs.st-and.ac.uk&#x2F;BigPictures&#x2F;Ulam_Feynman_von_Neumann.jpeg" rel="nofollow">http:&#x2F;&#x2F;www-history.mcs.st-and.ac.uk&#x2F;BigPictures&#x2F;Ulam_Feynman...</a><p>For the Banach match box problem, that is, flip a fair coin x + y times and find the probability of getting heads exactly x times. So, it&#x27;s a binomial probability problem.<p>A <i>Banach space</i> is a complete, normed linear space. There is a nice chapter on Banach space in<p>Walter Rudin, <i>Real and Complex Analysis</i>.<p>There are some nice applications of the Hahn-Banach theorem in<p>David G. Luenberger, <i>Optimization by Vector Space Methods</i>.<p>In<p>Patrick Billingsley, <i>Convergence of Probability Measures</i>.<p>is a nice presentation of Ulam&#x27;s result in measure theory Le Cam called <i>tightness</i>: Roughly, IIRC, for any probability measure P and any a &gt; 0 no matter how small, there exists a sphere S of finite radius so that P(S) &gt; 1 - a. Intuitively the probability mass can&#x27;t just keep avoiding all spheres; eventually some sphere, if large enough, must cover nearly all the mass. There are some cute technical details.<p>Once in a paper I used Ulam&#x27;s result to show that a goofy distribution-free statistical hypothesis test was not trivial. And I&#x27;ve seen other applications.<p>The hypothesis test was to improve on our work in artificial intelligence for zero day monitoring for problems in server farms and networks. So, Ulam&#x27;s tightness has played a role in at least one piece of work intended to be practical!<p>IIRC, Ulam was long head of Los Alamos. Once I heard his lecture on the role in evolution of having two sexes.<p>There was a Time-Life book on math with a few pages on Ulam. IIRC, Ulam did by hand or mechanical calculator some of the early Monte-Carlo evaluations of critical mass.<p>At<p><a href="http:&#x2F;&#x2F;www.brainyquote.com&#x2F;quotes&#x2F;quotes&#x2F;s&#x2F;stanislawu312043.html" rel="nofollow">http:&#x2F;&#x2F;www.brainyquote.com&#x2F;quotes&#x2F;quotes&#x2F;s&#x2F;stanislawu312043....</a><p>is<p>&quot;It is still an unending source of surprise for me how a few scribbles on a blackboard or on a piece of paper can change the course of human affairs.&quot;<p>Stanislaw Ulam

There is an intriguing reference here: &quot;...the concept of a spatial x-ray locating device came to [Steinhaus] during a winter stroll spent observing snowflakes falling on his fur coat.&quot; Elsewhere, I have found the comment &quot;Steinhaus designed and instrument for localization of strange bodies in the body of a sick person by means of X-rays, based on a simple and elegant geometrical conception (1938) [1].&quot; Does anyone know what this is? A form of tomography, perhaps, or an application of stereology? - which is distinct from tomography, according to this article [2], and is apparently somehow related to his Longimeter, recently discussed here [3].<p>[1] <a href="http:&#x2F;&#x2F;prac.im.pwr.edu.pl&#x2F;~hugo&#x2F;HSC&#x2F;Steinhaus.htm" rel="nofollow">http:&#x2F;&#x2F;prac.im.pwr.edu.pl&#x2F;~hugo&#x2F;HSC&#x2F;Steinhaus.htm</a> [2] <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Stereology" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Stereology</a> [3] <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=16647821" rel="nofollow">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=16647821</a>

&#x27;Adventures of a Mathematician&#x27; is an autobiography of Ulam. I&#x27;ve not read it, but it was recommended by one of my math professors.

Ulam&#x27;s memoirs are still in print, I think, and very readable.

&gt; .. mathematicians who dreamt big, wrote poems, constructed the atomic bomb and helped organise the first flights to the moon.<p>Wow! I want to purchase the movie rights -- where do I sign?