User tomcuchta - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T08:27:10Z http://mathoverflow.net/feeds/user/5841 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/80364/in-what-ways-did-leibnizs-philosophy-foresee-modern-mathematics/80443#80443 Answer by tomcuchta for In what ways did Leibniz's philosophy foresee modern mathematics? tomcuchta 2011-11-09T02:13:24Z 2011-11-09T02:13:24Z <p>Practically, Leibniz preceded computer science by inventing the <a href="http://en.wikipedia.org/wiki/Stepped_Reckoner" rel="nofollow">Stepped Reckoner</a>, a mechanical computer which was the first to be able to compute addition, subtraction, multiplication, and division. </p> <p>More abstractly, he sought after a "<a href="http://en.wikipedia.org/wiki/Calculus_ratiocinator" rel="nofollow">calculus ratiocinator</a>", a framework for dealing with logical statements. You can think of this as sort of a primitive formal language, although I doubt Leibniz had in mind as heavy restrictions that we use for formal grammars today.</p> http://mathoverflow.net/questions/50343/what-would-you-want-to-see-at-the-museum-of-mathematics/50385#50385 Answer by tomcuchta for What would you want to see at the Museum of Mathematics? tomcuchta 2010-12-26T00:17:53Z 2010-12-26T00:17:53Z <p>A working <a href="http://en.wikipedia.org/wiki/Differential_analyzer" rel="nofollow">differential analyzer</a> and other early computers would be pretty cool. </p> http://mathoverflow.net/questions/37301/why-did-the-word-exterior-get-chosen-for-the-idea-of-exterior-derivative Why did the word "exterior" get chosen for the idea of "exterior derivative"? tomcuchta 2010-08-31T19:27:10Z 2010-08-31T22:21:29Z <p>What are the intuitive and historical reasons for choosing the word "exterior" for the concept of an exterior derivative of a form? </p> <p>The reasoning I've heard about it is the following: let p(t) be a continuous parametric curve, then if you fix t_0, the tangent line to the curve p(t) at t_0 lies "exterior" of the curve p(t), since it is an approximation of p(t) itself.</p>