Is there a general reference of how mathematical talks, say academic talks, evolve in history? Before the International Congress of mthematics, is there any antecedent of todays talks?

3$\begingroup$ I do not know of a general reference, and I think the question is rather vague, but here is an account of an early talk with mathematical content:en.wikipedia.org/wiki/… $\endgroup$ – Margaret Friedland Jul 23 '13 at 17:04

1$\begingroup$ "On 28 November 1660, the 1660 committee of 12 announced the formation of a 'College for the Promoting of PhysicoMathematical Experimental Learning', which would meet weekly to discuss science and run experiments." from en.wikipedia.org/wiki/Royal_Society#Founding_and_early_years $\endgroup$ – Steve Huntsman Jul 23 '13 at 18:02

$\begingroup$ I think there was a time when they didn't use PowerPoint. $\endgroup$ – Gerry Myerson Jul 23 '13 at 23:12

2$\begingroup$ @Jaime: if you want a glimpse of how the talks were in 1893 (which is much more specific than your original question), here is a writeup of Felix Klein's lectures at Northwestern University (Evanston, IL) in connection with World Fair in Chicago that took place the same year. futuretg.com/FTHumanEvolutionCourse/FTFreeLearningKits/… (I was a grad student at NW some 100 years after). $\endgroup$ – Margaret Friedland Jul 24 '13 at 0:06

$\begingroup$ Margaret: Thank you for sharing this beautiful reference. Now I have a glimpse of how the talks were in 1893. $\endgroup$ – Jaime Arango Jul 24 '13 at 1:13
Well, if you are interested to learn how Euler lectured on math and physics to a lay audience, you might want to take a look at the Letters of Euler to a German Princess. This book collects the lectures on elementary science that Euler gave in Berlin to the Princess of Anhalt Dessau, in the early 1760's. Dominic Klyve gives a nice overview of "Euler as Master Teacher".
For a more technical/advanced talk, the lecture which Riemann delivered on June 10, 1854 has been preserved here. Dedekind writes about this lecture:
Gauss sat at the lecture, which surpassed all his expectations and on the way back from the colloquium meeting he spoke to Wilhelm Weber, with the greatest appreciation, and with an excitement rare for him, about the depth of the ideas presented by Riemann.

1$\begingroup$ If I remember correctly, Euler taught that princess by correspndence. And that is the reason why we can read this. $\endgroup$ – Alexandre Eremenko Jul 23 '13 at 22:20

$\begingroup$ certainly, as Euler himself writes: "The hope of having the honor to communicate in person to your highness my lessons in geometry becoming more and more distant, which is a very sensible mortification to me, I feel myself impelled to supply person instruction by writing, as far as the nature of the subjects will permit." Still, the style of the letters is quite informal and colloquial, I can imagine actually hearing Euler lecture. $\endgroup$ – Carlo Beenakker Jul 23 '13 at 22:26

$\begingroup$ The way we lecture has drastically changed in the last 200 years. We tend today to give more details. The answers I read are useful, but one thing is a paper, or a book, and a different think is a talk. I have no idea of how were the talks in the XVII Century or later, o more recently, how were the talks in the ICM in Chicago (1893)? The ICM 1893 papers are on line available (mathunion.org/ICM) but a glance at them suggest that the mathematical contents do not reflect entirely the talks. For example, how do they addressed the mathematical equations to the audience? $\endgroup$ – Jaime Arango Jul 23 '13 at 23:08