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In the What is Random? vlog of the Vsauce channel, Michael says (start from 3:25):

In the 1300s, random meant running or at great speed. Later, it would be used to describe things that have no definite purpose. It wasn't until the 1800s that random took on a particular mathematical definition. Then in the 1970s, MIT's student paper popularised the use of the word random to simply mean strange.

So, it must after 1970s that the word "random" started to have the meaning as we know today. So before that, what word was used instead, both for mathematicians/scientists and normal people?

And why did the word "random" spread out, when there was already another exactly term for that?

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I would say hazard or hasard (or for an adjective, fortuitous or fortuit), as in

At random (which seems to have been originally an artillery expression) translates into au hasard in Boyer (1711) and again in Laplace's System of the World (1809; original); the phrase to hazard at random is found in Voltaire (1760) and Adams (1794).

Edit. I now believe that the adjective you are really after is the French aléatoire or its German equivalent zufällig (whichever came first), as in

  • événement aléatoire (Lacroix 1816, Cournot 1843)
  • zufällige Werthe (Hauber 1830)
  • zufällige Ereignisse (Cournot 1849, Herr 1887, Bernoulli 1899, Czuber 1901, v. Mangoldt 1911)
  • zufällige Grösse (Hagen 1867, Kolmogorov 1933)
  • nombre aléatoire (Fréchet 1924)
  • variable aléatoire (Borel 1925).

It would be interesting if you could pinpoint when "in the 1800s" the adjective random took on a mathematical meaning comparable to the above.

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  • $\begingroup$ well, if you can, can you tell why does "random" got spread out while there was already the word "hazard"? $\endgroup$
    – Ooker
    Sep 12, 2015 at 19:08
  • $\begingroup$ @Ooker Maybe because unlike "hazard", "random" works as an adjective? $\endgroup$
    – Francois Ziegler
    Sep 12, 2015 at 22:14
  • $\begingroup$ I notice that you have added the fortuitous word, but don't see any reference in your answer. Can you add that? $\endgroup$
    – Ooker
    Sep 14, 2015 at 15:32
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    $\begingroup$ @Ooker I had no reference to offer, other than the occurrence of fortuit in the Furetière quote above: unlike hazard, I'm not finding it used in early probability literature. FWIW, this 1767 history of astronomy speaks of "random or fortuitous irregularities", and this 1768 dictionary defines hazard as "fortuitous hap." $\endgroup$
    – Francois Ziegler
    Sep 14, 2015 at 15:58
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    $\begingroup$ @fdb I focused my answer on references in the mathematics literature, where "random" seems to have appeared rather late (1800s according to the OP). But you're absolutely right, the question also asks about "normal people" usage. $\endgroup$
    – Francois Ziegler
    Sep 14, 2015 at 17:11
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I do not quite understand whether this is a question about history of science or about English usage. The Oxford English Dictionary points out that the phrase "at random" (earlier: "randon") occurs in English since the 16th century with this meaning:

haphazardly, without aim, purpose, or fixed principle; heedlessly, carelessly; (also) erratically, indiscriminately, unsystematically

For example in this quotation from 1543:

A certaine licenciousnes, or leude libertie..to ronne at randon hither, and thyther, through the wyde worlde perteygninge to no body.

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