# Cauchy's contribution

Sometime, I believe perhaps 2 years, ago I asked a question about breakthroughs, such as those within mathematics and physics which may lead a whole discipline forwards in many ways. One example from physics (perhaps also mathematics) is Newton’s Principia.

I considered the problem of infinitesimals, used by Newton and criticized by idealist bishop Berkeley as “ghosts of departed quantities”, being “neither finite of infinitely small” (by which I assume he meant =0). We consider this contradiction to be solved by the modern concept of the mathematical limit, by a relation between e.g. epsilon and delta.

My question was the following:

If this breakthrough (which I attribute to Cauchy) was a significant step forward, why did we not see a number of significant advances as a consequence such as for Newton and Leibniz regarding celeste mechanics?

I now take the view that the question was never properly answered. It was also put on hold being considered unclear. I also believe that I now have a clear answer: the concept can be used to define the real numbers. I am not sure but I guess that this was the first of several methods of defining the set of real numbers. That amounts to a major consequence, does it not?

• I believe assessment of historical processes will always be surrounded with uncertainty. We cannot expect mathematical rigor here. I don't think any editing can be used to improve the question. However I believe it to contain much more depth than the answers I orininal got. – Mikael Jensen Apr 9 '16 at 22:18
• Mikael, your question suffers from some typical misconceptions concerning both Cauchy and limits. See my answer here: math.stackexchange.com/questions/1254553/… – Mikhail Katz Apr 10 '16 at 11:13
• @user72694 Your comment is highly interesting. I didn’t know about that and would like to know more. Still, I seem to have two separate issues, i) that there is may be a need to re-edit Cauchy to another person or a point in time where a collective view prevailed similar to the one today, assuming that is a uniquely defined concept, i.e. $\epsilon,\delta$ “sufficiency”, and ii) the opinion of the people who voted minus points and put the question on hold, who I believe would not be impressed by such a re-edit. My speculation is mainly about consequences of breakthroughs. – Mikael Jensen Apr 11 '16 at 14:07
• Mikael, if you don't vote to reopen people will be less motivated to do so :-) – Mikhail Katz Apr 11 '16 at 14:32
• Thanks for the support but I am not sure what that means, "vote to reopen". – Mikael Jensen Apr 11 '16 at 15:46