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I realise that this isn't a very academic question, but after watching movies like First Man and Interstellar, it got me wondering:

How did all these formulas that we use on a regular basis come into being? I'm sure many answers would be "oh they conducted several experiments and got the formula", but even then, how did the first guy who arrived at any given formula know that this experiment would lead to that said formula?

My question is basically this- for the very first person who came up with any mathematical formula or equation that is used extensively in today's world, how did he/she know where to start? Most of the equations that we learn, such as escape velocity, use some reference formula that has already been arrived at. But what did the people who arrived at a formula for the first time use as a basis or a reference when nothing was discovered during their time?

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  • $\begingroup$ This is a rather broad request and, in some respects, possibly not even answerable. $\endgroup$
    – Kyle Kanos
    Commented May 1, 2019 at 13:38
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    $\begingroup$ I am not sure whether this is in the direction of addressing what you have in mind but the very first formulae (that we use even today) were very empirical. For example, Galileo noticed that a pendulum's time period only depended on its length as long as the pendulum is near the surface of the Earth and its oscillations are small. He presumably made some tables of time periods for various lengths and noticed that the relation is that $T\propto \sqrt{L}$. $\endgroup$
    – user87745
    Commented May 1, 2019 at 13:38
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    $\begingroup$ I am not voting your question as off-topic (as I don't think it is) but nonetheless, I feel that this question might be better received on the HSM site. PS: Also, if you have some time on your hand, read "To Explain Things: The Discovery of Modern Science" by S. Weinberg. $\endgroup$
    – user87745
    Commented May 1, 2019 at 13:41
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    $\begingroup$ Hi noorave, your question is really interesting, but I am afraid it falls out of scope of this website, which aims to provide a Q&A with "unique" answers to specifically posed questions. To get a peek into the mind into one of the first mathematicians of the European tradition, I would recommend to read about Pythagoras and his followers. $\endgroup$
    – Void
    Commented May 1, 2019 at 13:41
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    $\begingroup$ @noorav HSM site is History of Science and Mathematics $\endgroup$
    – Kyle Kanos
    Commented May 1, 2019 at 13:56

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