I also wondered how Leonhard Euler arrived at all those formulae and equations. In many cases he did a finite difference on the problem and then let h -> 0. Clever. Euler-Lagrange QuoteIn solving optimisation problems in function spaces, Euler made extensive use of this `methodof finite differences'. By replacing smooth curves by polygonal lines, he reduced the problem offinding extrema of a function to the problem of finding extrema of a function of n variables, andthen he obtained exact solutions by passing to the limit as n ! 1. In this sense, functions canbe regarded as `functions of infinitely many variables' (that is, the infinitely many values of x(t)at different points), and the calculus of variations can be regarded as the corresponding analog ofdifferential calculus of functions of n real variables.

QuoteThe tables were anticipated for many years, with pleas for its publication reaching as far as India and Jesuit missionaries in China.[1] Apart from external hindrances, Kepler himself deterred from such a monumental enterprise involving endless tedious calculations. He wrote in a letter to a Venetian correspondent, impatiently inquiring after the tables: "I beseech thee, my friends, do not sentence me entirely to the treadmill of mathematical computations, and leave me time for philosophical speculations which are my only delight.[2] They were finally completed near the end of 1623.If only Kepler had had a Commodore 64.

QuoteOriginally posted by: CuchulainnQuoteThe tables were anticipated for many years, with pleas for its publication reaching as far as India and Jesuit missionaries in China.[1] Apart from external hindrances, Kepler himself deterred from such a monumental enterprise involving endless tedious calculations. He wrote in a letter to a Venetian correspondent, impatiently inquiring after the tables: "I beseech thee, my friends, do not sentence me entirely to the treadmill of mathematical computations, and leave me time for philosophical speculations which are my only delight.[2] They were finally completed near the end of 1623.If only Kepler had had a Commodore 64.Without electricity, it would not have done him much good.We may stand on the shoulders of giants but giants stand on the rising gravel pile of every-day enabling technologies.

QuoteOriginally posted by: Traden4AlphaQuoteOriginally posted by: CuchulainnQuoteThe tables were anticipated for many years, with pleas for its publication reaching as far as India and Jesuit missionaries in China.[1] Apart from external hindrances, Kepler himself deterred from such a monumental enterprise involving endless tedious calculations. He wrote in a letter to a Venetian correspondent, impatiently inquiring after the tables: "I beseech thee, my friends, do not sentence me entirely to the treadmill of mathematical computations, and leave me time for philosophical speculations which are my only delight.[2] They were finally completed near the end of 1623.If only Kepler had had a Commodore 64.Without electricity, it would not have done him much good.We may stand on the shoulders of giants but giants stand on the rising gravel pile of every-day enabling technologies.True. They also did not have coffee.

QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: Traden4AlphaQuoteOriginally posted by: CuchulainnQuoteThe tables were anticipated for many years, with pleas for its publication reaching as far as India and Jesuit missionaries in China.[1] Apart from external hindrances, Kepler himself deterred from such a monumental enterprise involving endless tedious calculations. He wrote in a letter to a Venetian correspondent, impatiently inquiring after the tables: "I beseech thee, my friends, do not sentence me entirely to the treadmill of mathematical computations, and leave me time for philosophical speculations which are my only delight.[2] They were finally completed near the end of 1623.If only Kepler had had a Commodore 64.Without electricity, it would not have done him much good.We may stand on the shoulders of giants but giants stand on the rising gravel pile of every-day enabling technologies.True. They also did not have coffee.They did not need it. They had all those exciting table entries to compute!

QuoteHis colleague Alfréd Rényi said, "a mathematician is a machine for turning coffee into theorems",[15] and Erdős drank copious quantities (this quotation is often attributed incorrectly to Erdős,[16] but Erdős himself ascribed it to Rényi[17]).

Have a good day.

https://www.daysoftheyear.com/days/world-maths-day/

One write an ODE to maths day, what?

One write an ODE to maths day, what?

Good idea!
Or maybe the 57th way to compute [$]e^5[$]. I'm clean out of ideas.

One write an ODE to maths day, what?

Good idea!
Or maybe the 57th way to compute [$]e^5[$]. I'm clean out of ideas.

Twas a valiant effort and at least you got above [$]e^4[$] ways, what?

You can blame it all on a German mathematician(*), Carl Friedrich Gauss, who started  the futuristic "mega-trend" back in 1809: He showed us how to "train" a straight line to pass nicely through a cloud of unruly, scattered data points. To find, in effect, a path of least embarrassment.   

And later mathematicians Taylored a polynomial for this purpose, what?

You can blame it all on a German mathematician(*), Carl Friedrich Gauss, who started  the futuristic "mega-trend" back in 1809: He showed us how to "train" a straight line to pass nicely through a cloud of unruly, scattered data points. To find, in effect, a path of least embarrassment.   

And later mathematicians Taylored a polynomial for this purpose, what?

The solutions are manifold, what about Gauss' student Riemann?

You can blame it all on a German mathematician(*), Carl Friedrich Gauss, who started  the futuristic "mega-trend" back in 1809: He showed us how to "train" a straight line to pass nicely through a cloud of unruly, scattered data points. To find, in effect, a path of least embarrassment.   

And later mathematicians Taylored a polynomial for this purpose, what?

The solutions are manifold, what about Gauss' student Riemann?

He made math tensor.

what would the interpretation of the square root of a probability be? something in particular, something we can imagine in the "real" world? or just useful as math in intermediate calculations?