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Cuchulainn
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### Philosophy of Mathematics

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.
Last edited by Cuchulainn on February 11th, 2015, 11:00 pm, edited 1 time in total.
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Cuchulainn
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### Philosophy of Mathematics

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.
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### Philosophy of Mathematics

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.

Cuchulainn
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### Philosophy of Mathematics

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.
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### Philosophy of Mathematics

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!

Cuchulainn
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### Philosophy of Mathematics

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]).
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Cuchulainn
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### Re: Philosophy of Mathematics

Step over the gap, not into it. Watch the space between platform and train.
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### Re: Philosophy of Mathematics

One write an ODE to maths day, what?

Cuchulainn
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### Re: Philosophy of Mathematics

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.
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### Re: Philosophy of Mathematics

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?

Cuchulainn
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### Re: Philosophy of Mathematics

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.
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### Re: Philosophy of Mathematics

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?

Cuchulainn
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### Re: Philosophy of Mathematics

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?
Step over the gap, not into it. Watch the space between platform and train.
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Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Re: Philosophy of Mathematics

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?

Collector
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Joined: August 21st, 2001, 12:37 pm

### Re: Philosophy of Mathematics

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?

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