What does e represent in calculus and why is it used?

[dextercioby]

Deadwolfe,
hmm give me one name on that list which is not listed here
http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Full_Alph.html
as a mathematician.

Just because their contribution to the field of mathematics was little does not make them any less of a mathematician.

Okay,pal,check this link:
Niels Bohr mathematician?Not a chance!

Tell me whether Niels Bohr had any contribution to the field of mathematics...You might want to check this page as well:
References to article

Daniel.

 

[matt grime]

The second reference doesn't mention a single article written by Bohr, does it? In fact there is no description of any of Bohr's published papers or articles or books as far as my quick glance tells us. As there is no actual official firm boundary between what constitutes mathematics alone and what is physics alone the debate is highly subjective anyway.

If you wish to claim he made no contribution to the field of mathematics, then you ought to at least give a list of his publications.

As it is, in my mind I would say Bohr was a physicist, but that is because we tend to classify into distinct categories. He used mathematics in his work, and created the need for better mathematical techniques to describe quantum mechanical phenomena. I don't konw if he then did the maths himself or not. And I'd hazard a guess, as you didn't give any decent references to his cv, that you don't know either.

 

[dextercioby]

Leon Rosenfeld's 1972 book:"Niels Bohr,Collected Works" should come up with answer.Anyway,since i couldn't find a list of articles by Mr.Bohr on the internet,and at the library it's closed (i think;i'm too lazy to move my butt off the chair,get dressed properly and walk 300m to the library to check it out),i would have to do this trick,very mathematical indeed:

CONJECTURE:"Niels Bohr made no contribution to the field of pure mathematics as he was not a mathematician."

So i guess it's up to you to prove/disprove this assertion. Since i don't have that book,i cannot prove/disprove it.However,one needs to find only one article by Mr.Bohr on a subject from pure mathematics to disprove it.

Daniel.

PS.Niels Bohr had a brother,Harald Bohr,who was a mathematician.

 

[matt grime]

Before I prove or disprove your assertion (of which I will do neither) you should explain
1. why you have suddenly inserted the word 'pure'
2. what counts as mathematics and what as physics.

My view would be that if I needed to classify him I would opt for physicist. However, as well as experimental things, he did, or at least appeared to, theoretical physics which is mathematical, and thus he contributed to mathematics. The disticntion between theoretical physics and mathematics is at best fuzzy and almost certainly harmful.

 

[dextercioby]

Before I prove or disprove your assertion (of which I will do neither) you should explain
1. why you have suddenly inserted the word 'pure'
2. what counts as mathematics and what as physics.

My view would be that if I needed to classify him I would opt for physicist. However, as well as experimental things, he did, or at least appeared to, theoretical physics which is mathematical, and thus he contributed to mathematics. The distinction between theoretical physics and mathematics is at best fuzzy and almost certainly harmful.

1.It wasn't 'sudden'. To me,a mathematician is a person who works in the field of pure mathematics.He creates mathematics (notions,concepts,theories) or sometimes just puts known things in another perspective.Applied mathematics requires other types of knowledge (that's why bears the name "applied") and skills.

None of the theoretical physicists is a mathematician.Just that we know more mathematics than the exparimentalists or other scientists does not imply us having the word "mathematician" written all over us.You see a thin border,i see a very thick one.'Exceptions' don't count as exceptions:Newton was a physicist,Leibniz a mathematician,Gauss a mathematician,and the list is very long.
"...and thus he contributed to mathematics".He didn't.There's no single formula/proof/definition/theorem/lemma/conjecture/corollary/proposition...in the field of mathematics (pure & applied) which bears the name of/is linked to Niels Bohr,nor Albert Einstein,nor Paul Adrien Maurice Dirac,and so on and so forth.The list of theoretical physicsts i believe opens with the names of Ludwig Boltzmann and James Clerk Maxwell.

Notes:
a)Newton created calculus for physical purposes only.
b)Leibniz created calculus for mathematical purposes only.
c)Euler invented variational calculus for mathematical purposes only.
d)Gauss invented diff.geometry for mathematical purposes only.However,he was passionate for (physical) applications of his (and Ostrogradski's) integral formula and therefore resulted:Gauss's laws for electrostatics,magnetostatics and gravitostatics.
e)Paul Adrien Maurice Dirac invented "delta functional" for physical purposes only.Shilov,Gelfand & L.Schwarz took it to build distribution theory as a subchapter of functional analysis in pure math.
f)...

Daniel.

PS.2.The 'short' version is:the CLEAR difference between a theoretical physicst and a mathematician appears whenever both are faced with the same (very simple) problem from other's domain.Take for example:solving the Schroedinger's equation for the H atom.The mathematician will have no reason to reject irregular solutions (discrete spectrum),because he cannot see the physics that lies beyond equations.He will analytically continue those hypergeometric series and will come up with a brilliant mathematical expression without any physical relevance.After all,if he did know the phyiscs,he would be a physicist,right??

 

[matt grime]

So your notion of what a mathematician is differs markedly from some other people's then. LIke I keep saying if I were to label I would label Bohr a physicist. That doesn't a priori exclude him from having made a contribution to mathematics.

Here is a mathematical object:

\phi(n)

a function from N to N, that gives the number of numbers comprime with n between 1 and n. It is called Euler's totient function. Euler was a prolific mathematician and physicist.

Gauss also invented physical theories in astronomy I believe, though don't quote me. The origins of homological algebra lie in studying planetary motion. (hence the apparently disparate meanings of syzygy)

Ah, Dirac, that'd be the dirac who was from Bristol, where I work, as a mathematician, whose portrait hangs in my department? A department which, in a recent report, said that it wished to remove the artificial barriers between the applied and pure world, a department where applied mathematicians study the Riemann hypothesis? Where the applied colloquium two weeks ago was on L-functions and modular forms and where Paul Martin gave a talk aobut statisical mechanics in the pure seminar?


The original point was that although there is no Nobel prize for mathematics, there are prizes won by people who's work has had a strong influence on and been strongly influenced by mathematics, that is all.

The divisions are completely subjective as I believe we have shown here.

jon baez isn't a member of the physics department at UCR, atiyah has contributed abel winning theorems to mathematics that have uses in physics (and last i knew was studying electron distributions), grothendieck is now allegedly studying biology, soem famous category theorist/geometer whose name eludes me isn ow doing computer science, bott was an electrical engineer and mathematician.

The differences are sometimes marked, sometimes fuzzy, but it is all completely subjective, isn't it?

 

[danne89]

Hmm. I wonder, why did you invent natural logarithms. I mean, why don't one just stay to the common ones.

 

[TenaliRaman]

** perfectly agrees with matt **

Danne,
see here,
http://en.wikipedia.org/wiki/Natural_logarithm

I mean, why don't one just stay to the common ones.

Umm because "e" is more common than any other base.

-- AI

 

[danne89]

Hmm. The site states that natural logorithms has rare propertys that are applicable to decays and growth. But doesn't that also include 10-based ones. Ohh, the book I'm reading about this really sucks.

 

[matt grime]

e occurs naturally in solutions to differential equations.

 

[danne89]

Ahh. But when dealing with inverse exponet-problems, the choise between 10-based and e-based is arbitrary, right?