Who Was the Ultimate Genius: Newton or Riemann?

[DaveC426913]

...what's more fundamental to day to day life...

You've taken the word out of context. It was applying to mathematics; you're applying it to daily life.

And you're using a definition of fundamental that is synonymous with 'important', as opposed to a defintion of fundamental that is synonymous with 'upon which everything else is built'.

Nucleosynthesis is fundamental to atom-based life on Earth but I'm not convinced we could say it's fundamental to day-to-day life.

 

[Kajahtava]

I love it when people who just disagreed with me randomly re-stated what I said on another point in different words.

 

[humanino]

But what is proof theory then, or lambda calculus, or set theory, or recursion theory?

Maybe it would be best if I admitted I would rather classify them as "foundational mathematics". Since if I had to classify them either as "algebra" or "analysis", I would pick algebra, it is possible that we actually share the same point of view.

Maybe where we agree the least is that, when I say "foundational mathematics", I really mean that so few mathematicians actually work on "foundational mathematics", they are really on the fringe to me. But you may also call it the Heart, with a capital. The classification "algebra" vs "analysis" is just a gross feature to describe roughly in the vast world of mathematics. It is not a classification which is really relevant to the very specific field of "foundational mathematics", since it is already quite restricted and much better defined than "algebra" vs "analysis".

 

[Kajahtava]

Maybe it would be best if I admitted I would rather classify them as "foundational mathematics". Since if I had to classify them either as "algebra" or "analysis", I would pick algebra, it is possible that we actually share the same point of view.

Maybe where we agree the least is that, when I say "foundational mathematics", I really mean that so few mathematicians actually work on "foundational mathematics", they are really on the fringe to me. But you may also call it the Heart, with a capital. The classification "algebra" vs "analysis" is just a gross feature to describe roughly in the vast world of mathematics. It is not a classification which is really relevant to the very specific field of "foundational mathematics", since it is already quite restricted and much better defined than "algebra" vs "analysis".

Hmm, maybe this is your own environment, most I know are foundational mathematicians, but then again, that could be my own environment.

A forum like phyicsforums of course naturally draws nonfoundational maths. But is it truly that obscure or esoteric? Or well, you might have a point, seeing that when I still studied, one of the reasons I dropped out was that I found that a variety of courses I held to be foundational and essential were either optional or not given at all.

 

[humanino]

Maybe an objective answer could be obtained by doing some statistics on the arXiv preprints (for instance).

 

[DaveC426913]

I love it when people who just disagreed with me randomly re-stated what I said on another point in different words.

I assume you mean me.
1] We simul-posted. You beat me by a couple of minutes. It happens on popular boards, and around here quite a bit. I've only just seen your post now.
2] Just because I disagree with a point you've made doesn't mean I automatically agree with your opponent. I thought Jack's point about the definition of fundamental was a weak rebuttal, for the reasons I stated.

 

[Jack21222]

I assume you mean me.
1] We simul-posted. You beat me by a few seconds.
2] Just becasue I disagree with a point you've made doesn't mean I automatically agree with your opponent. I thought Jim's point about the definition of fundamental was a weak rebuttal for the reasons stated.

1) My name's not Jim.

2) My rebuttal was merely pointing out there is a difference in semantics in this argument.

Kaj is arguing that calculations and approximations aren't math. The rest of the world would claim that it is. Also, for many people, calculus is the basis for the "math" that they use every day. Kaj would call it "physics" or "biology," instead of math. Most real-world applications for math I can think of have their foundation in calculus.

Physics, engineering, economics, biology, statistics... none of these would be in its current state without calculus, and most people consider calculus as a type of math.

Therefore, I'd argue calculus is a "fundamental" type of math, even if it isn't fundamental "to" math.

 

[DaveC426913]

1) My name's not Jim.

What are you talking about. Are you hallucinating?

2) My rebuttal was merely pointing out there is a difference in semantics in this argument.
...
Therefore, I'd argue calculus is a "fundamental" type of math, even if it isn't fundamental "to" math.

You can argue that now, but when you stated it, you misstepped, asking about "fundamental to day-to-day life", which is a wild goose.

 

[Jack21222]

What are you talking about. Are you hallucinating?

You can argue that now, but when you stated it, you misstepped, asking about "fundamental to day-to-day life", which is a wild goose.

Agreed, I didn't make my intended point.

 

[Kajahtava]

I assume you mean me.
1] We simul-posted. You beat me by a couple of minutes. It happens on popular boards, and around here quite a bit. I've only just seen your post now.
2] Just because I disagree with a point you've made doesn't mean I automatically agree with your opponent. I thought Jack's point about the definition of fundamental was a weak rebuttal, for the reasons I stated.

Oh, I wasn't sarcastic, I love it when people see point 2.

The enemy of the enemy is only a friend in a dilemma. If only one of two options can be true, and if one is false, it implies the other is true, many people feel to appreciate this and I like it that you did.

Also, I think there is a difference between coming to a conclusion that is true, but not in a rigorous way and coming to a conclusion that it false by lack of rigour. As in, many results obtained by use of the infinitesimal are true. However the theory of the infinitesimal itself is an awkward thing.

 

[dx]

Einstein did not discover any new mathematics. Newton was one of the greatest mathematicians of all time, and certainly the foremost mathematician (and physicist) in the world during his lifetime.

 

[Kajahtava]

Didn't Einstein to some degree helped with tensor analysis?

Not sure about that one though.

 

[dx]

Well, he was the main reason tensor analysis entered the world of physics, but he didn't personally contribute anything to the mathematics. It was discovered and developed in the 1800s by Gauss, Riemann etc.

 

[Kajahtava]

Ahh, never knew it was that old.

Which brings us to another point though, if you ask a random person who the greatest mathematicians were, the response will almost always be 'Newton, Euler, Gauss, Riemann', that group of people. In fact, rarely will the response include a person that contributed profoundly to pure maths.

I think people have a tendency to greatly confuse brilliance / sophistication of work and importance of it.

 

[dx]

Ahh, never knew it was that old.

Which brings us to another point though, if you ask a random person who the greatest mathematicians were, the response will almost always be 'Newton, Euler, Gauss, Riemann', that group of people. In fact, rarely will the response include a person that contributed profoundly to pure maths.

I think people have a tendency to greatly confuse brilliance / sophistication of work and importance of it.

...What? Are you saying Euler, Gauss and Riemann did not contribute profoundly to pure math? I'm sorry but that's the most rediculous statement I've ever heard.

 

[Kajahtava]

That is exactly what I'm saying, they all contributed solely to applied mathematics. In fact, pure mathematics hardly existed in that era, it was about application, application and application and rigour was second to that.

Pure mathematics mainly got off the ground with people like Hilbert, Dedekind, Gödel, Frege, Russell, Cantor, for some reason a lot of German people...

 

[dx]

'Rigor' and 'pure math' are not synonyms. Number theory only became an applied field in the late 20th century, but Gauss, Euler and Riemann contributed greatly to it. Differential geometry only became an applied field after Einstein, but Gauss, Euler and Riemann contributed fundamentally to it.

 

[Kajahtava]

Frankly, I'd call any mathematics that deals with quantities and magnitudes and how to calculate them with some tricks 'applied'. It has an application outside serving as a lemma then, doesn't it?

 

[MotoH]

I voted for Alby because I figured he wouldn't have a lot of votes.

 

[M Grandin]

Maybe somewhat off-topic, but regarding thread title "Competition between geniuses"
and Newton involved, there is a very interesting youtube video about Robert Hooke in 6 parts, where first part at address

http://www.youtube.com/watch?v=KP7zeoYv1ZI&NR=1

 

[BobG]

I don't think it's off topic. In fact, I think you run into problems comparing geniuses of completely different eras.

A better competition would be between Newton, Hooke, and Murphy. Whose laws were more profound?

 

[kakarotyjn]

Einstein knew Riemann Geometry,but Newton didn't...

 

[dx]

I know Riemannian geometry, but Newton didn't.