# Would Gauss still make his comment today?

1. Aug 17, 2008

### tgt

Gauss said: "Mathematics is the queen of the sciences and number theory is the queen of mathematics." But would he still make this comment today after learning the new abstraction and foundations that mathematics has taken on?

2. Aug 22, 2008

### iopmar06

I think that statement is still true regardless of the newer branches of mathematics (even though I don't find number theory particularly interesting).

Besides, Gauss doesn't seem like a man who would take back something he has said.

3. Aug 22, 2008

### tgt

What kind of new branches of maths have you learned?

4. Aug 22, 2008

### gel

why would number theory be classed as the queen of mathematics?

I wouldn't agree - although it'd help if I knew why he said that.

...Maybe because number theory problems are very basic and can be explained to a layperson, but the proofs can be very deep. Other areas of maths can be just as involved and interesting imo, but can't really be explained to the ordinary man in the street.

5. Aug 22, 2008

### tgt

Any science with the minimal amount of quantification would first start with the use of numbers. That is the reason.

Gauss did work in many areas of science.

6. Aug 23, 2008

### iopmar06

To be honest I am only an undergraduate so not much.

Just basic topology and algebra.

7. Aug 23, 2008

### Antuan

If mathematics is the queen of the sciences, then who would be the king ? Any suggestions ?

8. Sep 7, 2008

### qntty

Possibly http://en.wikipedia.org/wiki/Mathematical_logic" [Broken]?

Last edited by a moderator: May 3, 2017
9. Sep 7, 2008

### Kurret

imo logic and mathematics are equivalent in this contex, mathematics is just more advanced and more developed logic. Maybe the king of science would be imagination? To be sucessful in science you both need to master logical reasoning, but without fantasy and imagination you will not be able to apply your mathematical skills to discover new science.

Last edited by a moderator: May 3, 2017
10. Sep 7, 2008

### qntty

If tgt and gel are correct about Gauss thinking that number theory is queen because it is so simple and fundamental, perhaps axiomatic set theory would be a better king.

11. Sep 7, 2008

### Hurkyl

Staff Emeritus
Number theory is not synonymous with arithmetic. :grumpy:

12. Sep 7, 2008

### Antuan

I would easily agree with Kurret's proposal for the King of science; Imagination. Thanks for that beautiful insight !

13. Sep 7, 2008

### qntty

To be pedantic, it's sometimes referred to as "higher arithmetic", perhaps that was the source of his confusion.

14. Sep 9, 2008

### Dragonfall

Number theory is one of the last branches of mathematics that is used in the sciences. Analysis would fill that role.

15. Sep 11, 2008

### mhill

" Physics is the Queen of Science , and Group theory is the queen of Physics " ...

nothing has changed our life or the way we see Universe as physics has done

16. Sep 21, 2008

I think Ego is the king.

17. Sep 25, 2008

### yasiru89

I should think Gauss would see his comment reaffirmed! Kronecker's 'God created the integers, all the rest is the work of man' seems particularly fitting after Godel's theorems on incompleteness!
The funny thing though, is the curious marriage of number theory with analysis, the result I will call the 'Prince' of mathematics (analytic number theory).

Also 'Queen' was probably meant to indicate superiority as well as beauty, hence there is no 'King' (but I'd go with analysis if I had to- logic itself, given that theories have a Godelian inconsistency, falls back within the realms of number theory).

18. Oct 26, 2008

### theIBnerd

Gauss is the king, or thought to be so. On the other hand I don't think he is the best; i would rather vote for Euler for his e$$^{i}$$$$\pi$$ + 1 = 0 (the most beautiful and elegant equation I have ever seen)

19. Oct 27, 2008

### mhill

Euler is the King.. not only by his greatest knowledge of almost every branch of mathematics, but he is a good example of what a mathematician should be ,

- not be taken back because you perform unrigorous operations

- A bright heart and a comprehensive personality towards other people (gauss was very Rude and understimated many people)

- A good an optimistic way of live

Euler will always (for me as a physicist) be the ' King of all mathematicians' not only a brainy but a kind-hearted person

Last edited: Oct 27, 2008
20. Oct 27, 2008

### yasiru89

I hope we didn't go about missing the point here- Gauss made this comment because mathematics was both elegant and a feat of prowess (hence 'Queen').

Regarding Euler, I cannot stress enough to the unsuspecting physicist what a grave mistake it is to think of Euler as a mathematician who disregarded rigour. Indeed, the modern course of pure mathematics has a great deal to do with the Eulerian attitude towards such matters seeing as it was he who paved many of the roads we venture on today. He understood the value of a fully rigourous argument, and his work often illustrates the great care he took in establishing definition and then the result (for instance, see his solution to the Basel problem; he sought other proofs until he could make the one using the infinite product for the sine function rigorous by showing that the sine function had only those roots that he used to establish the result).

I would make no judgement on these individuals, or indeed, any individual, based solely on what they may have been like in their social interations and attitudes. It is their contributions that hold any sway- and in this regard, the only one that counts, both Euler and Gauss were truly great men.