Was Giuseppe Peano Influenced by Euclid in Developing Axiomatic Systems?

[Knaapje]

Hello there,

First off: I realize this is not a history of math sub-forum, but I could not find any such thing.
Now, secondly: I'm writing an essay on the history axiomatic systems, and I found one or two sources that indicate that Giuseppe Peano was in fact influence by Euclid.I wonder whether any of it is true, since I can't find any book or trustable source that verifies it.

So, does anybody know a biography or other trustable article that sheds light on this matter?

 

[jedishrfu]

I would say yes but you'd have to make your case reviewing works of both Peano and Euclid to say.

Euclid influenced a lot of people prior to Peano and Peano had to have learned from them.

http://people.cst.cmich.edu/piate1kl/MTH_553_F07/Euclidean_Geometry_small.pdf

Maybe search first on Euclid influence in general and from there make a path to Peano and his Peano axioms and set theory.

 

[Knaapje]

Thanks for your reply!

I'm aware of the influential chain reaction of which you speak, but I was wondering if Euclid had a direct influence on Peano as he had with, say, Newton.

Unrelated sidenote:
I now absolutely hate wikipedia, for stating that Peano was influenced by Euclid, without any reference.

 

[oli4]

Hi Knaapje
I could recommend "From Frege to Gödel, a source book in mathematical logic" by van Heijenoort in which a section is dedicated to Peano
I don't remember any specific connection to Euclid there, so maybe I am being offtopic if what you really are after is showing or disproving such an influence (I would doubt such an influence didn't exist, for him or anyone else anyway)
But if you are after looking for what were possible influences, or even missed influences (Frege IIRC) for Peano, then it could be useful for you
Furthermore, and since the axiomatic way of building mathematics is such a huge concern, (I'm not sure about what you are really after in your essay), this book should give you a lot of food for thought, it really is incredible :)

 

[jedishrfu]

you could also check out the math genealogy:

http://genealogy.math.ndsu.nodak.edu/from there you could make the connections back to Euclid.

With respect to the wiki artile you mentioned, you could check the edit pages to see who contributed and email them asking for the references you were looking for.