In Zoku Owarimonogatari, why mirrored Sodachi's respected mathematician is Gauss?

Question

In Zoku Owarimonogatari, Koyomi meets with mirrored Sodachi Oikura, then Araragi asked if her most respected mathematician is Euler (real Sodachi respected Euler), but the mirrored Sodachi answers that her most respected mathematician is Gauss, and these formulae appear:

Euler's identity:

Gaussian integers:

So the question is, how is Gauss mirroring Euler? Or is it just a red herring?

Answer 1

Good question! Euler and Gauss are widely recognized as being the 2 most influential mathematicians in history. The greatest contrast between these 2 is that Euler worked on anything and everything, and published A LOT. In contrast, Gauss was more of a quality over quantity type of guy. He kept to a few topics and spent a lot of time improving his theorems and proofs before publishing anything.

Wikipedia on Euler:

Euler worked in almost all areas of mathematics, such as geometry, infinitesimal calculus, trigonometry, algebra, and number theory, as well as continuum physics, lunar theory and other areas of physics. He is a seminal figure in the history of mathematics; if printed, his works, many of which are of fundamental interest, would occupy between 60 and 80 quarto volumes.[25] Euler's name is associated with a large number of topics.

On Gauss:

Carl Gauss was an ardent perfectionist and a hard worker. He was never a prolific writer, refusing to publish work which he did not consider complete and above criticism. This was in keeping with his personal motto pauca sed matura ("few, but ripe").

So yeah this is probably why the "mirrored" Sodachi prefers Gauss over Euler.

Answer 2

Although najayaz's answer does an excellent job establishing why Gauss is a natural choice of mirror counterpart to Euler, keeping in mind that

the mirror world phenomenon is actually the "twenty percent of light which is absorbed by a mirror"; regrets and forgotten things, broadly speaking, the manifestation of which was also plausibly explained as showing the "other side" of those affected about up until the late Gaen Tooe showed up, and which in Oikura's case is specifically regret over not having gotten closer to Araragi,

I can think of three explanations connected to Oikura herself:

• In addition to Euler being her favorite mathematician, recall that she wanted to be nicknamed Euler, apparently for the phonetic similarity of their names. It's possible that she actually does hold Gauss's work in higher esteem, but considers Euler her favorite because he ties in closer to her identity. Mirrored Oikura, having a happier life with more to enjoy and less trauma to escape from, may not feel that she has to define herself around her love of math, so the nickname would not factor in.
• She may on some level actually be embarrassed about having cared about the nickname.
• In NisiOisiN's debut light novel, Kubikiri Cycle, the viewpoint character appraises Gauss as "the only genius I'd ever heard of who was at all good at human relationships". Although the subsequent musing about Michelangelo suggests it may just be more nonsense from the Nonsense User, I can't help thinking the same vague idea may also have influenced this element in Zoku Owarimonogatari, as mirrored Oikura is friendly and well-adjusted, contrasting her normal shut-in lifestyle and the hateful attitude with which she treated Araragi.