Editing Vladimir Arnold (section)

===Real algebraic geometry===
In the year 1971, Arnold published "On the arrangement of ovals of real plane algebraic curves, involutions of four-dimensional smooth manifolds, and the arithmetic of integral quadratic forms",<ref>Note: The paper also appears with other names, as in http://perso.univ-rennes1.fr/marie-francoise.roy/cirm07/arnold.pdf</ref> which gave new life to [[real algebraic geometry]]. In it, he made major advances in the direction of a solution to [[Gudkov's conjecture]], by finding a connection between it and [[Low-dimensional topology#Four dimensions|four-dimensional topology]].<ref>{{cite book|author1=A. G. Khovanskii|author2=Aleksandr Nikolaevich Varchenko|author3=V. A. Vasiliev|title=Topics in Singularity Theory: V. I. Arnold's 60th Anniversary Collection (preface)|url=https://books.google.com/books?id=n6MlbFDp5UwC&pg=PR10|year=1997|publisher=American Mathematical Soc.|isbn=978-0-8218-0807-8|page=10}}</ref> The [[conjecture]] was to be later fully solved by [[Vladimir Abramovich Rokhlin|V. A. Rokhlin]] building on Arnold's work.<ref>{{cite book|title=Arnold: Swimming Against the Tide|url=https://books.google.com/books?id=aBWHBAAAQBAJ&pg=PA159|page=159|isbn=9781470416997|last1=Khesin|first1=Boris A.|last2=Tabachnikov|first2=Serge L.|date=10 September 2014| publisher=American Mathematical Society }}</ref><ref>{{Cite journal |arxiv = math/0004134|doi = 10.1070/RM2000v055n04ABEH000315|bibcode = 2000RuMaS..55..735D|title = Topological properties of real algebraic varieties: Du coté de chez Rokhlin|journal = Russian Mathematical Surveys|volume = 55|issue = 4|pages = 735–814|year = 2000|last1 = Degtyarev|first1 = A. I.|last2 = Kharlamov|first2 = V. M.| s2cid=250775854 }}</ref>