According to the Jewish calendar, Abraham was born on the year 1948.
The state of Israel was declared in 1948 according to the secular calendar.
Is there any significance to this or is it just coincidence.
The bible does not explicitly state the year in which Abraham was born, and as such, there have been disagreements about the calculations of the biblical years. Thus, it is unclear if Abraham was actually born in the year 1948 from Creation.
The current civil calendar is the Gregorian Calendar, based on the Julian Calendar, which was created in 45 B.C.E. Thus, according to the original calendar, the State of Israel was established in
Even if it is not a coincidence, there does not appear to be any significance to these dates. And even if there was, and God indeed chose these dates, there are many more significant dates He could have chosen, such as the dates when the Israelites entered the Land of Israel, or were given the Torah at Mt Sinai, or the building of the Temple, etc.
Among Jews of a more mystical hashkafa, such as chassidim and many others, there is no such thing as a coincidence. This view -- that everything happens for a reason -- was strongly stated by the Baal Shem Tov, but is also discernible in previous sources (such as Rabbi Akiva's "Gamzu L'Tovah" story in the Gemara, and statements by rabbis such as Rabbeinu Bachya and R' Avraham ben Rambam.)
In addition, the more specific idea that Hashem send us "hints" is also found in rabbinic literature (For example, "Think about the thoughts, words and deeds that God sends you each day in order to understand His hints to you to draw closer to Him at every moment." Likutey Moharan I, 54.)
To more rationalist Jews, of course, the 1948 parallelism between the founding of modern Israel and Avraham Avinu's birth would be nothing more than a coincidence.
More mystically-inclined Jews could argue that it does in fact have a meaning. Since Hashem first promised the Land of Israel to Avraham, it may be a sign that the creation of the state is the fulfillment of His promise that the Jews would inherit the land.
The fact that 1948 is on the Christian calendar may pose difficulty to some, who may have trouble understanding why G-d would send messages through another religion's calendar. Yet logically, since G-d is all-powerful, it is not beyond His power to send subtle messages to Jews through another religion's calendar.
Perhaps the use of the Christian calendar was meant to hint that the mistreatment that Jews had suffered at the hands of Christians for 2000 years, culminating in the Holocaust, was now coming to an end, as the Jews returned to their divinely-promised homeland. In addition, the use of the Christian calendar could have been meant to hint to Christians that Hashem is still honoring His promises to the Jewish people, which could potentially induce Christians to become less anti-Semitic or more supportive of Israel.