Recently industry goes through enormous revolution. Related to this, major changes in applied mathematics are occurring while coping with the new trends like machine learning and data analysis. The last two decades have shown practical applicability of the long-developed mathematical theories, especially some advanced mathematics which had not been introduced to applied mathematics. In this concern some countries like the U.S. or Australia have studied the changing environments related to mathematics and its applications and deduce strategies for mathematics research and education. In this paper we review some of their studies and discuss possible relations with the history of mathematics.

In the 21st century, the era of artificial intelligence, it is demanded to make a change of the paradigm of education by the recent impact of the 4th industrial revolution. The education up to now has emphasized knowledge, meanwhile the human resources for the future are required to be armed with four C's: critical thinking, creativity, communication and collaboration capability, rather than being equipped with just knowledge. That is because the future society demands such abilities, especially the creativity of each individual. At this point, we are asked to consider the aim of education and teaching methods. In school education, students are to be respected and considered able to develop their potentials by themselves. They shouldn't be estimated by tests in the process of learning as they are now. We reconsider the aim of education here by taking a look at Whitehead's opinions and the present educational situations.

In general, there is summability among the mathematical tools that are the criterion for the convergence of infinite series. Many authors have studied on the summability of infinite series, the summability of Fourier series and the summability factors. Especially, $H{\ddot{u}}seyin$ Bor had published his important results on these topics from the beginning of 1980 to the end of 1990. In this paper, we investigate the minor academic genealogy of teachers and pupils from Fourier to $H{\ddot{u}}seyin$ Bor in section 2. We introduce the $H{\ddot{u}}seyin$ Bor's major results of the summability for infinite series from 1983 to 1997 in section 3. In conclusion, we summarize his research characteristics and significance on the summability of infinite series. Also, we present the diagrams of $H{\ddot{u}}seyin$ Bor's minor academic genealogy from Fourier to $H{\ddot{u}}seyin$ Bor and minor research lineage on the summability of infinite series.