**Logo of ICME-14**

The basic idea comes from Hetu (The River Map) in ancient China. Hetu, together with Luoshu (The Luo Writing), is commonly regarded as the origin of the Chinese civilization. The Book of Changes (I Ching) indicated that “The Yellow River gave forth the Map, the Luo River produced the Writing, and from them Saint Fuxi got the idea of the trigrams.” Many notions in Chinese traditional culture such as Taiji, Eight Trigrams, Fengshui may all originate from them. Hetu and Luoshu include mathematical contents such as the classification of numbers by their parity, the arrangements of numbers with equal differences or equal sums, as well as magic squares.

They are essentially the plain understandings of mathematics by people at that time. Hetu is also drawn as a round-styled picture, as shown on the left part of the ancient pot in the right picture.

The round-styled Hetu is used as the mould for the logo. In the logo, the chordal graph in the center can be regarded as the combination of five small geometric figures (four congruent right triangles and one square), replacing the five points in the center of the Hetu. The circle outside the chordal graph stands for the circle with ten dots in the Hetu. The two helix-shaped cantilevers in blue and red respectively circumscribed to the circle represent the ranges of yin numbers (even numbers, 2, 4, 6, 8) and yang numbers (odd numbers, 1, 3, 7, 9) rotating clockwise starting from the south (up) direction and north (down) direction respectively. Here, we only highlight and draw the yin dots representing number 2 and the yang dots representing number 7 in the south (up) direction.

The chordal graph is a perfect proof of the Gougu Theorem (known as Pythagorean Theorem in the west) proposed by Zhao Shuang, a mathematician during the Three Kingdoms period. It is now the logo of Chinese Mathematical Society. Therefore, it represents both the tradition of Chinese mathematics and mathematics education, and Chinese Mathematical Society, the hosting body of the Congress.

The two cantilevers symbolize that China is opening her arms to embrace participants from all over the world. It also shows China’s opening-up attitude.

The product of 2 and 7 is 14, indicating the session of this Congress.

At the lower right corner of the centerpiece picture under the “ICME-14” four Chinese traditional trigrams (guas) are used to write down number 3744 in octal system, which is 2020 in decimal system, indicating the year in which the Congress will be held. In addition, the binary code of “2020” can be read from the four trigrams: (0)11111100100. The octal system and the binary system connect the brilliant civilization of ancient China with modern science and technology.

Mathematical elements are extensively disseminated in the logo: the Gougu Theorem, even and odd numbers, the octal number system and the binary system, and so on. They are not only the achievement of ancient China, but also the content of teaching in modern elementary and secondary schools. The design is very geometric, particularly the centerpiece picture that consists of circles and helixes is centrally symmetric.

The use of helixes also represents the concept of spiral rise in modern teaching theory.

The centerpiece picture assumes the shape of “S”, meaning Shanghai, the city where the Congress will be held. Its momentum of moving forward indicates our proactive attitude.

Due to the pandemic of COVID-19, ICME-14 had to be postponed from 2020 to 2021, and was changed from a complete physical conference to a hybrid conference. For this reason, we changed the bottom line of the rightmost trigram from “Break” to “Connect”, and indicated in red to emphasize that this was a necessary change. In this way, the four trigrams in the lower right corner of the new logo represent the octal 3745, or the binary (0)11111100101, which thus representing 2021 instead.