History of sunspot research and forecast of the maximum of solar cycle 25

The paper provides a short historical overview of sunspot observations from their discovery until the present. The review goes beyond collecting all known historical information about the study of sunspots but highlights the research of five scientists of different epochs over five centuries since the 16th. Not as much attention is deliberately given to some well-known studies and discoveries. The focus is on the utmost long-term observations of sunspots, which provide information that expands the boundaries of classical Wolf numbers or the number of sunspots groups. Sunspots have been observed since ancient times and they were documented in ancient chronicles. Active observation of sunspots began after the invention of the telescope, probably by Hans Lippershey in the early 17th century. It is documented that Thomas Harriot was the first to observe sunspots with a telescope on December 8, 1610. It is probable that Galileo Galilei and Johann Fabricius observed sunspots almost simultaneously with him in December 1610 using a telescope, independently of each other and of Harriot. The first publication about sunspots was issued by Fabricius in June 1611. We dwell on the observations of Christoph Scheiner, Christian Horrebow, Heinrich Schwabe, and Hisako Koyama. Christoph Scheiner described his long-term observations and studies of sunspots from 1611 to 1630 in his book Rosa Ursina sive Sol, which became a model for the Sun observers for many years afterwards. Christian Horrebow was the first to speculate on the regularity of sunspots, and Heinrich Schwabe was the first in 1843 to discover the periodicity (with a period of approximately 10 years) of the number of groups of sunspots. In 1852 Rudolf Wolf, analyzing all available sources, clarified that solar activity has an 11-year periodicity. He introduced the concept of the relative sunspot number and organized regular observations and publication of their results. Hisako Koyama’s 40-year observations have helped reconcile current sunspot counts with earlier ones. Wolf’s system lasted until the beginning of the 21st century. In July 2015, a new version of the relative sunspot numbers was adopted (Version 2.0). In this paper, the ratio of “new” and “old” Wolf numbers is calculated and a table of characteristics of 11‑year cycles according to Version 2.0 is proposed. Two forecasts of the maximum of solar cycle 25 are also calculated. In the case when the precursor of the maximum is the value of the relative sunspot number in the cycle minimum (correlation coefficient r = 0.557 and P