Final answer:
The birth of Alexei in 1905 is significant because he was the heir to the Russian throne with hemophilia, which brought Rasputin into power and contributed to the public's loss of faith in the monarchy, leading towards the fall of the Romanov dynasty.
Step-by-step explanation:
The birth of Alexei in 1905 is significant due to the fact that he was the long-awaited male heir to the Russian throne, born to Tsar Nicholas II and Tsarina Alexandra. Alexei's birth was fraught with deep concerns within the royal family because he was diagnosed with hemophilia, a condition that affected his blood's ability to clot and posed numerous risks to his health and life. This condition brought Grigori Rasputin, an illiterate monk and faith healer, into significant influence within the royal household, as he seemed to have the ability to relieve Alexei's suffering.
The presence of Rasputin and the management of Alexei's condition contributed to undermining the legitimacy of the monarchy and escalating public discontent. Coupled with the strains caused by wars such as the Russo-Japanese War and World War I, the controversies surrounding Alexei's health issues and Rasputin's influence reflected the broader societal and political upheavals that would eventually lead to the fall of the Romanov dynasty.
These events are a part of the complex historical context that includes the Russian social order and the eventual push towards modernity that the empire faced during the early 20th century.