(Displayed in August 2022 to honor the 600 year anniversary of Henry 5 and Charles 6 passing in 1422. This is the second of two very very similar works.)
The piece is centrally about kings Henry 5 and his rival Charles 6 ('The Mad King") during the 100 Years War and some cursory information on the War of the Roses. The central question "what is left?" has many motivations: first, a teenage Henry was shot in the left side of his face at the battle of Shrewsbury (many feel the arrow likely deflected before entering his face). Thankfully, he survived the brutal injury, but the left side of his face was severely damaged, which probably explains why his portrait only shows one side of his face. Hence what is left? The math symbols representing the arrow's path feature mathematical "arrows" (also called morphisms) and the full diagram is relevant to the rest of the mathematical story. (It hints at what is called an injective object. These are integral to the construction of sheaf cohomology. The letter I, injective object, which is replaced by his face is hinted at by the I next to the crossed out s in “Is” at the top of the work. The word sheaf is certainly relevant to the long bow as in sheaf of arrows. see the below footnote for more about this)
Second, at the historic Battle of Agincourt, Henry's significantly outnumbered army thoroughly defeated the French with the brilliant use of the long bow and arrows. But, tragically, he had French prisoners of war executed (as he feared they might rearm and overwhelm the English), so what is left of the French prisoners?
Third, Henry's military victories forced Charles to name Henry his successor to the French throne (albeit after Charles died). Unfortunately, Henry died young (months before Charles) and could not assume this throne. After his death, the French reclaimed large tracts of the previously conquered land. Hence, what is left of the English lands in France? (on a side note, Henry’s son, Henry the 6's inept reign played a significant role in causing the War of the Roses).
(Finally, the global sections functor of a mathematical sheaf is left exact. This is important for sheaf cohomology)
As this is a short description, it is beyond its scope to go over detail of this work, but some more of the relevant history will. be detailed. The math referenced hints at sheaf cohomology, and to a lesser extentt very loosely refers Cousin Problems (although a more full picture arises when later works in this series are also studied and compared):
The night before the battle of Agincourt, Henry 5 ordered silence from his troops, threatening to cut off their ears if they failed to obey. The battle was fought on a rain-soaked field that significantly hampered the heavily armored French troops and cavalry. The portrait of van Gogh, with a missing ear, with an "X" over his mouth references Charles insanity and this episode as does the van Gogh picture of rain out his asylum window (on the right of my work).
Just as heavily armored knights did not function well on the rain soaked field of Agincourt allowing the English to defeat the French with arrows. To define a “good” cohomology theory for varieties over a finite field, more “open sets” are needed. The way this was accomplished was by defining open sets to be particular “arrows” (etale maps) to the space (as opposed to particular subsets of the space). This idea and the extensive use of the long bow by the English at the beginning of the battle of Agincourt are hinted at by “open with arrows”.
Charles the 6th was known as the mad king as he believed he was made of glass and had iron rods inserted into his clothes to prevent from breaking.
Henry 5th was the first English monarch to primarily use English as his language. This is pointed to with the two spellings of Henry (i).
The 100 years war actually lasted 116 years….100=116
As previously mentioned Charles 6 struggled badly with mental illness and during these bouts he could be completely incoherent for days. This was a far cry from the brilliant military leader Henry 5.
Wars and problems between cousins determined who would rule the English throne directly before and after Henry's reign.
Japan refers to the Japanese print on the wall behind Van Gogh in his original painting, but its also the name of the country where a journal published the revolutionary Tohoku paper.
Long exact sequences play an important role in cohomology and those terms are also relevant to the long bow.