gallery pic is from HG Contemporary 2019
"Napoleon would approve but Alexander was Greater". Refusing to sit while an artist slowly painted his features, Napoleon would tell artists to focus on his genius. This declaration forms the basis for my mathematical description of Napoleon’s rise, but in the end, I conclude Alexander was still greater and peace is superior to war.
Included in the words and symbols are some of the most important places and sites where Napoleon displayed his brilliance. Central to his famous victory over the 3rd Coalition was his ingenious scheme to first lure his adversaries to war at Austerlitz by feigning weakness. (He then tricked his adversaries into attacking his deliberately weakened right flank so he could counter strike their center).
An important aspect of Napoleon's collapse was Tsar Alexander's scorched earth policy in which Russia's army burned crops as they retreated. With hardly any grain left to consume the French army was left to starve. This flew in the face of Napoleon's prescient observation that armies march on their stomachs.
This abstract painting of the French tricolor (3 colors) flag was painted on an 8x5 white nylon flag (the Bourbon monarchy used a white flag). The painted portion ends before the right border symbolizing Russia’s victory which stopped France as it headed east.
Finally, three Alexanders are referenced in the work (most famously “the Great” and secondly the aforementioned Tsar). The third was a fantastic mathematician, who was also a pacifist. The mathematics shown is loaded with plays on words and metaphors. It starts by juxtaposing “locations” he fought some of his greatest mathematical battles, including the topos and the site, with locations where Napoleon demonstrated his military ingenuity. For example, Austerlitz is compared to the topos (which means ‘place’ in Greek) which is loosely speaking all sheaves over a site (the category of all sheaves over a site in mathematical parlance). It also includes one of his ingenious mathematical developments called the scheme. Other terms like descent have a role in his mathematical work, but also relate to the Bourbon dynasty whose fall (Louis the 16th who succeeded his grandfather of Louis the 15th) set the stage for Napoleon’s rise. More importantly, when Napoleon crowned himself emperor it threw out the age old conventional of genealogical descent with monarchs.
Several side notes:
Although a titan in art history, Cezanne’s snail-like pace painting models would not have been approved of by Napoleon.
For clarity, the blue shape is an abstract portrayal of a mountain with a pass through it.
Beethoven’s 3rd symphony was named in honor of Buonaparte. Once the former realized Napoleon was no different than other kings he scratched out the original dedication and retitled the work Eroica. This is referenced in one version of this painting with Eroica partially erased.
As there are several versions of JL David’s work “Crossing the Alps” which inspired this piece. There are several versions of Saiers’ work (two are shown in the images).
Finally, the phrase ‘War and Peace” also references Tolstoy’s famous novel about the Napoleonic era.
When being displayed, it should be installed with a red flag (hanging from a clothes hanger and bottle of glue) to the right of it.
This piece wrestles with the categories of representational and non-representational art (and the jump from one category to the other).
Irrespective of how one interprets the black scribbles, the work’s message is about not-representability. If the black marks on this painting have zero mathematical significance, then this work, which comprises a red shape on a white ground covered with black scribbles is not representable.
If the black glyphs “represent” mathematics, they point (albeit very loosely…see notes below) to the definition of a functor (a “map” from one category to another ) that is not representable (in the mathematical sense of the word).
Side note: To wrestle with the ambiguity of these two art styles (such as Monet’s late haystack painting that had a significant influence on Kandinsky in 1896) and the fact that at times abstract representations of objects (think cubism) can sometimes often appear nonrepresentational, some “nonstandard” symbols and a confusing/ambiguous ordering of the marks blurs the mathematical message. Using an art nomenclature, lets just say the way the artist appears to represent a functor that is not representable was not done “photo-realistically”.
This should not be displayed with any pieces of a similar title.
Borrowing language from Mininimalism (and related mathematics) 3 flat modules (or objects which are modules) are presented. One has black marks on it.
This work addresses the nature of representation in art, and is a gestural painterly response to Minimalism incorporating mathematical nomenclature 'consistent' with that school of art.
(Note: the dolly is part of the object, storage bubble wrap is not).
(shown on display Dec 2021)
As the title would suggest, this is a quick sketch whose concepts will be developed further in future work. The piece starts with a fundamental construction in category theory, a related notion called a fibred category, and the unique diet of the mathematical genius who developed both concepts. In addition to its mathematical significance, Cat has other connotations: the logo for Caterpillar, the construction vehicle manufacturer, and Dr. Suess’s famous hatted character. Here the latter is depicted with stacks of objects in his hand. The sketch points to several other stacks from art, and finally (yet subtly), one from mathematics. (This mathematics notion is further hinted at by the cat’s thought bubble which has two creatures descending a stair banging a drum and the arrow pointing down over the stack of rocks. A fibred category needs to have “descent” to become a stack.)
Footnote: The Dr. Suess’ feline is displayed twice partially to reflect Cat being a 2-category.
2022
This piece is a bit too complex to explain at this point, but ill gjve a quick exposition and a hint. Fundamentally the work is about the topos (mathematical term), which means place in latin, ie one interpretation could be what is the point of this mathematical concept. But then it hints at literally a point of topos (like you might describe a point in geometry). A topos is the category of all sheafs over a site. Words like sheaf and stalk certainly apply to Kansas where Dorthy’s house was on a farm, but also to a topos. A giant of 20th century math developed important ideas during his several year tenure at U. of Kansas before moving back to Europe. The phrase "we arent in Kansas anymore" (or "maybe we never left") has many interpretations but one interpretation relates to the idea that many of his ideas about the topos which he developed in France had some of their origins in his prior work in Kansas.
Toto is "represented" by the loyal dog at the feet of Venus in Titian's iconic painting Venus of Urbino.
(Stack in Studio 2022)
In Western art, Wasily Kandinsky made one of the first abstract paintings. His inspiration partially came from being unable to initially recognize what was being represented in one of Claude Monet's late haystack paintings. Despite this fact, Kandinsky still appreciated the work. Decades later, with a series of works called "Stacks" which consisted of colorful metal boxes vertically ascending a wall, the artist Donald Judd pushed the boundaries of abstract art further. His boxes were just objects to be viewed -they made no reference to any other thing- they were just boxes.
My work wrestles with the nature and categories of representational and non-representatational art (art that does not depict things from the real world such as a flower or person). I start by addressing the above anecdotes and works with the help of math. In this instance with a concept called a stack. Here I have asceding blue plexi-glass boxes displayed in a manner similar to how Judd installed his "Stack", the difference is I have filled my boxes with hay. By doing this I have puningly produced a "haystack". Subsequently, what was once nonrepresentational has now been trans-formed into a referent to Judd and Monet. To return my work to the abstract I have written symbols that point to a mathematical" stack" (roughly speaking a type of mathematical sheaf) on the wall next to the blue boxes. By doing this I show how my work is simultaneously representational, non-representational and abstractly representable via mathematics.
Warhol’s generation of artists had to address their abex predecessors in particular Jackson Pollock.
Warhol’s solution to this puzzle was to go in the completely opposite direction screen printing flat "unoriginal" images. A bowl of cornflakes was his favorite breakfast.
The math is about an object called a sheaf and hints at steps to generalize or recast it in a much more general and abstract setting...a sheaf is written outside the box..ie a sheaf of cereal. A key axiom of these objects is what’s called the gluing axiom. Glue is also what Warhol did to his wig and more generically he would often call getting ready for a party getting glued to keep his image intact. Glue is also used on cereal box images in lieu of milk as the cereal doesn’t get soggy or sink making it appear better on the box but it also destroys its use as food. One way to construct these more general sheaves is to start with a sieve S (sieve instead of mesh which would be used in screen printing). The numbers are vacuous and will be explained later.
Must be displayed with the pollock puzzle box next to the work.
Minimalism, sometimes called ABC art, emerged as an important art movement in the 1960s. Frank Stella, a prominent figure in this movement, was recognized for his paintings featuring black-and-white concentric rectangles, much like the upper section of this artwork. The term "ABC art" reflects the basic, simple shapes typical of this style, which drew both criticism for its simplicity and praise as a radical response to abstract expressionism.
On the bottom potion of the painting two simple equations are scribbled that hint at the important ABC Conjecture. A fundamental aspect of this conjecture is the term radical abc, rad(abc). While its constituent expressions are quite simple the conjecture itself has deep and far-reaching consequences throughout number theory. This illustrates that simplicity of form can actually heighten instead of diminishing the importance of something.
