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Hilbert was a German mathematician who worked primarily at a university in Germany, a leading center for mathematics in the early 20th century. He made foundational contributions to algebra, number theory, the calculus of variations, and the foundations of geometry. Lastly, he famously proposed 23 unsolved problems (Hilbert's Problems) in 1900, which influenced much of 20th-century mathematics.

Hilbert believes mathematics to be a game of symbols governed by rules —suggesting it is more of a human invention than a discovery of pre-existing truths. However, his work also revealed deep structures in math that some argue have a discovered quality.

Plato was an ancient Greek philosopher of the Classical period who is considered a foundational thinker in Western philosophy and an innovator of written dialogue and dialectic forms.

Plato believes that mathematical knowledge is discovered instead of invented due to the feature of revealing realities (e.g., 2+2=4) that math contains. Which is not from a mind or idea of the human brain. It's from the observation and summary.

Fibonacci's work demonstrates the complex relationship between invention and discovery. He discovered the well-known Fibonacci sequence itself (1, 1, 2, 3, 5, 8, 13...), an arrangement that occurs in nature, where the spiral patterns of sunflowers and pinecones usually align with Fibonacci numbers (e.g., 34 and 55). Fibonacci's biggest success was recognizing its potential and applying it in real-world solutions.

Winger was a Hungarian physicist, but to escape from persecution of Nazis , he moved to America and naturalized America in 1937. Since he was a experienced physicist, he was involved in Manhattan project during World War.

He received novel prize in Physics in 1973 for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles.

Winger believes that the maths are discovered. He said that " The unreasonable effectiveness of mathematics, pushing strongly of the idea that mathematics is real and discovered by people."

Bernhard Riemann was a German mathematician who worked primarily in Gottinggen, Germany but studied and taught at the University of Gottingen. His "Riemannian geometry"<- 1854 became the mathematical foundation for Einstein's theory of general relativity.

Riemann likely leaned toward discovery, as his work often revolved around uncovering deep mathematical truths and structures that seemed to exist independently of human creation, for example the geometry of space. he also engaged in creative invention, such as formulating new mathematical methods and tools.

He was born in Cranleigh, England, and was a British mathematician who worked at  Cambridge University.  He was known for his achievements in number theory and mathematical analysis in maths. He is also known in the biology field, as he is known for the Hardy–Weinberg principle, a basic principle of population genetics

G. H. Hardy was a mathematical Platonist. He believes that math is discovered. He thinks maths is an objective reality. For example, he believed the Riemann Hypothesis was either true or false, even though humans have proven it. He thinks that math is pure and values its purity. He once said, A mathematician, like a painter or poet, is a maker of patterns... more permanent than theirs."

He was well known for developing the qualitative theory of differential equations and resolving the three body problems

Deceased: December 29, 1891

• German mathematician who contributed to number theory, algebra, and mathematical knowledge. Lived primarily in Germany, mainly in Berlin and Breslau. Leopold is on the discovery side argument, as he says, "God made the integers; all else is the work of man," Fun fact, he was strongly opposed to the use of irrational numbers.

In the mathematical dispute between innovation and discovery, Riemann's work indicates that he favored the perspective of discovery. His investigations gave rise to deep, abstract structures that seem to exist independently of human knowledge. Rather than constructing arbitrary rules, he seemed to uncover fundamental facts about the mathematical cosmos. His theories continue to impact mathematics and physics today, confirming the concept that he was revealing something essential to reality rather than simply constructing it.