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Leonardo Fibonacci or known as Fibonacci was born on January 01, 1175 (died on January 01, 1250, in Pisa. Fibonacci was a mathematician from Italy who mostly lived and worked in Pisa. He is known for publishing Liber Abaci in 1202, in which he introduced the Hindu-Arabic numerical system to Europe.

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.

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He was born on November 17, 1902 and died on January 1, 1995 (aged 92).

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."

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He is born on January 23, 1862 (Königsberg, Prussia) and died on February 14, 1943 (Göttingen, Germany).

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.

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Pythagoras of Samos was born around 570 BC in Greece and dying around 495 BC in Southern Italy. Not only a mathematician, but he is also a philosopher. He is known because of the Pythagorean Theorem, but its still a mystery if he is the one who discovered it or not. A fun fact about him is that he made a school in Croton where they have unique rules like keeping the teachings secret. Based on an article on the internet he might believed that mathematics didn’t just describe the world but was actually a part of it. Where they thought that physical reality was made up of mathematical objects in the same way that matter is made of atoms. This means like Phytagoras might saw math as something discovered since its a part of the universe. Pythagoreans focused on how math exists within the world and helps explain it.

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Euclid was born in the mid 4th Century BC and lived in Alexandria; he was mostly active during the reign of Ptolemy I (323-283BC). He was a greek Mathematician considered the “Father of Geometry”.His textbook ‘Elements’ remained a highly influential mathematics teaching book until the late 19th Century and is one of the most widely published books in the world. Some historians feel the works of Euclid may have been the result of several authors, but most agree that he was the one who bring them together.

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He is born on September, 1826(Jameln, Germany) and died on July 20, 1866( Verbania, Italy)

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.

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G. H. Hardy was born on February 7, 1877, and passed away on December 1, 1947.

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."

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427 BCE – 347 BCE Athens, Greece.

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.

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He was born on 29th April in 1854 and passed away on 17th July in 1912.He was a French mathematician,theoretical physicist,engineer and philosopher of science .Henri Poincaré was the first to introduce four-vectors, the Lorentz group and its invariants (including the space-time metric), “Poincaré stresses,” as well as making other valuable contributions to relativity theory.

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

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Born: December 7th 1823 in Breslau Peussia

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.

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Find out: their dates (birth and death), and a very brief background (where they lived and worked, one other fact about them), their position on the invention vs. discovery debate.

Add your thoughts to the padlet under your assigned person.

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Bernhard Riemann was born on September 17, 1826, in Breselenz, Kingdom of Hanover (present-day Germany), and died on July 20, 1866, in Selasca, Italy. He was a highly important German mathematician who spent most of his career at the University of Göttingen, where he made important contributions to analysis, number theory, and differential geometry. Riemannian geometry, which eventually became important for Einstein's theory of general relativity, and the still-unsolved Riemann hypothesis about prime numbers are two of his best-known achievements.

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.