Mathematical Theorem facts
While investigating facts about Mathematical Theorems and Mathematical Theorems And Their Proofs, I found out little known, but curios details like:
a Futurama writer with a PhD in applied math created a mathematical theorem just for the purpose of using it in a Futurama episode to expose young people to higher level math.
how many mathematical theorems are there?
Futurama writer Ken Keeler wrote and proved a completely new mathematical theorem just for a single episode, called the Futurama Theorem. It is the first known theorem to be created for the sole purpose of entertainment in a TV show.
What is a well known mathematical theorem?
In my opinion, it is useful to put together a list of the most interesting details from trusted sources that I've come across answering what does mathematical theorems mean. Here are 46 of the best facts about Mathematical Theorems And Their Proofs Pdf and Mathematical Theorems List I managed to collect.
what is a mathematical theorem?

Pythagoras cannot have been the first to discover the Pythagorean theorem because it was known and used by the Babylonians over a millennium before he was born. Classical historians dispute whether he himself ever actually made any significant contributions to the field of mathematics.

In a 60's government funded LSD study, "26 men unleashed a slew of widely embraced innovations shortly after their LSD experiences, including a mathematical theorem for NOR gate circuits, a conceptual model of a photon, a linear electron accelerator beamsteering device," [and more....]

Euler's work in mathematics and physics touched upon so many fields that he is often the earliest written reference on a given matter. In an effort to avoid naming everything after Euler, some discoveries and theorems are attributed to the first person to have proved them after Euler.

Pythagoras studied mathematics in Egypt and Babylon. Particularly notable as the Babylonians had the 'Pythagorean theorem' at least five hundred years before Greece.

There is no evidence that Pythagoras worked on or proved the Pythagorean theorem, or, for that matter, any mathematical problems at all.

There is an XFiles episode, that predates Good Will Hunting, where a mentally challenged janitor working the night shift at the Mahan Washington Institute of Technology solves advanced mathematical theorems on a white board.

Ken Keeler, a writer for Futurama devised and proved a new mathematical theorem in an episode.
What are mathematical proofs and why they are important?
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Both of Wiles" papers proving Fermat's Last Theorem were published in 1995 in the Annals of Mathematics.
One of Noether's theorems has been called "one of the most important mathematical theorems ever proved in guiding the development of modern physics."
There is a theorem in mathematics (Classification of finite simple groups) whose proof consists of more than 10,000 pages spread across about 500 journal articles, written by over 100 different authors.  source
Fermat's Last Theorem (Fermat Conjecture) , which held the Guiness World Record for being the world's toughest mathematical problem until it was proven by Andrew Wiles after 358 years of unsuccessful attempts.
Alan Turing claimed his concrete solution to Gödel's Incompleteness Theorem, which became the mathematical foundation of the computer, came to him in a "vision".  source
How might mathematical induction be useful when analyzing problems?
James A. Garfield, the 20th president of the United States, published a proof of the Pythagorean Theorem, making him the only US president to have published a mathematical proof so far
How to prove mathematical theorems?
Pythagoras (570495 BC) is credited with his theorem, but there is no evidence of his mathematical proof. There is evidence the theorem predates him. Mesopotamian, Indian and Chinese mathematicians all discovered it independently and, in some cases, provided proofs for special cases.
About Godel's Incompleteness Theorems which prove that any mathematical system will have truths that cannot be proven
In high school he devoured books on mathematics and discovered advanced theorems.
The Banach–Tarski paradox, a mathematical theorem in set theory geometry which proves that it's possible to convert one sphere into two using nothing but cuts and rotations, but only with objects that don't actually exist.
Guillaume de l'Hôpital, who is best known for his mathematical theorem “l'Hôpital’s Rule” was completely based on off of the lessons he purchased from Johann Bernoulli and published without his knowledge.