How does one “invent new maths”? Like Isaac Newton inventing Calculus, or John Napier logs. How does one answer a mathematical question that’s never been answered?

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How does one “invent new maths”? Like Isaac Newton inventing Calculus, or John Napier logs. How does one answer a mathematical question that’s never been answered?

In: Mathematics

29 Answers

Anonymous 0 Comments

To quote Newton “If I saw further than others it was by standing upon the shoulders of giants.” There are only a few fundamental math principles (ex. numbers) that were invented by people seeking to explain their observations of the natural world. Everything else follows from that, but everything else is also still an invention. Newton wasn’t just sitting around someday and thought maybe he should create calculus, the principles of calculus were documented in various eastern mathematically text 1,000’s of years before Newton was even born. Newton and Leibniz just combined all those principles they read into a single consistent notation, they did not event something new.

Anonymous 0 Comments

For what it’s worth, some people think that math is discovered by people rather than invented by people. It’s a bit of a philosophical question in mathematics.

Anonymous 0 Comments

Newton didn’t invent calculus. Newton plagiarized most of the things that we attribute to him.

Anonymous 0 Comments

This is the reason why people generally refer to new ideas in math as discoveries and not inventions. It all already exists, it’s just that no one has looked at it in the right way or in the right place for a solution.

Anonymous 0 Comments

The simplest way to answer this is it is not invented. Math is at its basis a Language. A banana exists. We didn’t invent the banana. We invented a word to describe it. Gravity exists. A mathematician used the language of math to describe how it works.

Math is a language to describe patterns numerically.

Anonymous 0 Comments

It’s probably best to think of math as a language and not as a physical, measurable property. Math is the language that allows us to describe certain fundamental, universal phenom on. It has it’s own syntax and grammar, and it can be used to communicate ideas. Therefore, great thinkers are not actually inventing new ‘math’ as some sort of physical object, but instead are figuring out new ways to speak the language and describe phenomenon in new ways or, sometimes, even phenomenon we weren’t aware of before.

Anonymous 0 Comments

Well actually… Building the branch of mathematics we call calculus was the collaborative effort of many people over many years. Fermat, Cavalieri, Barrow and others had laid the foundations of calculus in the generation before Newton and Leibniz. See [The Wrong Queston](https://hopsblog-hop.blogspot.com/2021/05/the-wrong-question-who-invented.html)

Anonymous 0 Comments

Most answers here aren’t “ELI5 enough” in my opinion.

See, the universe works by a certain set of rules, just like a game. You can do a lot of different things, as long as you play by the rules.

Newton was doing just that. He saw a falling object and decided he wanted to describe its behavior. However, the velocity of a falling object is not constant, thanks to gravity. Now how do you express that in maths? Newton took the concept of “rate of change” and invented a way of doing maths with the concept using calculus.

So inventing things in maths is usually all about getting new perspectives and finding different ways to solve a new problem. It doesn’t mean writing new rules. It means defining the rules by which your universe works.

The more you play the game, the better you understand it.

Anonymous 0 Comments

It’s a philosophical debate on whether mathematics exists in reality or whether it is a human creation.

Most mathematical systems (algebra, geometry, calculus, group theory) and such are sets of rules. You can really create any set of rules that you want. These systems are obviously more useful and studied if they have practical use in the real world. I can make up a system where 1 = 2. That can be a “legitimate” system, but it has little practical use.

Mathematics, such as calculus and logarithms, are “invented” in that Newton and Euler came up with new sets of rules. Those rules were consistent and actually helped calculate things in the real world.

Another example was non-Euclidean geometry. Everyone “knew” what geometry was and how it modeled the real world. It wasn’t until 2,000 years after Euclid “invented” geometry that a couple of mathematicians dropped one of his five rules and came up with a whole new, consistent, geometry.

Anonymous 0 Comments

Y’all remember when the actor Terrence Howard “invented” his own math called Terryology? What a weird news story that was.