Will we ever discover all of math?

Math is absolutely still being discovered, and that won’t stop anytime soon. That’s what mathematicians do, we discover new math. There are new discoveries made every day, ranging from minor things that only a few people will ever care about, to occasional big groundbreaking discoveries.

What are the latest discoveries in mathematics?

The 10 Biggest Math Breakthroughs of 2019

• Progress on the Riemann Hypothesis. Creative Commons.
• The Sum of Three Cubes. Andrew Daniels.
• The Collatz Conjecture.
• The Sensitivity Conjecture.
• A Great Year for Cancer Research.
• Kirigami Gets Mathematized.
• The Sunflower Conjecture.
• A Breakthrough in Ramsey Theory.

What did Einstein mean when he used the term axioms?

These axioms are free creations of the human mind. All other propositions of geometry are logical inferences from the axioms (which are to be taken in the nominalistic sense only). Schlick in his book on epistemology has therefore characterised axioms very aptly as “implicit definitions.”

Is mathematics discoverable or invented?

Personally, I believe that by asking simply whether mathematics is discovered or invented, we forget the possibility that mathematics is an intricate combination of inventions and discoveries. Indeed, I posit that humans invent the mathematical concepts—numbers, shapes, sets, lines, and so on—by abstracting them from the world around them.

Is there any connection between mathematics and the physical world?

There is a lot of very sophisticated mathematics which as yet (now I’m not saying that it never will have any connection to the physical world, they might). but, as yet, there is no evident connection with the physical world.

Is it possible to invent mathematical schemes?

You could have certain ideas which in mathematics have a deeper existence than others, and you can maybe invent various mathematical schemes, and I use the word ‘invention’ there because they might be interesting to play with. But then some of these have features which reveal deep truths which you had no conception of before.

How did humans invent mathematics?

Indeed, I posit that humans invent the mathematical concepts—numbers, shapes, sets, lines, and so on—by abstracting them from the world around them. They then go on to discover the complex connections among the concepts that they had invented; these are the so-called theorems of mathematics.