Henri Poincar´e is not very strictwith formulations. But this is solved in the next few years by other mathematicians.
The main problem is that almost all of his arguments are very specific. Therefore they are very complicatedand ad hoc. The biggerpicture is missing. Most of his definitions are also not very general.
But his paper is still very influentialand inspires lots of other mathematicians. The next two decades reveal new insights, e.g. torsions coefficients, the K¨unneth-formula and Brouwer’s fixed point theorem.
But it takes quite long and lots of theorems have a complicated proof.
The beginning of topology Categorification of the concepts Category theory as a research field Grothendieck’s n-categories Henri Poincar´e - The founder of topology
A new point of view
Henri Poincar´e is not very strictwith formulations. But this is solved in the next few years by other mathematicians.
The main problem is that almost all of his arguments are very specific. Therefore they are very complicatedand ad hoc.
The biggerpicture is missing. Most of his definitions are also not very general.
But his paper is still very influentialand inspires lots of other mathematicians. The next two decades reveal new insights, e.g. torsions coefficients, the K¨unneth-formula and Brouwer’s fixed point theorem.
But it takes quite long and lots of theorems have a complicated proof.
The beginning of topology Categorification of the concepts Category theory as a research field Grothendieck’s n-categories Henri Poincar´e - The founder of topology
A new point of view
Henri Poincar´e is not very strictwith formulations. But this is solved in the next few years by other mathematicians.
The main problem is that almost all of his arguments are very specific. Therefore they are very complicatedand ad hoc. The biggerpicture is missing.
Most of his definitions are also not very general.
But his paper is still very influentialand inspires lots of other mathematicians. The next two decades reveal new insights, e.g. torsions coefficients, the K¨unneth-formula and Brouwer’s fixed point theorem.
But it takes quite long and lots of theorems have a complicated proof.
The beginning of topology Categorification of the concepts Category theory as a research field Grothendieck’s n-categories Henri Poincar´e - The founder of topology
A new point of view
Henri Poincar´e is not very strictwith formulations. But this is solved in the next few years by other mathematicians.
The main problem is that almost all of his arguments are very specific. Therefore they are very complicatedand ad hoc. The biggerpicture is missing. Most of his definitions are also not very general.
But his paper is still very influentialand inspires lots of other mathematicians. The next two decades reveal new insights, e.g. torsions coefficients, the K¨unneth-formula and Brouwer’s fixed point theorem.
But it takes quite long and lots of theorems have a complicated proof.
The beginning of topology Categorification of the concepts Category theory as a research field Grothendieck’s n-categories Henri Poincar´e - The founder of topology
A new point of view
Henri Poincar´e is not very strictwith formulations. But this is solved in the next few years by other mathematicians.
The main problem is that almost all of his arguments are very specific. Therefore they are very complicatedand ad hoc. The biggerpicture is missing. Most of his definitions are also not very general.
But his paper is still very influentialand inspires lots of other mathematicians.
The next two decades reveal new insights, e.g. torsions coefficients, the K¨unneth-formula and Brouwer’s fixed point theorem.
But it takes quite long and lots of theorems have a complicated proof.
The beginning of topology Categorification of the concepts Category theory as a research field Grothendieck’s n-categories Henri Poincar´e - The founder of topology
A new point of view
Henri Poincar´e is not very strictwith formulations. But this is solved in the next few years by other mathematicians.
The main problem is that almost all of his arguments are very specific. Therefore they are very complicatedand ad hoc. The biggerpicture is missing. Most of his definitions are also not very general.
But his paper is still very influentialand inspires lots of other mathematicians. The next two decades reveal new insights, e.g. torsions coefficients, the K¨unneth-formula and Brouwer’s fixed point theorem.
But it takes quite long and lots of theorems have a complicated proof.
The beginning of topology Categorification of the concepts Category theory as a research field Grothendieck’s n-categories Henri Poincar´e - The founder of topology
A new point of view
Henri Poincar´e is not very strictwith formulations. But this is solved in the next few years by other mathematicians.
The main problem is that almost all of his arguments are very specific. Therefore they are very complicatedand ad hoc. The biggerpicture is missing. Most of his definitions are also not very general.
But his paper is still very influentialand inspires lots of other mathematicians. The next two decades reveal new insights, e.g. torsions coefficients, the K¨unneth-formula and Brouwer’s fixed point theorem.
But it takes quite long and lots of theorems have a complicated proof.
The beginning of topology Categorification of the concepts Category theory as a research field Grothendieck’s n-categories Homology groups