New invariant, less complex manifold

[Wheezer]

A bit late, but one worth reading about: Friedrich Hirzebruch.

[J. Walter Weatherman]

Hirzebruch’s first great mathematical achievement was the proof in 1954 of the generalization of the classical Riemann-Roch theorem to higher dimensional complex manifolds, now known as the Hirzebruch-Riemann-Roch theorem. This used the new techniques of sheaf cohomology and was one of the centerpieces of the explosion of new results in geometry and topology during the 1950s. Further generalization of this led to the Grothendieck-Riemann-Roch theorem, and the Atiyah-Singer index theorem.

Sure... It all sounds so obvious and basic to us now, but there was a time half a century ago when the above looked like pure gibberish to the common man.

[Wheezer]

Hirzebruch’s first great mathematical achievement was the proof in 1954 of the generalization of the classical Riemann-Roch theorem to higher dimensional complex manifolds, now known as the Hirzebruch-Riemann-Roch theorem. This used the new techniques of sheaf cohomology and was one of the centerpieces of the explosion of new results in geometry and topology during the 1950s. Further generalization of this led to the Grothendieck-Riemann-Roch theorem, and the Atiyah-Singer index theorem.

Sure... It all sounds so obvious and basic to us now, but there was a time half a century ago when the above looked like pure gibberish to the common man.

Geometry, set theory, and topology? This is the essence of elegance. If you can understand that a coffee mug is a torus, you're good to go.

[CT III]

Hirzebruch’s first great mathematical achievement was the proof in 1954 of the generalization of the classical Riemann-Roch theorem to higher dimensional complex manifolds, now known as the Hirzebruch-Riemann-Roch theorem. This used the new techniques of sheaf cohomology and was one of the centerpieces of the explosion of new results in geometry and topology during the 1950s. Further generalization of this led to the Grothendieck-Riemann-Roch theorem, and the Atiyah-Singer index theorem.

Sure... It all sounds so obvious and basic to us now, but there was a time half a century ago when the above looked like pure gibberish to the common man.

Geometry, set theory, and topology? This is the essence of elegance. If you can understand that a coffee mug is a torus, you're good to go.

So, it turns out I'm not good to go...

[CBStew]

Hirzebruch’s first great mathematical achievement was the proof in 1954 of the generalization of the classical Riemann-Roch theorem to higher dimensional complex manifolds, now known as the Hirzebruch-Riemann-Roch theorem. This used the new techniques of sheaf cohomology and was one of the centerpieces of the explosion of new results in geometry and topology during the 1950s. Further generalization of this led to the Grothendieck-Riemann-Roch theorem, and the Atiyah-Singer index theorem.

Sure... It all sounds so obvious and basic to us now, but there was a time half a century ago when the above looked like pure gibberish to the common man.

Geometry, set theory, and topology? This is the essence of elegance. If you can understand that a coffee mug is a torus, you're good to go.

So, it turns out I'm not good to go...

I owned a Taurus once, but it tended to accelerate whenever it felt like accelerating.  I also have had a haddock.  What do you take for a haddock?  Pardon me, I have to go and watch a re-run of "Big Bang Theory".

[PANK!]

I like that Stew is no longer apprehensive about coming into this section.

The Dead Pool really is the best part of this shit-for-brains site these days.  Oh, how humiliating.

[Wheezer]

Hirzebruch’s first great mathematical achievement was the proof in 1954 of the generalization of the classical Riemann-Roch theorem to higher dimensional complex manifolds, now known as the Hirzebruch-Riemann-Roch theorem. This used the new techniques of sheaf cohomology and was one of the centerpieces of the explosion of new results in geometry and topology during the 1950s. Further generalization of this led to the Grothendieck-Riemann-Roch theorem, and the Atiyah-Singer index theorem.

Sure... It all sounds so obvious and basic to us now, but there was a time half a century ago when the above looked like pure gibberish to the common man.

Geometry, set theory, and topology? This is the essence of elegance. If you can understand that a coffee mug is a torus, you're good to go.

So, it turns out I'm not good to go...

I don't believe you. This is a basic example of homeomorphism: the connected surface can be deformed, but you can't get rid of the hole in the handle.

[PANK!]

Hirzebruch’s first great mathematical achievement was the proof in 1954 of the generalization of the classical Riemann-Roch theorem to higher dimensional complex manifolds, now known as the Hirzebruch-Riemann-Roch theorem. This used the new techniques of sheaf cohomology and was one of the centerpieces of the explosion of new results in geometry and topology during the 1950s. Further generalization of this led to the Grothendieck-Riemann-Roch theorem, and the Atiyah-Singer index theorem.

Sure... It all sounds so obvious and basic to us now, but there was a time half a century ago when the above looked like pure gibberish to the common man.

Geometry, set theory, and topology? This is the essence of elegance. If you can understand that a coffee mug is a torus, you're good to go.

So, it turns out I'm not good to go...

I don't believe you. This is a basic example of homeomorphism: the connected surface can be deformed, but you can't get rid of the hole in the handle.

The ability to make Photoshops without a computer?

[Wheezer]

Hirzebruch’s first great mathematical achievement was the proof in 1954 of the generalization of the classical Riemann-Roch theorem to higher dimensional complex manifolds, now known as the Hirzebruch-Riemann-Roch theorem. This used the new techniques of sheaf cohomology and was one of the centerpieces of the explosion of new results in geometry and topology during the 1950s. Further generalization of this led to the Grothendieck-Riemann-Roch theorem, and the Atiyah-Singer index theorem.

Sure... It all sounds so obvious and basic to us now, but there was a time half a century ago when the above looked like pure gibberish to the common man.

Geometry, set theory, and topology? This is the essence of elegance. If you can understand that a coffee mug is a torus, you're good to go.

So, it turns out I'm not good to go...

I don't believe you. This is a basic example of homeomorphism: the connected surface can be deformed, but you can't get rid of the hole in the handle.

The ability to make Photoshops without a computer?

Do not make me figure out the topology of panniers.

[CBStew]

I like that Stew is no longer apprehensive about coming into this section.

"I wake up every morning at nine and grab for the morning paper. Then I look at the obituary page. If my name is not on it, I get up." Harry Hershfield (1885-1974) American comic artist

[Bort]

Hirzebruch’s first great mathematical achievement was the proof in 1954 of the generalization of the classical Riemann-Roch theorem to higher dimensional complex manifolds, now known as the Hirzebruch-Riemann-Roch theorem. This used the new techniques of sheaf cohomology and was one of the centerpieces of the explosion of new results in geometry and topology during the 1950s. Further generalization of this led to the Grothendieck-Riemann-Roch theorem, and the Atiyah-Singer index theorem.

Sure... It all sounds so obvious and basic to us now, but there was a time half a century ago when the above looked like pure gibberish to the common man.

Geometry, set theory, and topology? This is the essence of elegance. If you can understand that a coffee mug is a torus, you're good to go.

So, it turns out I'm not good to go...

I don't believe you. This is a basic example of homeomorphism: the connected surface can be deformed, but you can't get rid of the hole in the handle.

The ability to make Photoshops without a computer?

Do not make me figure out the topology of panniers.

I laughed.