The day will come when not only will computers be doing good mathematics, but they will be doing mathematics beyond the ability of (non-enhanced) humans to understand. Denying it is understandable, but ultimately as short-sighted as it was to deny computers could ever win at Go.

This is not as depressing as it might sound, as we humans don't need to be left behind. Direct brain-computer interfaces will come too, and even the distinction between them will become blurred.

COMMENT: We were amazed when someone built a machine that could travel faster than a horse, then amazed when a machine let us fly into the air, and even go to the moon, then amazed again that millions of us could carry a tiny machine that identifies our position on the planet within meters and lets us talk instantly to anyone else on the planet, and amazed again that someone invented a machine that can edit life forms to make new life forms. But the very idea that a machine could do mathematics, that one is surely impossible! (By the way, I love the down-votes.)

QUESTION: Is there a way to know how many down-votes there have been, rather than just up-votes minus down-votes?

The day will come when not only will computers be doing good mathematics, but they will be doing mathematics beyond the ability of (non-enhanced) humans to understand. Denying it is understandable, but ultimately as short-sighted as it was to deny computers could ever win at Go.

This is not as depressing as it might sound, as we humans don't need to be left behind. Direct brain-computer interfaces will come too, and even the distinction between them will become blurred.

COMMENT: We were amazed when someone built a machine that could travel faster than a horse, then amazed when a machine let us fly into the air, and even go to the moon, then amazed again that millions of us could carry a tiny machine that identifies our position on the planet within meters and lets us talk instantly to anyone else on the planet, and amazed again that someone invented a machine that can edit life forms to make new life forms. But the very idea that a machine could do mathematics, that one is surely impossible! (By the way, I love the down-votes.)

The day will come when not only will computers be doing good mathematics, but they will be doing mathematics beyond the ability of (non-enhanced) humans to understand. Denying it is understandable, but ultimately as short-sighted as it was to deny computers could ever win at Go.

This is not as depressing as it might sound, as we humans don't need to be left behind. Direct brain-computer interfaces will come too, and even the distinction between them will become blurred.

The day will come when not only will computers be doing good mathematics, but they will be doing mathematics beyond the ability of (non-enhanced) humans to understand. Denying it is understandable, but ultimately as short-sighted as it was to deny computers could ever win at Go.

This is not as depressing as it might sound, as we humans don't need to be left behind. Direct brain-computer interfaces will come too, and even the distinction between them will become blurred.

COMMENT: We were amazed when someone built a machine that could travel faster than a horse, then amazed when a machine let us fly into the air, and even go to the moon, then amazed again that millions of us could carry a tiny machine that identifies our position on the planet within meters and lets us talk instantly to anyone else on the planet, and amazed again that someone invented a machine that can edit life forms to make new life forms. But the very idea that a machine could do mathematics, that one is surely impossible! (By the way, I love the down-votes.)

QUESTION: Is there a way to know how many down-votes there have been, rather than just up-votes minus down-votes?