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Using AI and computer automation, Technion researchers have developed a ‘conjecture generator’ that creates mathematical conjectures, which are considered to be the starting point for developing mathematical theorems. They have already used it to generate a number of previously unknown formulas. The study, which was published in the journal Nature, was carried out by undergraduates from different faculties under the tutelage of Assistant Professor Ido Kaminer of the Andrew and Erna Viterbi Faculty of Electrical Engineering at the Technion.

Computer-aided calculations have played a crucial part in producing the proofs of several high-profile results. And more recently, some mathematicians have made progress towards AI that doesn’t just perform repetitive calculations, but develops its own proofs. Another growing area has been software that can go over a mathematical proof written by humans and check that it is correct.

Algorithm named after mathematician Srinivasa Ramanujan suggests interesting formulae, some of which are difficult to prove true.

Richard Feynman, one of the most respected physicists of the twentieth century, said “What I cannot create, I do not understand.” Not surprisingly, many physicists and mathematicians have observed fundamental biological processes with the aim of precisely identifying the minimum ingredients that could generate them. One such example are the patterns of nature observed by Alan Turing. The brilliant English mathematician demonstrated in 1952 that it was possible to explain how a completely homogeneous tissue could be used to create a complex embryo, and he did so using one of the simplest, most elegant mathematical models ever written. One of the results of such models is that the symmetry shown by a cell or a tissue can break under a set of conditions.

No one has yet managed to travel through time – at least to our knowledge – but the question of whether or not such a feat would be theoretically possible continues to fascinate scientists.

As movies such as The Terminator, Donnie Darko, Back to the Future and many others show, moving around in time creates a lot of problems for the fundamental rules of the Universe: if you go back in time and stop your parents from meeting, for instance, how can you possibly exist in order to go back in time in the first place?

It’s a monumental head-scratcher known as the ‘grandfather paradox’, but in September last year a physics student Germain Tobar, from the University of Queensland in Australia, said he has worked out how to “square the numbers” to make time travel viable without the paradoxes.

To understand ourselves and our place in the universe, “we should have humility but also self-respect,” the physicist writes in a new book.

In the spring of 1970, colleges across the country erupted with student protests in response to the Vietnam War and the National Guard’s shooting of student demonstrators at Kent State University. At the University of Chicago, where Frank Wilczek was an undergraduate, regularly scheduled classes were “improvised and semivoluntary” amid the turmoil, as he recalls.

It was during this turbulent time that Wilczek found unexpected comfort, and a new understanding of the world, in mathematics. He had decided to sit in on a class by physics professor Peter Freund, who, with a zeal “bordering on rapture,” led students through mathematical theories of symmetry and ways in which these theories can predict behaviors in the physical world.

Even for the brain of a worm, the best theory on offer would, she says, take several billion years to calculate. That can’t be the right answer.

Annotated!

Aubrey David Nicholas Jasper de Grey is an English author and biomedical gerontologist. He is the Chief Science Officer of the SENS Research Foundation and VP of New Technology Discovery at AgeX Therapeutics.
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Welcome to “The curious observer’s guide to quantum mechanics”–featuring particle/wave duality.

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