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.
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. Feel free to ask any related questions that you want Aubrey to try and answer!
Futurist Foundation is a non-profit organization with the goal to connect futurists and promote crowd-sourced projects in science, technology, engineering, mathematics & design.
In this video I talk about a few approaches to mathematically describe consciousness and their shortcomings. I also briefly talk about what such studies could one day be good for. You can watch the talks from the workshop that I mention (and many more!!) here:
For mathematicians and computer scientists, 2020 was full of discipline-spanning discoveries and celebrations of creativity. We’d like to take a moment to recognize some of these achievements.
1. A landmark proof simply titled MIP = RE” establishes that quantum computers calculating with entangled qubits can theoretically verify the answers to an enormous set of problems. Along the way, the five computer scientists who authored the proof also answered two other major questions: Tsirelson’s problem in physics, about models of particle entanglement, and a problem in pure mathematics called the Connes embedding conjecture.
2. In February, graduate student Lisa Piccirillo dusted off some long-known but little-utilized mathematical tools to answer a decades-old question about knots. A particular knot named after the legendary mathematician John Conway had long evaded mathematical classification in terms of a higher-dimensional property known as sliceness. But by developing a version of the knot that yielded to traditional knot analysis, Piccirillo finally determined that the Conway knot is not slice.
3. For decades, mathematicians have used computer programs known as proof assistants to help them write proofs — but the humans have always guided the process, choosing the proof’s overall strategy and approach. That may soon change. Many mathematicians are excited about a proof assistant called Lean, an efficient and addictive proof assistant that could one day help tackle major problems. First, though, mathematicians must digitize thousands of years of mathematical knowledge, much of it unwritten, into a form Lean can process. Researchers have already encoded some of the most complicated mathematical ideas, proving in theory that the software can handle the hard stuff. Now it’s just a question of filling in the rest.
