I've posted it partly just because it's interesting, but partly also as something to show the antivaxxers and antimaskers. This is a general interest article published in a general interest publication: it's accessible to anybody who is educated. I don't mean an educated person will understand all the problems (I sure don't), but they will have a sense of what most of them are about, and will certainly understand the thrust of the article as a whole.
The point is that the kind of people who lead science and maths (and a pandemic is as much a mathematical problem as a biological one) read articles like this for pleasure: in fact, they attempt (and occasionally succeed) to solve such problems for pleasure. The anti-science brigade have no concept how out of touch with reality they are, and a piece like this will at least show them, even if it is unlikely to have much effect.
https://www.thetimes.co.uk/article/mathematicians-sum-up-the-big-questions-of-our-time-szsqdqzn7
Mathematicians sum up the 23 big problems of our time
Tom Whipple, Science Editor
Saturday June 12 2021, 12.01am, The Times
Eight of the mathematician David Hilbert’s original 23 problems have been solved since 1900
As a wish list, no one could accuse it of lacking ambition. There’s the problem of free will, the quest for truly intelligent AI and the mathematical basis of mortality. There’s a theory of quantum gravity, of course. And, as befits any collection of great unsolved mathematical problems, there is the Riemann hypothesis.
In 1900 the great mathematician David Hilbert published a list of 23 problems he wanted the world’s mathematicians to apply themselves to.
More than a century on, the London Institute for Mathematical Sciences has published its own. They range from finding a unifying theory of mathematics to providing a rigorous underpinning to quantum field theory, to determining the laws of genetic information processing. Some, such as tackling free will, seem as though they are barely mathematics at all.
That, said Thomas Fink, director of the independent not-for-profit organisation modelled on Princeton’s famous Institute for Advanced Studies, is partly the point. “Sometimes just to pose a problem mathematically means you understand a fair bit about it already,” he said. Serious researchers, such as the Nobel laureate Roger Penrose, have tried to formulate a neurological basis for free will. Fink’s own work has looked at the theoretical basis of mortality.
“Why do we age? Is it a ticking time bomb? For a long time we have just thought it is the accumulation of errors in how our body stores information. But there’s increasing evidence that ageing is not an essential component to life itself.” He has been looking at whether it is a consequence of the mathematics of natural selection.
The institute, based in the Royal Institution in London, produced the list in part because of the creation of Aria, a funding body for blue skies research. “Now’s a great time to focus on the great challenges of our time,” said Fink. “We thought, let’s brainstorm and think what are the great problems of our time.”
Of Hilbert’s original 23 problems, eight are judged solved and 12 partially solved. The solved Hilbert problems include the question of whether if you have two polyhedra — straight-edged shapes — of equal volume it is always possible to chop one up into polyhedral pieces to make the other (it isn’t), and what’s the best way of densely packing spheres such as oranges. The latter problem was solved only in 1998.
Despite 120 years of attempts, three are little closer to completion, among them the Riemann hypothesis, a classic theory that relates to the distribution of prime numbers. Solving that, said Fink, would be revolutionary.
“Countless theorems begin, ‘If the Riemann hypothesis is true, then the following holds’. So, first of all, proving it true or false would have immediate knock-on effects.” Doing so would also, he suspects, yield a revolution. Just as uniting quantum mechanics and general relativity to create a “theory of everything” — a longstanding goal, also on the list — would require new physics, the same would be true here. “I think the Riemann hypothesis is going to require a new type of mathematics,” he said.
But will we get it? Riemann remains intractable. Many of the other problems feel impossible to formulate, let alone solve. How does he think his list will do, compared with Hilbert’s? “This will be a map for 100 years,” he said. “If we can make a start on half or two thirds, I think that would be incredible.”
Head scratchers
1 Theory of everything
We lack a single theory that describes the universe. Gravity, described by general relativity, is not consistent with our quantum field theory of the other three forces. Will this be resolved by string theory, loop quantum gravity, or something new? What are the testable consequences of such a theory, which is beyond the limit of human experimentation?
2 Riemann hypothesis
Attempts to settle the Riemann hypothesis have inspired new branches of mathematics. For example, the Riemann zeta-function is the simplest kind of L-function, and these seem to play a role in modern mathematics similar to polynomials in ancient mathematics. What new concepts are needed to resolve this most important of open problems?
3 Thermodynamics of life
According to Darwin’s theory, evolution is the result of mutation, selection and inheritance. But from a physics perspective, we do not understand how life began in the first place. What is the thermodynamic basis for emergent self-replication and adaptation, of which biology is just one instance? Can it be used to create digital artificial life?
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