Birth of a Theorem: A Mathematical Adventure by Cédric Villani – review

To really appreciate mathematics, you have to see it evolve, to work through the twists and turns yourself; it’s almost never enough for someone to just tell you about it. These wise words from my secondary school maths teacher have stuck with me ever since. Cédric Villani knows this, too. To put it in his words: “Appreciating a theorem in mathematics is like watching an episode of Columbo: the line of reasoning by which the detective solves the mystery is more important than the identity of the murderer.” Villani should know. He is widely regarded as one of the most talented mathematicians of his generation. His work has won him almost every prize going: the Fermat prize (a big deal) the Poincaré prize (a very big deal) and even the Fields medal (off-the-chart big deal). For those who aren’t familiar, the Fields medal is often referred to as the Nobel prize of mathematics but, as it is only awarded once every four years, and even then only to mathematicians under 40, it is much, much harder to win. Villani’s medal was awarded in 2010 for his work in mathematical physics describing the behaviour of particles in gases and plasmas.

The Birth of a Theorem is written as a diary, taking us through the early evolution of the idea in Lyon in 2008, through six months of frustration trying to wrestle the beast of a theorem to the ground at Princeton (his words, not mine) and culminating in the news that he has won the most coveted prize.

This twisting mathematical path is there for you to experience, not just to spectate. At the end of each entry, Villani includes email correspondence with colleagues about the progress of the theorem in its full technical glory. He partners the sections with a historical and mathematical overview of the methods applied, along with pencil sketches of each inventor. There are even extracts from the prizewinning theorem in proofs that go on for pages and pages with nothing but the most severe mathematical notation to rescue the faint-hearted reader.

I like these extra sections. The change in typeface that signposts their presence makes it clear that they are not compulsory. Instead – like a “pick your own adventure” book – they are there to add to the story if you happen to choose that route. But more detail isn’t always a good thing. There are times when the density bleeds into the story of Villani’s discovery and risks obscuring what makes this book so interesting. For example, on the second page, he recalls a light and playful conversation with one of his colleagues: “My old demon is back again – regularity for the inhomogeneous Boltzman.” “Conditional regularity? You mean, modulo minimal regularity bounds?” “No, unconditional.” “Completely? Not even in a perturbative framework?” And so it goes on. For pages.


Study identifies children at risk for persistent mathematics difficulties

UNIVERSITY PARK, Pa. — A recent study published in the Journal of Learning Disabilities suggests early screening and intervention may prevent persistent math difficulties (PMD) for at-risk children.

The study identifies at-risk children as being those as young as 2 years old from low socioeconomic status (SES) households; with cognitive and behavioral issues; and with vocabulary and reading difficulties.

Previous studies have found that young children experiencing mathematics difficulties will likely continue to experience these difficulties as they grow older. Yet researchers, policymakers and practitioners previously knew very little about which children are likely to experience PMD, according to Paul L. Morgan, associate professor of education in Penn State’s College of Education and lead author of the study funded by the U.S. Department of Education’s Institute of Education Sciences.

Morgan said the study strongly indicates that the SES status of the family matters quite a lot in terms of increasing children’s risk of repeatedly experiencing low mathematics achievement.

“Schools can’t do much to change a family’s economic circumstances, but schools can decide how they allocate extra resources and how early they intervene to help children who seem to be struggling academically,” Morgan said.

Morgan suggested that early screening and intervention efforts for PMD should be happening systematically at school entry, which he believes often is more beneficial and cost-effective than providing them when children are older.

He added that the findings indicate that interventions may need to be multi-faceted, so that they target both early mathematics and reading difficulties, and behavior problems. He added that struggles in mathematics increase children’s risk for behavioral problems in school.

The analyses by Morgan and his colleagues indicated that attending preschool or Head Start could lower the risk for PMD, suggesting that greater access to these early-learning environments may help more U.S. children from experiencing PMD.

“Before entering school, children may not have much informal exposure to mathematics. Conversations and activities that include talking about mathematics may help reduce children’s later struggles when they are being taught more formally in the elementary- and middle-school grades,” Morgan said.

For this study, Morgan and his colleagues analyzed two nationally representative, longitudinal data sets of U.S. children maintained by the U.S. Department of Education’s National Center for Education Statistics. One sample of children was followed from birth to kindergarten entry; the other was followed from kindergarten entry to the end of eighth grade.

For the preschool children, factors that increased the children’s risk for PMD included low general cognitive functioning, vocabulary difficulties and being from low socioeconomic status households.

For elementary- and middle-school students, experiencing reading difficulties, mathematics difficulties and attention-related behavioral difficulties increased the risk of PMD, as did being from lower SES households.

“It appears that children who struggle in mathematics often do not ‘grow out of it,’ and so a ‘wait and see’ approach might only have ‘wait to fail’ consequences for many children.” said Morgan.

Editorial: The Mathematics of Up Wing Democracy on Future Day 2015

The year 2015 may be remembered in transhumanist circles as the year transhumanism got political with the formation of a U.S. based and global Transhumanist Party and other h+ oriented political groups. Of course previously transhumanists have been political, h+ Chair Natasha Vita-More ran for and won a political office in Los Angeles, and some transhumanists have run high profile campaigns and won political offices. And despite the recent attention, none of these efforts were really very future oriented or transhuman in implementation. The current transhumanist political movement isn’t either but it should be.

In his book Are You a Transhuman?: Monitoring and Stimulating Your Personal Rate of Growth in a Rapidly Changing World, transhumanist founding father FM 2030 presented his view for transhumanist approach to politics which he called “Up Wing” in order to set it apart from the usual dichotomy between left and right wing ideologies.

The UpWing philosophy is a visionary new thrust beyond Right and Left-wing, beyond conservative and conventional radical. Beyond all our age-old philosophies and ideologies.

We UpWingers want to facilitate the flow to the emerging post-industrial world.

We also want to accelerate humanity’s thrust to the next stage in evolution.

Specifically we want to marshall humanity’s genius to overcome our supreme tragedies – aging and death.

We want to help accelerate the colonization of our solar system and open up this infinite Universe of infinite space, infinite resources, infinite potentials.

We want to speed up the thrust to post-industrial telespheres, such as teleduction and telemedicine which can instantly provide services to anyone anywhere.

We want to help accelerate the surge to upcoming worlds of undreamed abundance. Clean, cheap, limitless energy. Limitless food. Limitless raw materials.

We want to help spread the benefits of the Biological Revolution, the new genetics, the Brain Revolution giving each one of us control over our own bodies, our own minds, our own emotions. Allowing us biological freedoms never before possible.

We want to hasten the evolution to universal telegenesis and universal parenthood where every child is genetically preplanned, every child wanted, every child cared for. We want to help liberate children from the traumas of exclusive parenthood that every child may belong biologically and socially to the whole world.

We want to move beyond Capitalist/Socialist economies to the upcoming teleconomics of Cybernation, Abundance, Leisure.

We want to advance beyond leadership and representative democracies to ELECTRONIC DEMOCRACY enabling everyone to participate directly and immediately in all important decision-making.

We want to help the thrust beyond feudal mud villages and decaying industrial cities to 21st century instant modular communities which fuse the best of nature with the new tele technologies and the new liberated life styles.

We want to help accelerate the thrust beyond nations, ethnic groups, races to create a global conscious-ness, global institutions, a global language, global citizenship, global free flow of people, global commitments.

We want to surge ahead in all these areas because we believe that all areas of life are increasingly interdependent – to advance rapidly in any one area, we must advance vigorously in all areas.

We want to spread a new triumphant spirit – an Optimism free of guilt, free of shame, free of self-denial. We want to spread the awareness that we are at the dawn of a beautiful New Age. There is a new Hope in the world.

~ FM 2030