Dramathematicians: Historic figures in the Mathematical Sciences

Dramathematicians (Julia Thouas)

Mathematicians have been handed the short end of the stick in history. Isaac Newton battled mental illness his entire life, Galileo Galilei was persecuted by the Church and spent his final days under house arrest, and Albert Einstein, who by all accounts led a perfectly pleasant life, is primarily remembered as a physicist. But through the years there have been more than a couple bad-ass m’fuckers in the mathematical sciences, reminding us all that scribbling away at proofs, and hemming and hawing in front of a blackboard can make for a very dramatic – and inspirational pursuit.

Having too much fun: Tycho Brahe (1546 – 1601)

Brahe was a Danish nobleman and scientist so well connected that he was, at one point, best mates with or related to every single person in the entire government of Denmark. A larger than life figure, his eccentricities didn’t stop there. As a precocious youth, 19 year old Brahe replaced his nose with a brass prosthetic after losing it in a duel over the validity of a mathematical formula. He also owned a pet elk, Brahe’s frequent stand-in at social engagements, who later died after drunkenly falling down the stairs. Not unlike his elk, at 55, Brahe himself died of a burst bladder from partying so hard he refused to leave the banquet table to relieve himself. While Brahe was an astronomer at heart, his dedication to consistent and accurate measurements and observations helped pave the way for the Scientific Revolution of the 17th Century.

Predicting the future: Ada Lovelace (1815 – 1852)

Patron of the arts, a countess and a… programmer? From humble beginnings teaching mathematics as a very 19th century attempt to ward against her father’s ‘amoral tendencies’, Ada Lovelace is now credited with the basis for modern computers. In 1842, she was invited to translate a paper on computational engines from Italian to English. She upstaged the paper all-together with the appendices she wrote to clarify its convoluted mathematics. The algorithm in these appendices is now considered the first example of a computer program. Where other mathematicians saw no application for computers, Lovelace recognised that computation engines could go beyond number crunching, and be extended into programs that could write music, design patterns and transfer information. Ada Lovelace saw what no one else in the mathematical establishment of the time could see, and preempted the rise of modern computers almost 150 years in advance.

Living for nothing else: Paul Erdős (1913 – 1996)

Taking the phrase “suffering for your art” to the extreme, Hungarian mathematician Paul Erdős was so dedicated to mathematics that he eschewed Maslow’s Hierarchy of Needs all-together and never bothered with friendships, marriage or a permanent place of residence. Yep, Erdős lived most of his life homeless, effectively couch-surfing from one prominent mathematician’s house to another, and penniless, donating the majority of his earnings not spent on travel to charity. However, Erdős’ love for mathematics bordered on single-minded obsession. He was known to frequently abandon conversations about non-mathematical subjects, and would apparently fall asleep at parties where mathematics was not the topic of conversation. But despite (or perhaps because of) this self-imposed vagabond lifestyle, Erdős published 1,500 mathematical papers during his lifetime. As a testament to his dedication, this figure has yet to be surpassed.

Making herself known: Katherine Johnson (1918 – present)

Perhaps the only name you may recognise, Katherine Johnson is an African-American mathematician and astrophysicist known for her invaluable contributions to NASA. Beginning in the 1950s, Johnson was initially hired as a ‘computer’ in a pool of woman labelled ‘Coloured Computers’. Johnston then worked her way up through NASA’s flight engineering department to become one of the most respected and reliable mathematicians at the agency. At a time when women, and especially black women, were barred from key planning meetings and left uncredited on reports, Johnson broke both of these barriers. She was unrelenting in her assertion that she belonged and was more than capable of the work. During her career, her calculations were not only responsible for determining the flight trajectories of key NASA missions, the first full Earth orbit and the Apollo 11 Moon landing, but they also ensured the safe return of the crew in the Apollo 13 crisis. Awarded the Presidential Medal of Freedom in 2015, and now recognised in major film Hidden Figures, Katherine Johnson rose out of relative obscurity to become one of the most well-known mathematicians in the United States.

Going to war with Mathematics: Alex Grothendieck (1928 – 2014)

Starting his Dramathematician career young, a 12-year-old Alexander Grothendieck broke  out of the Nazi internment camp, where he and his family were being held, with the express purpose of “killing Hitler”. After a tumultuous youth spent sheltered in the French countryside, Grothendieck suddenly grew to prominence among French mathematicians for his unmatched ability to revolutionise new mathematical concepts. An activist at heart, Grothendieck held an uncompromising anti-war stance which would inform his years to come. He refused a position at Harvard University because he would not pledge his allegiance to the United States Government; he gave seminars in the forests surrounding Hanoi to protest the Vietnam War, while the city was being bombed; and in 1970, he left the French mathematical school which was founded almost entirely for his work, when he discovered that it was funded in part by the military. While he died in relative obscurity in south-west France, Grothendieck’s passion for both his profession and his politics have led him to be remembered as one of the most influential mathematicians of the 20th century.


read more

Healthy Skepticism



Health advertising, like any other advertising, is meant to be compelling. Health ads may promise to fix anything and everything, to entice you to hand over exorbitant amounts of money. Adverts for health products and services, however, come with an extra proviso: they not only have a financial influence over consumers but dangerously sway community perceptions around healthcare.

Like me, you may remember this unfortunate billboard (pictured) or its more explicit companions from when you were just old enough to vaguely understand what it meant. Due to this insensitive advertising, provocatively preying on the fears of men, the Advanced Medical Institute pocketed several millions selling their shonky products and services. AMI was receiving 7,000 calls a week allowing for thousands of clients to be locked into deceptive contracts for products that were not only ridiculously marked-up, but scientifically ineffective compared to mainstream medications. Whilst the Advertising Standards Bureau banned the billboards in 2008 (acting on an influx of complaints), only recently was the entire AMI charade legally unmasked. In 2015, AMI was charged with unconscionable conduct in the Federal Court against the ACCC (Australian Competition and Consumer Commission) and ordered to halt advertising and providing services.

You would think that the problem was solved. Sadly, it wasn’t. Despite this official ruling, a simple trip to the AMI website reveals the serious limitations in the regulatory framework.

Misleading advertising

As educated university students, why should we give a second thought to this little anecdote about an obvious scam? Well, firstly because the conduct of AMI is merely symbolic of the ridiculous behaviour which pervades the world of health advertising. Many health-related businesses have little regard for consumer protection when promoting their products, which results in a widespread culture of routinely deceiving consumers for financial gain.

You may recall Reckitt Benckiser was recently fined $6 million for their blatantly deceptive marketing of Nurofen (which provides non-specific pain relief) as “targeted pain relief” for period pain or back pain. Many consumers opted for these “targeted” products, unaware they had simply paid an outrageous premium for the same active ingredient in a normal Nurofen tablet. It was an evil but easy way for an already enormously wealthy company to make a profit anew.

The same goes for companies like Swisse, whose products are “based on scientific research” but their trials are generally self-funded and non-transparent. This is because it is more economical to pay for Nicole Kidman’s star power in your ad campaigns and sign million dollar partnerships with La Trobe, ABC and CSIRO, than scientifically prove your products.

The list continues with modern health hacks and fads, such as giving your gut a charcoal cleanse (yummo) or the IV vitamin clinics that have been in and out of the news, being promoted as the cure for a hangover.

Plot twist: sticking liquid vitamins into your bloodstream is a dangerous placebo with little or no scientific basis. And sure, charcoal cleansing “works”- because they use charcoal in hospitals for drug overdoses to “get rid of the toxins,” it will certainly work for your “toxins” too. Unfortunately, it seems the human body is not quite that simple. This, however, doesn’t prevent people from making their fair share of cash out of pseudoscience.

A failing system

The second parallel to the AMI saga is that the Australian regulatory framework, screening processes and penalties for misleading and deceptive health advertising are not stringent enough to eradicate this kind of conduct. The many costs of this reality end up falling upon consumers.

For example, the Therapeutic Goods Administration, which among other things currently regulates the registration and advertising of complementary medicines (mostly vitamin and herbal supplements), does not assess these products for efficacy.

So, if I wanted to sell a sugar pill and market it for bone health, I would first have to register the product in the Australian Register of Therapeutic Goods. I must also state my claim that the sugar pill “supports bone health” in the Australian Register. In terms of “evidence” to support my claim, all I need do is declare that I “hold” the scientific evidence supporting those claims. Then I can advertise my sugar pill for bone health on any garish yellow billboard I choose. I might get into trouble because someone will complain that my claim breaches the Therapeutic Goods Advertising Code and is deceptive and misleading advertising, but the complaint will likely take several months to be resolved. By this I mean that with some luck on the complainant’s behalf, I might merely have to remove my advertising, but I will still walk away with a lovely net profit.

In summary, the current system here doesn’t focus on removing the misleading adverts before they are published but “remedying” the situation (somehow without fining the offenders) after the damage has been done to consumers’ wallets and perceptions. Despite reforms on the horizon for this terrible system, there is still a long road ahead to ensure consumer protection.

Healthy skepticism and evidence-based science: What you can do

From the small vitamin collection in the kitchen pantry, to those irregular physio visits, we are and will continue to be consumers of many health-related goods and services. University students may not be the target demographic of all Swisse commercials, but health advertising can still subtly influence our perceptions of health and what we end up buying on that chance visit to Chemist Warehouse.

It really comes down to consumers being educated and equipped with the skills to protect themselves against the pitfalls of the regulatory system and the greed of the industry. We deserve to enter a Pharmacy and clearly see what is worth buying from the labels, without a science degree or years of professional exposure to evidence-based medicine. But until a consumer utopia arrives, applying a bit of evidence-based knowledge to your encounters with health advertising will leave you better off.

This might involve double checking the advice of a friend or shop assistant who said a certain pill banished all her health problems against the body of validated scientific research easily available online. For example, a simple search in Pubmed (a free online database of medically-related scientific studies) may reveal that Vitamin C supplements are unlikely to shorten the length of your cold.

For those from a non-science background, the studies on this database generally compare a group of people on the same intervention, whether it is a pill or a type of treatment, with another group of people who are given a placebo pill. Theoretically, this allows for the efficacy of the pill in question to be properly examined. Although large trials with heavily controlled variables are difficult to conduct, the results of these studies provide us with a wealth of knowledge that is used to inform the practice of health professionals. If it is used by our Doctors and Pharmacists, then it is probably worth considering.

Admittedly, the average student wanting to get rid of their cold faster is unlikely to spend their energy trawling through Pubmed. A uni-friendly option is to search for the medicine on NPS Medwise (, a government-funded Australian website providing evidence-based information about all medications from grandma’s cholesterol-lowering meds to the Vitamin C you are contemplating purchasing. It is the easiest way to get informed by just reading the small summary of the evidence for that medication.

Otherwise it is just worth becoming very sceptical of the following phrases on labels and in ads:

“Clinically/ scientifically tested/ proven:” hmmm how intriguing. The implication here is that the product has been the subject of a clinical trial, however what you probably won’t find on the label is that the trial was:

a) funded by the company themselves leaving them to tamper or selectively alter results to appear positive.

b) included bias that significantly altered the validity of results. For example, if the participants knew whether they were given the intervention or placebo.

c) conducted by another company that literally guaranteed a positive trial result by rigging everything.

d) not tested for the specific health issues it is advertised as being able to treat.

“More effective than the leading treatment:” an ambiguous statement that requires scepticism. What was the leading treatment? Was it a fair trial where both participant groups were given the same dose in equivalent conditions? Hmmm?? Approach with caution.   

“Natural:” Ummmm ok. What do you mean natural? Do you mean plant-based? Or not synthetic? Are you implying because it is “natural” that it is less harsh on the body? Or do you mean it hasn’t been refined and processed? Natural unrefined arsenic can still kill you so the fact that the product is “natural” doesn’t really tell us much. It is useful to remember that there is a definite distinction between “natural” and “harmless,” even when it comes to vitamins.

“Traditionally used:” the only validation needed to make this claim is…. oh wait, no validation needed! Picking an obscure Peruvian root and selling it for back pain with the label “traditionally used” (even though Peruvians have never heard of it) occurs more than you would think. Yes, there are traditionally used herbs that have actually been traditionally used, so just make sure you google the name of it to check before spending on some useless placebo.

So next time you find yourself perusing the aisles at Priceline, avoid taking the ads at face value and apply your healthy scepticism and evidence-based know-how instead: was that clinical trial actually transparent and independently funded? Did 95% of users truly feel they had more energy? And is that obscure Peruvian root really “traditionally used”? With a simple change of thinking, you can avoid falling prey to the world of health advertising.

read more

I want to believe (but the math says no)


Almost a year ago, civilisation was shattered when citizen astronomers prepublished a paper on arXiv titled: Planet Hunters X. KIC 8462852 – Where’s the Flux? What originally appeared to be a tepid report of a tedious astronomical phenomena detected by the Kepler telescope between 2009 and 2013 soon became the subject of global gossip and speculation.

KIC 8462852 (now known as Tabby’s Star after the lead author of the paper) lies roughly 1,400 light years away in the constellation of Cygnus, the swan*. The paper reported“aperiodic dips in flux of up to ~20\%. The dipping activity can last for between 5 and 80 days. They concluded that the most likely explanation was the passage of a family of exocomets or planetesimal fragments in front of the star.

That would have been fine, if the boffins had left it alone. However, Professor Schaefer from Louisiana State University examined half a million photographs of the sky taken between 1890 and 1989 and found that the star had been dimming consistently over that hundred years.

Not to be outdone, a grad student at CalTech published a study showing that the dimming of the star was even more excessive than that. Over the first thousand days of the Kepler mission, Tabby’s Star dimmed at 0.34% (twice as fast as over the period looked at by Professor Schaefer) then dimmed by more than 2% over the next 200 days, and then steadied out. As the authors wrote: “No known or proposed stellar phenomena can fully explain all aspects of the observed light curve.”

So, what explanation does that leave? That’s right: Aliens. As Jason Wright, an astronomer from Penn State University, said: “this looked like something you would expect an alien civilization to build”. The idea was that the dimming was caused by an alien civilisation building a Dyson Swarm, which is a large number of objects orbiting a star and capturing its energy, such as solar powered space stations with vast solar panels. Don’t worry, maths proves that it’s not an alien megastructure.

Our galaxy, the Milky Way, contains about 100 billion stars. That’s a whopping big number. While we don’t know how many alien civilisations there are in the galaxy, Frank Drake once proposed an equation to estimate how many we could detect. He argued that the number would be equal to the average rate of star formation in our galaxy multiplied by the fraction of formed stars that have planets, multiplied by the average number of planets per star that has planets that can support life, multiplied by the fraction of those planets that actually develop life, multiplied by the fraction of those planets bearing life on which intelligent, civilised life has developed, multiplied by the fraction of those that have developed communications, multiplied by the length of time over which such civilisations release detectable signals.

That’s a lot of things to take into account, but the important thing is to notice how many of those are fractions. Most stars seem to have planets, but very few of those planets would be capable of supporting life. They have to be the right size, with the right components, at the right distance from the star. Even those planets that could support life don’t automatically generate it – as far as we know life has spontaneously generated exactly once, even though other planets in our solar system have been capable of supporting life in the past. So I think it’s safe to say that only a small fraction of planets that can sustain life actually develop it.

How many planets that have a genesis event actually go on to develop an advanced civilisation that we could detect? The formation of eukaryotes and multicellular organisms is not a given, and most life events would stay at the primordial ooze stage. If intelligent life develops, but finds itself on a planet without an easy fuel source or without many metals, it’s not going to get very far.

I won’t put any numbers in here – you can play with that – but it’s safe to say that for every star that contains an advanced civilisation building a Dyson Swarm, there are hundreds of millions – or even billions – of stars that are just doing their own thing based on non-living processes. Remember, Kepler only looked at 145,000 stars.

So any time we detect an irregularity, no matter how difficult it is for us to come up with an explanation that fits its peculiarities, the chances of the cause being alien civilisations rather than astronomical processes is in the order of 1 in billions. If we found a strangely behaving star every day we would, on average, have to look for hundreds of thousands of years before we found a peculiarity that was actually the result of aliens. This argument applies to everything regarding aliens.

If a strange craft floats down before you one lonesome night, and a little green man with silly antennae on his head struts up and down in front of you making “meep meep” noises, it’s far more likely that you ate the wrong mushrooms than that you’ve made inter-planetary contact. If this craft came down in a city and thousands of people saw and took photos and videos and posted them to instagram, it is statistically far more likely to be a hoax perpetrated by Russia or Coca Cola than alien life forms popping over to say “hey gurl”.

*Of course, everyone missed the obvious “Black Swan” pun. This is because news organisations keep firing sub-editors.

read more