September 30, 2025 • 31 mins
What does it cost to carry a brilliant idea? Ludwig Boltzmann gave us the statistical foundations of entropy and the famous S = k log W, yet his life was marked by relentless skepticism, isolation, and personal struggle. In this episode, we weave Boltzmann’s story with the modern mental health crisis in academia, where anxiety, depression, and burnout affect scientists at alarming rates. We’ll explore how probability explains not only the arrow of time, but also why community, resilience, and care are essential for science to thrive.
3 Things Listeners Will Learn:
- How Ludwig Boltzmann’s statistical mechanics shaped modern physics and why his ideas met fierce resistance.
- The scale of today’s mental health crisis in academia — from graduate students to faculty.
- Practical tools like cognitive behavioral therapy (CBT) and community support that can help foster resilience in science.
Resources & Further Reading:
- 988 Suicide & Crisis Lifeline (U.S.)
- International Association for Suicide Prevention Global Helpline Directory
- Evans, T. M., et al. “Evidence for a mental health crisis in graduate education.” Nature Biotechnology (2018).
- Stanford Encyclopedia of Philosophy – Boltzmann’s Work in Statistical Physics
- Nobel Prize: Jean Perrin’s Nobel Lecture (1926)
🔗 Explore more on our website: mathsciencehistory.com
📚 To buy my book Hypatia: The Sum of Her Life on Amazon, visit https://a.co/d/g3OuP9h
🌍 Let’s Connect!
Bluesky: https://bsky.app/profile/mathsciencehistory.bsky.social
Instagram: https://www.instagram.com/math.science.history
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Transcript
Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
(00:01):
In the sciences, we celebrate big ideas.
We celebrate the people who see patterns the
rest of us miss, but we rarely celebrate
something more fundamental, the whole human mind that
carries those ideas with its strengths and its
storms.
Today, I'm going to talk about one of
the brightest lights of 19th century physics, a
(00:22):
person who shouldered the weight of both scientific
opposition and personal suffering, Ludwig Boltzmann.
We'll be right back after a quick word
from my advertisers.
Today, I'm going to normalize a conversation that
too often sits in the shadows of our
labs and lecture halls, mental health and science.
(00:45):
Imagine Vienna in the 1870s.
A young Ludwig Boltzmann sits at his desk
surrounded by chalk-stained papers, wrestling with a
question that has haunted physics for decades.
Why does heat always spread out?
James Clerk Maxwell had shown that the velocities
of gas molecules follow a statistical pattern, but
(01:07):
Boltzmann couldn't let it rest there.
He wondered, could this same logic apply not
just to gases, but also to liquids and
even the vibrating atoms inside a crystal?
Night after night, he calculated.
He sketched particles colliding, scattering and vibrating, and
then the insight hit him, not as a
(01:28):
bolt from nowhere, but as the culmination of
years of struggle.
Disorder increases not because nature wants it to,
but because there are simply more ways for
particles to be spread out than bunched together.
Dispersion, he realized, was not mysterious at all.
It was mathematics.
It was probability.
(01:49):
And in that moment, he penned the relation
that still sits at the foundation of modern
physics.
S equals K times the logarithm of W,
which is entropy equals a constant that is
multiplied times the logarithm of the number of
microscopic states that make up a macroscopic reality,
(02:11):
basically showing that if there are more ways
to be disordered than ordered, then disorder wins.
It was brilliant.
It was a unifying vision.
Gases, liquids, solids, they all obeyed the same
statistical law.
Thermodynamics was no longer an island apart from
mechanics.
Boltzmann had shown that the chaotic dance of
(02:33):
countless molecules, when viewed statistically, produces the smooth
one-way drift toward equilibrium that we experience
in everyday life.
Like when coffee cools and smoke spreads and
heat flows, what feels like the arrow of
time emerges not from a hidden force, but
(02:54):
from the overwhelming probability that disorder will increase.
But his triumph didn't come without a cost.
Many of his contemporaries rejected the very idea
that atoms were real.
To them, Boltzmann's equations were abstract fantasies.
He was mocked, criticized, and even dismissed.
(03:16):
As he clung to the conviction that the
arrow of time could be explained by mathematics,
his self-esteem and view of his self
-worth began to crumble.
It soon began to destroy him emotionally.
And Boltzmann's despair wasn't unique to his time.
The pressure to perform, the sting of rejection,
and the loneliness of carrying ideas that others
(03:38):
refused to believe, these are still with us.
Today, scientists and students across academia face similar
struggles.
They take the shape of anxiety, depression, burnout,
and sometimes even suicide.
And the numbers tell us just how heavy
the burden has become.
The academic world, from students to tenured faculty,
(04:01):
is grappling with a serious mental health crisis.
Roughly 37% of academics experience anxiety or
depression, compared to only 19% in the
general population.
Among students, the figures are particularly alarming.
Up to 44% report depressive symptoms, 36
to 41% endure anxiety, and 14%
(04:24):
contemplate suicide, with self-harm incidences found in
nearly 3 in 10 students.
PhD candidates fare no better.
Almost 1 in 4 suffer from clinical depression,
and 1 in 6 face anxiety.
Suicide attempts further underscore the severity.
Approximately 24,000 occur each year among college
(04:48):
students, making it the second leading cause of
death on campuses.
These statistics reflect the devastating impact of poor
work-life balance in academia, where relentless pressures,
insufficient support, and blurred boundaries between professional and
personal life contribute to mounting psychological distress.
(05:09):
Academia's mental health crisis is being driven by
overlapping pressures that are measurable in the data.
The culture of overwork is intense.
Three out of four graduate students report working
for more than 40 hours a week, and
1 in 4 exceeds 60 hours.
Faculty often log over 50 hours themselves, with
(05:33):
the mindset of publish or perish looming over
every career stage.
Job insecurity compounds the stress.
Nearly 70% of university instructors in the
United States are now off the tenure track,
and half are part-time with median adjunct
pay only about $3,900 per course.
(05:56):
A quarter of adjuncts live below the poverty
line.
Just let that sink in for a second.
Adjuncts.
These are people who devote their lives to
educating students, and yet they are treated so
poorly that they barely have enough money to
survive.
And it would take one healthcare crisis, just
(06:17):
one, to force them into a situation where
they are unhoused.
This is heartbreaking.
And then for students, financial strain is relentless.
Average loan debt hovers near $39,000 per
semester.
Tuition has more than doubled in real terms
since the 1990s.
And 59% report food or housing insecurity,
(06:41):
with 14% of students experiencing homelessness.
Even stipends for graduate students often fall short.
In physics, about 70% of first year
students earn below the local living wage.
Social isolation adds yet another layer, with roughly
one in four PhD students reporting severe loneliness,
(07:03):
which correlates strongly with burnout and depression.
Meanwhile, access to mental healthcare lags behind the
need for mental healthcare.
More than a third of students screen positive
for depression or anxiety.
Nearly 40% never receive therapy or medication,
often due to cost, time, and long waits.
(07:26):
For marginalized groups, yeah, you guessed it, the
risks are even higher.
One in five students entering counseling reports recent
discrimination, which is directly tied to elevated distress
and suicidal thoughts.
And the pandemic's aftershocks intensified everything, driving anxiety
and depression rates among students up more than
(07:48):
12% points in just five years.
Together, these pressures explain why depression, anxiety, and
suicidal ideation are not isolated experiences, but systemic
outcomes of academic life today.
These are not side notes to science.
This is the in which science happens.
(08:11):
So today, as we visit Boltzmann's battles over
atoms and entropy, I'm also going to talk
about bipolar disorder and explain what treatments like
cognitive behavioral therapy, along with access to medication,
actually do and how they really do help
and why mental healthcare is so necessary in
(08:33):
academia.
So who was Ludwig Boltzmann?
Well, Ludwig Eduard Boltzmann was born in Vienna
in 1844.
He trained at the University of Vienna, and
by his mid-twenties, he was a full
professor.
From the very start, he cared about a
question that sounds simple and turns out to
(08:55):
be profound.
How do the motions of unimaginably small particles
give rise to the warm, smooth behavior we
see at the human scale, temperature, pressure, friction,
heat flow?
Well, the bridge he built between the microscopic
and the macroscopic is what we now call
statistical mechanics.
(09:15):
When Boltzmann earned his doctorate in Vienna in
1866, he was barely 22.
His mentor, Joseph Stephan, introduced him to the
revolutionary ideas of James Clerk Maxwell, and young
Boltzmann was instantly captivated by the hidden dance
of molecules.
He was restless, brilliant, and determined to push
(09:36):
Maxwell's kinetic theory further than anyone had imagined.
His first professorial job was in Graz.
The university halls echoed with chalkboards scrawled full
of collisions and equations, while outside, Europe's scientific
community buzzed with debates about the nature of
heat.
He spent seasons abroad working with the likes
(09:59):
of Bunsen, Kirchhoff, and Hemholtz, sharpening his tools
and testing his ideas.
Each city, Graz, Munich, Leipzig, Vienna, became another
stage for his restless energy.
Then in 1872, he made his first great
leap.
Boltzmann wrote down what is now called the
Boltzmann equation, a description of how the velocities
(10:22):
of particles in a gas evolve as they
strike and scatter off one another.
It was bold, it was new, and from
it, he carved the H-theorem, a mathematical
proof that gases do not linger in disorder
forever, but overwhelmingly drift toward equilibrium.
This H-theorem suggested that the second law
(10:44):
of thermodynamics, the law that says heat flows
from hot to cold, that entropy always increases,
was not just a mysterious principle of nature.
It was the inevitable outcome of statistics, the
law of large numbers written in the language
of atoms.
But with the ambition came the headwinds.
The second half of the 19th century was
(11:06):
not universally friendly to atom talk.
Some of the most influential voices in European
science either doubted or openly rejected the reality
of atoms.
The chemist Wilhelm Otzwald, a towering figure in
physical chemistry, promoted an alternative program he often
called energetics, which aimed to explain nature solely
(11:28):
in terms of energy transformations without commitments about
microscopic particles.
The philosopher and physicist Ernst Mach was skeptical
of unobservable entities in general and of atmospheric
pictures in particular.
Boltzmann found himself not only doing hard physics,
but defending the very idea that microscopic particles
(11:51):
existed.
It was more than a style of difference.
If you say that entropy goes up because
systems move to more probable configurations, then probability
must have a meaning.
If you say gases have pressure because molecules
ricochet off the walls, you must accept molecules.
Boltzmann did both, and he did it loudly,
(12:14):
publicly, and bravely.
But not everyone agreed that his H-theorem
showed what he said it did.
A former mentor, Josef Lakschmid, raised the reversibility
objection.
If microscopic laws are reversible, how can macroscopic
behavior be irreversible?
Later, Ernst Zermelo, drawing on Poincaré's recurrence insight,
(12:38):
argued that systems should eventually return close to
their initial states.
These were not petty criticisms.
They were deep challenges that pushed Boltzmann to
emphasize the statistical character of his reasoning.
In response, he clarified that the march toward
equilibrium is overwhelmingly likely, not metaphysically guaranteed.
(13:00):
The universe does not break its laws.
It plays the odds.
We'll be right back after a quick word
from my advertisers.
Meanwhile, while he was doing all of this,
the human story was unfolding.
Boltzmann was gregarious in lectures and could be
(13:20):
wonderfully funny.
Yet, he was also very sensitive to criticism
and subject to bouts of depression that worsened
when work turned combative.
He moved between posts.
He struggled physically with poor eyesight and asthma.
He poured his life into a view of
nature that many of his contemporaries called speculative.
(13:43):
Vienna, the late 1870s.
The air in the seminar room was thick
with smoke and chalk dust.
Boltzmann had just finished lecturing on his H
-theorem when a voice rose from the back.
Johann Loschmidt, calm but pointed, asked why entropy
must always increase.
If every molecule's motion could be reversed, he
(14:06):
argued, then Newton's law demanded that order should
rise again.
Did this not undo Boltzmann's law?
Boltzmann leaned forward, animated.
Yes, in principle, he conceded.
The reversal could happen.
But think of the odds.
The probability was so vanishingly small that in
practice it never would.
(14:27):
Entropy's rise was not impossible to escape.
It was simply inevitable by numbers.
The arrow of time, he insisted, was born
of probability.
The room stirred with debate.
Years later, in Berlin, the returned to a
new form.
Ernst Zermelo stood armed with Poincaré's recurrence theorem.
(14:50):
No matter how vast the system, Zermelo argued,
given enough time, the molecules must eventually return
to their original state.
Entropy could not march forward forever.
Boltzmann's response was passionate but weary.
Recurrence was mathematically certain, yes, but the time
scales were longer than the age of the
(15:10):
stars, longer than the universe itself.
For all practical purposes, the coffee would never
heat itself.
The smoke would never gather back into the
match.
Equilibrium remained the destiny of matter.
But the harshest blows came not only from
paradoxes but from philosophy.
In Vienna, Ernst Mach raised his hand and
(15:33):
dismissed atoms altogether.
They were metaphysics, he said.
Energy was real.
Molecules were mere speculation.
Boltzmann bristled, his voice tightened.
Molecules were no metaphysics, he insisted.
They explained the second law.
They gave substance to kinetic theory.
They made sense of heat.
(15:55):
Dismiss them if you must, but one day
experiments would reveal their fingerprints beyond doubt, the
audience murmured, unconvinced.
Boltzmann looked around, convinced himself but increasingly isolated.
By the 1890s, the weight of skepticism was
heavy.
His hair had turned gray.
(16:15):
His study cluttered with letters, some supportive, many
were critical.
He read them aloud bitterly.
They say atoms are figments that probably has
no place in nature.
After all these years, am I just talking
to myself?
He sighed, pressing his hands into his face.
And yet, in Leipzig, around 1900, among his
(16:37):
students, Boltzmann's spark returned.
His booming lectures lit up the chalkboard.
Do not fear probability, he cried, the chalk
striking emphatically.
Embrace it.
The laws of thermodynamics flow from the countless
possible states of molecules.
Entropy is not a curse.
It is the mathematics of time itself.
(17:01):
His students leaned forward, laughing at his jokes,
sensing the scale of his vision.
They adored him.
For a moment, he was invigorated.
Still, whispers of doubt lingered at the edges.
He pressed his insight into other problems too.
He argued publicly against the energetics program, insisting
(17:23):
that energy without particles is a reshuffling of
words, not an explanation.
He taught courses in natural philosophy.
He mentored.
He argued.
He laughed.
And at times, he despaired.
He watched as critics with enormous influence doubt
the microscopic world he considered essential.
(17:43):
He kept going.
His story faded into silence, leaving behind the
lingering question of what brilliance costs and what
it means when a mind is left alone
to fight it.
It is tempting to quarantine the struggles of
the past inside sepia photographs.
(18:05):
It is tempting to believe that the pressures
that weighed on Boltzmann evaporated with time.
But talk to scientists today and you hear
a different story.
Long hours, insecurity, a feeling that asking for
help is a liability, not a strength.
We talk a lot about brilliance in academia,
about ideas, discoveries, and breakthroughs.
(18:26):
But brilliance needs fuel, and it can burn
out fast if we don't take care of
the mind behind the work.
Exhaustion, anxiety, depression, even bipolar disorder, or even
schizophrenia.
These are not rare in universities.
They are common human realities.
And while no podcast can replace professional care,
(18:46):
there are tools, both psychiatric and psychological and
practical, that can help.
And one of the most studied methods is
cognitive behavioral therapy, or CBT.
At its heart, CBT is about noticing the
stories we tell ourselves, like, I'll never finish
this paper, or I don't belong here, or
I don't deserve this high grade, or I
(19:09):
am a failure.
We hear these we tell ourselves, and it's
important to gently test these thoughts.
Many of us fall into common traps.
Catastrophizing, assuming the worst, black and white thinking,
where we label ourselves as total failures for
a single mistake.
Or mind reading, where we convince ourselves that
everyone around us is judging us.
(19:32):
CBT invites us to challenge those patterns.
If we catch ourselves thinking, this presentation is
going to be a disaster, we can ask,
what evidence do we actually have?
Has every talk we've ever given been a
disaster?
Usually, the answer is no.
Reframe that.
Reframe that with, I may feel nervous, but
(19:52):
I've prepared before, and I can do it
again.
It is like retraining a restless horse.
The thoughts will still buck and pull, but
with practice and steady stirrups, we can guide
them in a healthier direction.
There are also behavioral techniques, setting realistic goals,
breaking tasks into smaller steps, and rewarding progress,
(20:14):
rather than seeking perfection.
A simple list of three achievable tasks for
the day can feel more powerful than a
crushing to-do list that never ends.
I feel that one.
Lifestyle changes matter too.
Predictable routines, waking, working, and resting at regular
times can stabilize mood and energy, especially for
(20:38):
those managing bipolar disorder and even schizophrenia.
Movement and exercise act like natural antidepressants, improving
focus and sleep.
Even a 10-minute walk between classes or
lab sessions can make a difference.
Sleep hygiene is another cornerstone, keeping devices away
from the bed, winding down with calming cues
(21:00):
like a dim light or reading, and aiming
for consistency.
And finally, connection.
Isolation magnifies struggle, while community lightens it.
Talking with your peers, joining support groups, or
simply admitting to a friend, hey, I'm having
a hard week, that can turn the weight
(21:21):
of silence into shared strength.
Resilience isn't about toughing it out alone.
It's about building a network of people who
remind us that we are not defined by
our hardest days.
Academia may glorify long hours and endless output,
but the real foundation of discovery is well
(21:42):
-being.
Protecting your mind is not separate from the
work of science and scholarship.
It is the work.
If you or someone you know is struggling
in the United States, you can always call
or text 988 to connect with the Suicide
and Crisis Lifeline.
Hopefully that will never go away.
Outside of the United States, the International Association
(22:04):
for Suicide Prevention, IASP, maintains a global directory
of crisis centers at IASP.info crisis-centers
-helplines.
And I'm going to put that link in
the show notes and in the blog.
And if you are in immediate danger, please,
(22:25):
please call your local emergency number and know
deep within your heart that you are loved
and you are wanted in the world and
that you are surrounded by people who genuinely
love you and care about you.
It may not feel like it, but it's
true.
There are people in the world who love
you and care about you.
(22:46):
And I don't even know you.
I don't know who's listening to this, but
if you're out there and you are struggling
in academia or even in your job as
you're driving into work and you're feeling the
weight of the world, know that I don't
know you, but I love you and I
appreciate you.
And I appreciate you being part of this
world of knowledge and curiosity.
(23:07):
Know that you are loved.
We'll be right back after a quick word
from my advertisers.
It wasn't until 33 years later when Albert
Einstein published a theory of Brownian motion that
showed that subtle fluctuations and measurable diffusion could
be explained if molecules were real and numerous.
(23:30):
Boltzmann's theories were validated.
Within a few years after Einstein's theory on
Brownian motion, the experimentalist Jean Perrin carried out
careful experiments testing Einstein's predictions.
By tracking microscopic particles under a microscope, he
was able to measure their displacement statistically and
thus calculate Avogadro's number with remarkable accuracy.
(23:54):
His results were published in a 1909 paper
and they confirmed the molecular kinetic theory of
heat.
The atom was no longer convenient fiction.
It was palpable in the statistics of wandering
specks.
Both of these brilliant minds validated Boltzmann's theories.
(24:15):
Tragically, Boltzmann did not live to see that
vindication fully accepted.
When Einstein's 1905 work on Brownian motion appeared,
Boltzmann's defenders could finally point to an effect
that was both visible under a microscope and
calculable on paper.
Jean Perrin's measurements in the years that followed
(24:36):
cemented that connection.
The world of atoms and molecules did not
merely tidy up the equations.
It left Boltzmann's fingerprints in a jittering, dusty
light.
We cannot know how Boltzmann would have felt
to see that vindication turn into consensus.
We can say that his work now carries
(24:57):
the weight of an entire century of physics.
His equation threads through statistical mechanics, quantum theory,
cosmology, and information theory.
His legacy is etched into the very language
of physics.
A single lowercase k, the Boltzmann constant, quietly
carrying his name as it links temperature to
(25:19):
energy.
And his legacy raises a moral we should
not ignore.
Ideas do not walk into the world alone.
People carry them.
So let's return to 1906 when Boltzmann was
struggling under the weight of his emotions.
Boltzmann was worn down, his eyesight failing, his
(25:41):
health fragile, his spirit battered by decades of
rejection.
The debates with Mach and Otzwald had left
deep scars.
And though new experiments were beginning to confirm
the atomic world he fought for, he would
never live to see his ideas fully vindicated.
(26:03):
In September of that year at a seaside
retreat in Duino, Italy, Ludwig Boltzmann ended his
own life.
His students, his colleagues, his family, all were
left to reckon with the loss of a
mind that stretched physics into new realms.
It's easy to turn Boltzmann into a statue
(26:24):
and place him under a glass dome.
The great scientist who had an equation engraved
on his tombstone.
But a more honest telling is humbler and
more useful.
He was a person who found a way
to make sense of the world's order and
disorder by counting possibilities.
He was a teacher who defended a picture
of nature that many people called metaphysics.
(26:46):
He was a colleague who felt the sting
of public criticism.
He was a father and a husband.
He struggled.
Today his equation is carved on his gravestone
in Vienna and it remains one of the
most profound insights in science.
That the universe does not run on destiny
but on probability.
(27:08):
We do not honor him by romanticizing his
pain.
We honor him by learning from him.
We honor him by building research environments where
bright minds can do bright work without pretending
to be invulnerable.
We honor him by listening when a colleague
says I am not okay.
And by welcoming not punishing that honesty.
(27:30):
We honor him by recognizing that routine is
medicine.
Sleep is medicine.
Therapy is medicine.
Community is medicine.
Work-life balance is medicine.
We honor him by remembering that probability.
The mathematics of what is likely applies to
culture too.
(27:51):
If we increase the number of supportive configurations
of academic life, we make it overwhelmingly likely
that more people will thrive.
If today's conversation stirred something in you, here
are three ways forward.
First, share this episode with a friend.
Normalize conversations about mental health the way we
(28:12):
normalize lab meetings and pre-prints.
Second, if you are in academia, help nudge
your lab or department toward healthier defaults.
Predictable schedules, clear boundaries, kind feedback, and explicit
encouragement to seek help when needed.
If you lead a group or if you
are a professor, please put resources in your
(28:35):
syllabus and onboarding packets so that support is
built into the culture, not left to chance.
Please do this for the next generation of
academics.
Third, if you are struggling, please reach out.
In the United States, you can call or
text 988 to connect with the suicide and
(28:55):
crisis lifeline.
Outside the United States, the International Association for
Suicide Prevention has a global directory of resources.
You can find that at IASP.info. And
if you are in immediate danger, please call
your local emergency number because science only advances
(29:15):
when people do.
History may not remember every equation, but it
will remember whether we built environments where minds
could thrive.
Boltzmann's story reminds us how fragile even the
greatest among us can be.
And so I'm going to leave you with
words I return to often.
(29:35):
Resilience is not about going at it alone.
Resilience is a group activity.
Resilience is about being there for each other.
That is how we grow as a healthy
society.
And I believe all of those words with
all of my heart, and I hope you
do too.
Until next time, carpe diem.
(29:59):
Thank you for tuning in to Math Science
History.
If you enjoyed today's episode, please leave a
quick rating and review.
They really help the podcast.
You can find our transcripts at mathsciencehistory.com.
And while you're there, remember to click on
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(30:22):
Again, thank you for tuning in.
And until next time, carpe diem.
In the sciences, we celebrate big ideas.
We celebrate the people who see patterns the
rest of us miss, but we rarely celebrate
something more fundamental, the whole human mind that
carries those ideas with its strengths and its
storms.
Today, I'm going to talk about one of
the brightest lights of 19th century physics, a
(00:22):
person who shouldered the weight of both scientific
opposition and personal suffering, Ludwig Boltzmann.
We'll be right back after a quick word
from my advertisers.
Today, I'm going to normalize a conversation that
too often sits in the shadows of our
labs and lecture halls, mental health and science.
(00:45):
Imagine Vienna in the 1870s.
A young Ludwig Boltzmann sits at his desk
surrounded by chalk-stained papers, wrestling with a
question that has haunted physics for decades.
Why does heat always spread out?
James Clerk Maxwell had shown that the velocities
of gas molecules follow a statistical pattern, but
(01:07):
Boltzmann couldn't let it rest there.
He wondered, could this same logic apply not
just to gases, but also to liquids and
even the vibrating atoms inside a crystal?
Night after night, he calculated.
He sketched particles colliding, scattering and vibrating, and
then the insight hit him, not as a
(01:28):
bolt from nowhere, but as the culmination of
years of struggle.
Disorder increases not because nature wants it to,
but because there are simply more ways for
particles to be spread out than bunched together.
Dispersion, he realized, was not mysterious at all.
It was mathematics.
It was probability.
(01:49):
And in that moment, he penned the relation
that still sits at the foundation of modern
physics.
S equals K times the logarithm of W,
which is entropy equals a constant that is
multiplied times the logarithm of the number of
microscopic states that make up a macroscopic reality,
(02:11):
basically showing that if there are more ways
to be disordered than ordered, then disorder wins.
It was brilliant.
It was a unifying vision.
Gases, liquids, solids, they all obeyed the same
statistical law.
Thermodynamics was no longer an island apart from
mechanics.
Boltzmann had shown that the chaotic dance of
(02:33):
countless molecules, when viewed statistically, produces the smooth
one-way drift toward equilibrium that we experience
in everyday life.
Like when coffee cools and smoke spreads and
heat flows, what feels like the arrow of
time emerges not from a hidden force, but
(02:54):
from the overwhelming probability that disorder will increase.
But his triumph didn't come without a cost.
Many of his contemporaries rejected the very idea
that atoms were real.
To them, Boltzmann's equations were abstract fantasies.
He was mocked, criticized, and even dismissed.
(03:16):
As he clung to the conviction that the
arrow of time could be explained by mathematics,
his self-esteem and view of his self
-worth began to crumble.
It soon began to destroy him emotionally.
And Boltzmann's despair wasn't unique to his time.
The pressure to perform, the sting of rejection,
and the loneliness of carrying ideas that others
(03:38):
refused to believe, these are still with us.
Today, scientists and students across academia face similar
struggles.
They take the shape of anxiety, depression, burnout,
and sometimes even suicide.
And the numbers tell us just how heavy
the burden has become.
The academic world, from students to tenured faculty,
(04:01):
is grappling with a serious mental health crisis.
Roughly 37% of academics experience anxiety or
depression, compared to only 19% in the
general population.
Among students, the figures are particularly alarming.
Up to 44% report depressive symptoms, 36
to 41% endure anxiety, and 14%
(04:24):
contemplate suicide, with self-harm incidences found in
nearly 3 in 10 students.
PhD candidates fare no better.
Almost 1 in 4 suffer from clinical depression,
and 1 in 6 face anxiety.
Suicide attempts further underscore the severity.
Approximately 24,000 occur each year among college
(04:48):
students, making it the second leading cause of
death on campuses.
These statistics reflect the devastating impact of poor
work-life balance in academia, where relentless pressures,
insufficient support, and blurred boundaries between professional and
personal life contribute to mounting psychological distress.
(05:09):
Academia's mental health crisis is being driven by
overlapping pressures that are measurable in the data.
The culture of overwork is intense.
Three out of four graduate students report working
for more than 40 hours a week, and
1 in 4 exceeds 60 hours.
Faculty often log over 50 hours themselves, with
(05:33):
the mindset of publish or perish looming over
every career stage.
Job insecurity compounds the stress.
Nearly 70% of university instructors in the
United States are now off the tenure track,
and half are part-time with median adjunct
pay only about $3,900 per course.
(05:56):
A quarter of adjuncts live below the poverty
line.
Just let that sink in for a second.
Adjuncts.
These are people who devote their lives to
educating students, and yet they are treated so
poorly that they barely have enough money to
survive.
And it would take one healthcare crisis, just
(06:17):
one, to force them into a situation where
they are unhoused.
This is heartbreaking.
And then for students, financial strain is relentless.
Average loan debt hovers near $39,000 per
semester.
Tuition has more than doubled in real terms
since the 1990s.
And 59% report food or housing insecurity,
(06:41):
with 14% of students experiencing homelessness.
Even stipends for graduate students often fall short.
In physics, about 70% of first year
students earn below the local living wage.
Social isolation adds yet another layer, with roughly
one in four PhD students reporting severe loneliness,
(07:03):
which correlates strongly with burnout and depression.
Meanwhile, access to mental healthcare lags behind the
need for mental healthcare.
More than a third of students screen positive
for depression or anxiety.
Nearly 40% never receive therapy or medication,
often due to cost, time, and long waits.
(07:26):
For marginalized groups, yeah, you guessed it, the
risks are even higher.
One in five students entering counseling reports recent
discrimination, which is directly tied to elevated distress
and suicidal thoughts.
And the pandemic's aftershocks intensified everything, driving anxiety
and depression rates among students up more than
(07:48):
12% points in just five years.
Together, these pressures explain why depression, anxiety, and
suicidal ideation are not isolated experiences, but systemic
outcomes of academic life today.
These are not side notes to science.
This is the in which science happens.
(08:11):
So today, as we visit Boltzmann's battles over
atoms and entropy, I'm also going to talk
about bipolar disorder and explain what treatments like
cognitive behavioral therapy, along with access to medication,
actually do and how they really do help
and why mental healthcare is so necessary in
(08:33):
academia.
So who was Ludwig Boltzmann?
Well, Ludwig Eduard Boltzmann was born in Vienna
in 1844.
He trained at the University of Vienna, and
by his mid-twenties, he was a full
professor.
From the very start, he cared about a
question that sounds simple and turns out to
(08:55):
be profound.
How do the motions of unimaginably small particles
give rise to the warm, smooth behavior we
see at the human scale, temperature, pressure, friction,
heat flow?
Well, the bridge he built between the microscopic
and the macroscopic is what we now call
statistical mechanics.
(09:15):
When Boltzmann earned his doctorate in Vienna in
1866, he was barely 22.
His mentor, Joseph Stephan, introduced him to the
revolutionary ideas of James Clerk Maxwell, and young
Boltzmann was instantly captivated by the hidden dance
of molecules.
He was restless, brilliant, and determined to push
(09:36):
Maxwell's kinetic theory further than anyone had imagined.
His first professorial job was in Graz.
The university halls echoed with chalkboards scrawled full
of collisions and equations, while outside, Europe's scientific
community buzzed with debates about the nature of
heat.
He spent seasons abroad working with the likes
(09:59):
of Bunsen, Kirchhoff, and Hemholtz, sharpening his tools
and testing his ideas.
Each city, Graz, Munich, Leipzig, Vienna, became another
stage for his restless energy.
Then in 1872, he made his first great
leap.
Boltzmann wrote down what is now called the
Boltzmann equation, a description of how the velocities
(10:22):
of particles in a gas evolve as they
strike and scatter off one another.
It was bold, it was new, and from
it, he carved the H-theorem, a mathematical
proof that gases do not linger in disorder
forever, but overwhelmingly drift toward equilibrium.
This H-theorem suggested that the second law
(10:44):
of thermodynamics, the law that says heat flows
from hot to cold, that entropy always increases,
was not just a mysterious principle of nature.
It was the inevitable outcome of statistics, the
law of large numbers written in the language
of atoms.
But with the ambition came the headwinds.
The second half of the 19th century was
(11:06):
not universally friendly to atom talk.
Some of the most influential voices in European
science either doubted or openly rejected the reality
of atoms.
The chemist Wilhelm Otzwald, a towering figure in
physical chemistry, promoted an alternative program he often
called energetics, which aimed to explain nature solely
(11:28):
in terms of energy transformations without commitments about
microscopic particles.
The philosopher and physicist Ernst Mach was skeptical
of unobservable entities in general and of atmospheric
pictures in particular.
Boltzmann found himself not only doing hard physics,
but defending the very idea that microscopic particles
(11:51):
existed.
It was more than a style of difference.
If you say that entropy goes up because
systems move to more probable configurations, then probability
must have a meaning.
If you say gases have pressure because molecules
ricochet off the walls, you must accept molecules.
Boltzmann did both, and he did it loudly,
(12:14):
publicly, and bravely.
But not everyone agreed that his H-theorem
showed what he said it did.
A former mentor, Josef Lakschmid, raised the reversibility
objection.
If microscopic laws are reversible, how can macroscopic
behavior be irreversible?
Later, Ernst Zermelo, drawing on Poincaré's recurrence insight,
(12:38):
argued that systems should eventually return close to
their initial states.
These were not petty criticisms.
They were deep challenges that pushed Boltzmann to
emphasize the statistical character of his reasoning.
In response, he clarified that the march toward
equilibrium is overwhelmingly likely, not metaphysically guaranteed.
(13:00):
The universe does not break its laws.
It plays the odds.
We'll be right back after a quick word
from my advertisers.
Meanwhile, while he was doing all of this,
the human story was unfolding.
Boltzmann was gregarious in lectures and could be
(13:20):
wonderfully funny.
Yet, he was also very sensitive to criticism
and subject to bouts of depression that worsened
when work turned combative.
He moved between posts.
He struggled physically with poor eyesight and asthma.
He poured his life into a view of
nature that many of his contemporaries called speculative.
(13:43):
Vienna, the late 1870s.
The air in the seminar room was thick
with smoke and chalk dust.
Boltzmann had just finished lecturing on his H
-theorem when a voice rose from the back.
Johann Loschmidt, calm but pointed, asked why entropy
must always increase.
If every molecule's motion could be reversed, he
(14:06):
argued, then Newton's law demanded that order should
rise again.
Did this not undo Boltzmann's law?
Boltzmann leaned forward, animated.
Yes, in principle, he conceded.
The reversal could happen.
But think of the odds.
The probability was so vanishingly small that in
practice it never would.
(14:27):
Entropy's rise was not impossible to escape.
It was simply inevitable by numbers.
The arrow of time, he insisted, was born
of probability.
The room stirred with debate.
Years later, in Berlin, the returned to a
new form.
Ernst Zermelo stood armed with Poincaré's recurrence theorem.
(14:50):
No matter how vast the system, Zermelo argued,
given enough time, the molecules must eventually return
to their original state.
Entropy could not march forward forever.
Boltzmann's response was passionate but weary.
Recurrence was mathematically certain, yes, but the time
scales were longer than the age of the
(15:10):
stars, longer than the universe itself.
For all practical purposes, the coffee would never
heat itself.
The smoke would never gather back into the
match.
Equilibrium remained the destiny of matter.
But the harshest blows came not only from
paradoxes but from philosophy.
In Vienna, Ernst Mach raised his hand and
(15:33):
dismissed atoms altogether.
They were metaphysics, he said.
Energy was real.
Molecules were mere speculation.
Boltzmann bristled, his voice tightened.
Molecules were no metaphysics, he insisted.
They explained the second law.
They gave substance to kinetic theory.
They made sense of heat.
(15:55):
Dismiss them if you must, but one day
experiments would reveal their fingerprints beyond doubt, the
audience murmured, unconvinced.
Boltzmann looked around, convinced himself but increasingly isolated.
By the 1890s, the weight of skepticism was
heavy.
His hair had turned gray.
(16:15):
His study cluttered with letters, some supportive, many
were critical.
He read them aloud bitterly.
They say atoms are figments that probably has
no place in nature.
After all these years, am I just talking
to myself?
He sighed, pressing his hands into his face.
And yet, in Leipzig, around 1900, among his
(16:37):
students, Boltzmann's spark returned.
His booming lectures lit up the chalkboard.
Do not fear probability, he cried, the chalk
striking emphatically.
Embrace it.
The laws of thermodynamics flow from the countless
possible states of molecules.
Entropy is not a curse.
It is the mathematics of time itself.
(17:01):
His students leaned forward, laughing at his jokes,
sensing the scale of his vision.
They adored him.
For a moment, he was invigorated.
Still, whispers of doubt lingered at the edges.
He pressed his insight into other problems too.
He argued publicly against the energetics program, insisting
(17:23):
that energy without particles is a reshuffling of
words, not an explanation.
He taught courses in natural philosophy.
He mentored.
He argued.
He laughed.
And at times, he despaired.
He watched as critics with enormous influence doubt
the microscopic world he considered essential.
(17:43):
He kept going.
His story faded into silence, leaving behind the
lingering question of what brilliance costs and what
it means when a mind is left alone
to fight it.
It is tempting to quarantine the struggles of
the past inside sepia photographs.
(18:05):
It is tempting to believe that the pressures
that weighed on Boltzmann evaporated with time.
But talk to scientists today and you hear
a different story.
Long hours, insecurity, a feeling that asking for
help is a liability, not a strength.
We talk a lot about brilliance in academia,
about ideas, discoveries, and breakthroughs.
(18:26):
But brilliance needs fuel, and it can burn
out fast if we don't take care of
the mind behind the work.
Exhaustion, anxiety, depression, even bipolar disorder, or even
schizophrenia.
These are not rare in universities.
They are common human realities.
And while no podcast can replace professional care,
(18:46):
there are tools, both psychiatric and psychological and
practical, that can help.
And one of the most studied methods is
cognitive behavioral therapy, or CBT.
At its heart, CBT is about noticing the
stories we tell ourselves, like, I'll never finish
this paper, or I don't belong here, or
I don't deserve this high grade, or I
(19:09):
am a failure.
We hear these we tell ourselves, and it's
important to gently test these thoughts.
Many of us fall into common traps.
Catastrophizing, assuming the worst, black and white thinking,
where we label ourselves as total failures for
a single mistake.
Or mind reading, where we convince ourselves that
everyone around us is judging us.
(19:32):
CBT invites us to challenge those patterns.
If we catch ourselves thinking, this presentation is
going to be a disaster, we can ask,
what evidence do we actually have?
Has every talk we've ever given been a
disaster?
Usually, the answer is no.
Reframe that.
Reframe that with, I may feel nervous, but
(19:52):
I've prepared before, and I can do it
again.
It is like retraining a restless horse.
The thoughts will still buck and pull, but
with practice and steady stirrups, we can guide
them in a healthier direction.
There are also behavioral techniques, setting realistic goals,
breaking tasks into smaller steps, and rewarding progress,
(20:14):
rather than seeking perfection.
A simple list of three achievable tasks for
the day can feel more powerful than a
crushing to-do list that never ends.
I feel that one.
Lifestyle changes matter too.
Predictable routines, waking, working, and resting at regular
times can stabilize mood and energy, especially for
(20:38):
those managing bipolar disorder and even schizophrenia.
Movement and exercise act like natural antidepressants, improving
focus and sleep.
Even a 10-minute walk between classes or
lab sessions can make a difference.
Sleep hygiene is another cornerstone, keeping devices away
from the bed, winding down with calming cues
(21:00):
like a dim light or reading, and aiming
for consistency.
And finally, connection.
Isolation magnifies struggle, while community lightens it.
Talking with your peers, joining support groups, or
simply admitting to a friend, hey, I'm having
a hard week, that can turn the weight
(21:21):
of silence into shared strength.
Resilience isn't about toughing it out alone.
It's about building a network of people who
remind us that we are not defined by
our hardest days.
Academia may glorify long hours and endless output,
but the real foundation of discovery is well
(21:42):
-being.
Protecting your mind is not separate from the
work of science and scholarship.
It is the work.
If you or someone you know is struggling
in the United States, you can always call
or text 988 to connect with the Suicide
and Crisis Lifeline.
Hopefully that will never go away.
Outside of the United States, the International Association
(22:04):
for Suicide Prevention, IASP, maintains a global directory
of crisis centers at IASP.info crisis-centers
-helplines.
And I'm going to put that link in
the show notes and in the blog.
And if you are in immediate danger, please,
(22:25):
please call your local emergency number and know
deep within your heart that you are loved
and you are wanted in the world and
that you are surrounded by people who genuinely
love you and care about you.
It may not feel like it, but it's
true.
There are people in the world who love
you and care about you.
(22:46):
And I don't even know you.
I don't know who's listening to this, but
if you're out there and you are struggling
in academia or even in your job as
you're driving into work and you're feeling the
weight of the world, know that I don't
know you, but I love you and I
appreciate you.
And I appreciate you being part of this
world of knowledge and curiosity.
(23:07):
Know that you are loved.
We'll be right back after a quick word
from my advertisers.
It wasn't until 33 years later when Albert
Einstein published a theory of Brownian motion that
showed that subtle fluctuations and measurable diffusion could
be explained if molecules were real and numerous.
(23:30):
Boltzmann's theories were validated.
Within a few years after Einstein's theory on
Brownian motion, the experimentalist Jean Perrin carried out
careful experiments testing Einstein's predictions.
By tracking microscopic particles under a microscope, he
was able to measure their displacement statistically and
thus calculate Avogadro's number with remarkable accuracy.
(23:54):
His results were published in a 1909 paper
and they confirmed the molecular kinetic theory of
heat.
The atom was no longer convenient fiction.
It was palpable in the statistics of wandering
specks.
Both of these brilliant minds validated Boltzmann's theories.
(24:15):
Tragically, Boltzmann did not live to see that
vindication fully accepted.
When Einstein's 1905 work on Brownian motion appeared,
Boltzmann's defenders could finally point to an effect
that was both visible under a microscope and
calculable on paper.
Jean Perrin's measurements in the years that followed
(24:36):
cemented that connection.
The world of atoms and molecules did not
merely tidy up the equations.
It left Boltzmann's fingerprints in a jittering, dusty
light.
We cannot know how Boltzmann would have felt
to see that vindication turn into consensus.
We can say that his work now carries
(24:57):
the weight of an entire century of physics.
His equation threads through statistical mechanics, quantum theory,
cosmology, and information theory.
His legacy is etched into the very language
of physics.
A single lowercase k, the Boltzmann constant, quietly
carrying his name as it links temperature to
(25:19):
energy.
And his legacy raises a moral we should
not ignore.
Ideas do not walk into the world alone.
People carry them.
So let's return to 1906 when Boltzmann was
struggling under the weight of his emotions.
Boltzmann was worn down, his eyesight failing, his
(25:41):
health fragile, his spirit battered by decades of
rejection.
The debates with Mach and Otzwald had left
deep scars.
And though new experiments were beginning to confirm
the atomic world he fought for, he would
never live to see his ideas fully vindicated.
(26:03):
In September of that year at a seaside
retreat in Duino, Italy, Ludwig Boltzmann ended his
own life.
His students, his colleagues, his family, all were
left to reckon with the loss of a
mind that stretched physics into new realms.
It's easy to turn Boltzmann into a statue
(26:24):
and place him under a glass dome.
The great scientist who had an equation engraved
on his tombstone.
But a more honest telling is humbler and
more useful.
He was a person who found a way
to make sense of the world's order and
disorder by counting possibilities.
He was a teacher who defended a picture
of nature that many people called metaphysics.
(26:46):
He was a colleague who felt the sting
of public criticism.
He was a father and a husband.
He struggled.
Today his equation is carved on his gravestone
in Vienna and it remains one of the
most profound insights in science.
That the universe does not run on destiny
but on probability.
(27:08):
We do not honor him by romanticizing his
pain.
We honor him by learning from him.
We honor him by building research environments where
bright minds can do bright work without pretending
to be invulnerable.
We honor him by listening when a colleague
says I am not okay.
And by welcoming not punishing that honesty.
(27:30):
We honor him by recognizing that routine is
medicine.
Sleep is medicine.
Therapy is medicine.
Community is medicine.
Work-life balance is medicine.
We honor him by remembering that probability.
The mathematics of what is likely applies to
culture too.
(27:51):
If we increase the number of supportive configurations
of academic life, we make it overwhelmingly likely
that more people will thrive.
If today's conversation stirred something in you, here
are three ways forward.
First, share this episode with a friend.
Normalize conversations about mental health the way we
(28:12):
normalize lab meetings and pre-prints.
Second, if you are in academia, help nudge
your lab or department toward healthier defaults.
Predictable schedules, clear boundaries, kind feedback, and explicit
encouragement to seek help when needed.
If you lead a group or if you
are a professor, please put resources in your
(28:35):
syllabus and onboarding packets so that support is
built into the culture, not left to chance.
Please do this for the next generation of
academics.
Third, if you are struggling, please reach out.
In the United States, you can call or
text 988 to connect with the suicide and
(28:55):
crisis lifeline.
Outside the United States, the International Association for
Suicide Prevention has a global directory of resources.
You can find that at IASP.info. And
if you are in immediate danger, please call
your local emergency number because science only advances
(29:15):
when people do.
History may not remember every equation, but it
will remember whether we built environments where minds
could thrive.
Boltzmann's story reminds us how fragile even the
greatest among us can be.
And so I'm going to leave you with
words I return to often.
(29:35):
Resilience is not about going at it alone.
Resilience is a group activity.
Resilience is about being there for each other.
That is how we grow as a healthy
society.
And I believe all of those words with
all of my heart, and I hope you
do too.
Until next time, carpe diem.
(29:59):
Thank you for tuning in to Math Science
History.
If you enjoyed today's episode, please leave a
quick rating and review.
They really help the podcast.
You can find our transcripts at mathsciencehistory.com.
And while you're there, remember to click on
that coffee button because every dollar you donate
supports a portion of our production costs and
keeps our educational website free.
(30:22):
Again, thank you for tuning in.
And until next time, carpe diem.
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